CEE 335
Soils and Hydraulics Lab
Spring 2011 Course Coordinators: Prof. Isao Ishibashi
Department of Civil & Environmental Engineering Old Dominion University Norfolk, VA 23529
Table of Contents Page
Course Instructions ..........................................................................................................................1 Lab Schedule.................................................... ........................................................ ............................................................................. ..................... 2 Experiment Design Lab Common Lab Permeability Test............................................................. ................................... Soils Lab #1 Soils Lab #2 Soils Lab #3 Soils Lab #4 Soils Lab #5 Soils Lab #6
Hydrometer Test ................................................... .............................................. Liquid Limit & Plastic Limit Test ............................................. .......................... Compaction Test ............................................ .................................................... ...................................................... .. Consolidation Test ............................................... ................................................ Direct Shear Test.................................................................................................. Test.................................................................................................. Unconfined Compression Test .................................................. ...........................
Hydraulics Lab #1 Hydraulics Lab #2 Hydraulics Lab #3 Hydraulics Lab #4 Hydraulics Lab #5 Hydraulics Lab #6
Reynolds Experiment ................................................ ............................... Venturi as a Flow Measurement Device ............................................... ... Flow over Sharp Crested Weir …………………………..… …………………………..…………….. ………….. Energy Head Loss due to a Hydraulic Jump ………..……................... Impact of Jet on Vanes .................................................... ............................................................................. ......................... Steady Axisymmetric Unconfined Flow ..................................................
2
3 6 10 12 14 16 17 19 21 29 35 38 43
Table of Contents Page
Course Instructions ..........................................................................................................................1 Lab Schedule.................................................... ........................................................ ............................................................................. ..................... 2 Experiment Design Lab Common Lab Permeability Test............................................................. ................................... Soils Lab #1 Soils Lab #2 Soils Lab #3 Soils Lab #4 Soils Lab #5 Soils Lab #6
Hydrometer Test ................................................... .............................................. Liquid Limit & Plastic Limit Test ............................................. .......................... Compaction Test ............................................ .................................................... ...................................................... .. Consolidation Test ............................................... ................................................ Direct Shear Test.................................................................................................. Test.................................................................................................. Unconfined Compression Test .................................................. ...........................
Hydraulics Lab #1 Hydraulics Lab #2 Hydraulics Lab #3 Hydraulics Lab #4 Hydraulics Lab #5 Hydraulics Lab #6
Reynolds Experiment ................................................ ............................... Venturi as a Flow Measurement Device ............................................... ... Flow over Sharp Crested Weir …………………………..… …………………………..…………….. ………….. Energy Head Loss due to a Hydraulic Jump ………..……................... Impact of Jet on Vanes .................................................... ............................................................................. ......................... Steady Axisymmetric Unconfined Flow ..................................................
2
3 6 10 12 14 16 17 19 21 29 35 38 43
CEE 335 Lab Assistants:
Soils and Hydraulics Lab Soils Lab Amir Arablouei Office: Room 122 KH Office Hours:_____________ Hours:_____________
Spring 2011
Hydraulics Lab
Alireza Shahvari Office: Room 115 KH Office Hours:____________________ Hours:____________________
Experiment Design Labs There is a lab for which each group will design the experiment. The topics and requirements for this lab are assigned at the beginning beginning of the semester. A separate group report for the experiment design design is due on February 16 (Wednesday lab), 18 (Friday lab ). After the instructor has reviewed the reports and provided some constructive feedback, each group will conduct the experiment at a later scheduled lab session. The final group lab report is due two weeks after lab experiment is performed. Many of the regular lab sessions may be concluded in a shorter time than scheduled scheduled 110 minutes. It is anticipated that students will utilize this spare time effectively to work on the experiment design.
Laboratory Reports Individual (not group, except for the experiment design lab) written reports shall be neat and in professional quality. Lab reports are due at the beginning of the following lab class. Late lab report may be accepted with deducted points only if the instructor accepts the reason for the delay. Reports shall include the following information: 1. Cover page ...test date, course name, type of test, members in the lab group, reporter's name, etc. 2. Purpose and principles...a brief description of the test's purpose and no more than four to five sentences concerning the physical principles used to develop the measurements. 3. Laboratory equipment...a listing of the principal apparatus used during the test. 4. Procedure...clear and reasonably complete statements of the test method. 5. References...references on the test, which should include the ASTM Standard where applicable. 6. Data...neat and well-organized raw data and corresponding computations. 7. Results...presentation of test results may include tables, graphs and figures, etc. 8. Discussions... (a) discuss your results. What is the engineering significance of the results? Do you think they are accurate?, etc., (b) comment on any possible sources of errors, etc. . Items 1. 2. 3. 4. 5. & 8. in the report shall be typed. . Students are encouraged to create spreadsheets for analyzing data and graphical presentation.
Note: 1. The lab grade for the experiments missed will be an automatic zero, except for those made-up with the permission of the instructor. Make-up of the test will be only granted for exceptional cases. 2. Students are not allowed to leave the laboratory until the experiment is successfully over, and the area is cleaned and all tools are returned to the proper locations.
Grading : (all lab reports including an experiment lab are equally weighted for grading purpose.) A B C D F
90-100 (A-: 80-89.9 (B-: 70-79.9 (C-: 60-69.9 (D-: below 60
90-92.9) 80-82.9, B+: 70-72.9, C+: 60-62.9, D+:
1
87-89.9) 77-79.9) 67-69.9)
CEE 335
Soils and Hydraulics Lab Schedule
Soils Lab (at Room 122 KH) Soil-1. Hydrometer test Soil-2. Liquid limit and plastic limit tests Soil-3. Compaction test Soil-4. Consolidation test Soil-5. Direct shear test Soil-6. Unconfined compression test Hydraulics Lab (at Room 138 KH) H-1. Reynolds experiment H-2. Venturi as a Flow Measurement Device H-3. Flow over sharp crested weir H-4. Energy head loss due to a hydraulic jump H-5. Impact of jet on vanes H-6. Steady axisymmetric unconfined flow Common Lab (all at 122 KH) – permeability test ( Experiment Experiment Design ) Lab Schedule by Groups Date 1/12, 1/14 1/19, 1/21 1/26, 1/28 2/2, 2/5 2/9, 2/11 2/16, 2/18 2/23, 2/25 3/2, 3/4
3/16/ 3/18 3/23, 3/25 3/30, 4/1 4/6, 4/8 4/13, 4/15 4/20, 4/22 4/27, 4/29
Lab schedule Introduction and organization meeting at KH138 S-1 H-1 S-2 H-2 S-3 H-3 Permeability test Spring Break !!! H-4 S-4 H-5 S-5 H-6 S-6 No lab, due for S-6 lab report
Soils lab sessions are divided into 3 groups (S-1, S-2, S-3). Hydro lab sessions are divided into two groups (H-1, H-2).
2
Spring 2011
EXPERIMENT DESIGN Effect of Gradation on Permeability (Common Lab: Permeability Test)
Permeability is the water flow capability of porous media (soil). The property will depend on various parameters, such as soil type, gradation, void ratio, etc. Students are asked to design laboratory experiment to determine the effect of gradation on soil’s permeability. The tasks will include: 1. Literature survey on the subject of permeability and its influencing parameters. 2. Design laboratory experiment to determine the effect of soil’s gradation on permeability. 3. Submit group report including results results of the literature literature survey and lab procedures by the due day for review. 4. Conduct experiments. 5. Relate gradation parameters to permeability. 6. Compare the above relationship with readily available relations if any. 7. Prepare the final group report by the due day. The following standard permeability testing procedures are provided for your reference. Group may utilize a similar procedure to meet design criteria.
_____________________________________________ Standard Permeability Test Method Purpose: To determine the coefficient of permeability of soils by (1) constant head and (2) falling head permeability tests in the laboratory. References: .ASTM D2434 Standard Test Method for Permeability of Granular Granular Soils (Constant Head) Specimens: Sandy specimens with various grain sizes Equipment and tools: Permeability tube and sets filled with sandy specimens, caliper, graduated cylinder, stopwatch, thermometer Procedures: 1. Measure the dimension of the specimens (specimen tube diameter D, length L) and other dimensions in the permeability test sets (head difference Δh for the constant head test, and the inner cross- sectional area of the burette "a" for the fall head test). 2. Record the water temperature during the test for the temperature correction of k.
Constant Head Test (Fig.1 a) 3
3. Run the water through the system until a steady condition is established. 4. For a given time interval "t", collect the amount of water flow Q through the system in a graduated cylinder. Repeat several measurements for t and Q. Falling Head Test (Fig. 1 b) 5. At time zero, read the water height h1 in the burette and at time "t" read the same as h2 . Repeat this measurement for several times.
6. Thoroughly clean the tools and the testing area.
Fig. 1 Permeability test (a) Constant head test (b) Falling (variable) head test Report: .Test procedures .Calculated values of coefficient of permeability k with types of soils .Comparison of k with empirical values such as the Hazen's formula Notes: 4
Coefficient of permeability k Constant head test: k = (Q L)/(A Δh t) Falling head test: k = 2.303 (a L) log (h1/ h2 ) / {A (t2- t1)}
where Q: the amount of water collected during time period t in constant h ead test. L: Length of soil specimen A: Cross-sectional area of soil specimen Δh: Hydraulic head loss in constant head test setup a: Cross-sectional area of the burette in falling head test h1: water height in the burette at time t1 in falling head test h2: water height in the burette at time t2 in falling head test Temperature correction for k o The value k is usually given at a test temperature of water at 20 C. So that o o k ( 20 C) = k (T C) x (ηT /η20 ) o o where ηT and η20 are viscosities of water at T C and 20 C, respectively and given in Fig. 2.
Fig. 2 Temperature correction for coefficient of permeability k
5
Soils Lab #1 Hydrometer Test Purpose: The hydrometer test is to determine the distribution of grain size of soils for the particle size less than 75 μm (#200 sieve) based on the Stokes' law, while the sieve analysis mechanically determines the grain size distribution of soils for larger than 75 μm (#200 sieve) particles. References: .ASTM D-422 Standard Test Method for Particle-Size Analysis of Soils. Specimens: Oven dried fine soil passing #200 sieve. Equipment and tools: .Balance .Mixing beaker .Distilled water .Calgon solution with deflocculating agent - 4 % solution with distilled water of sodium hexametaphoshate (Calgon) .Mixing cup and mixer .Hydrometer cylinders (1000 cc) - need two. .Rubber stopper .Hydrometer (ASTM 152-H type) .Thermometer .Stopwatch
Fig. 1 Hydrometer in solution Procedure: 1. Take exactly 50 g of oven-dry well-pulverized soil in a mixing beaker. 2. Mix thoroughly the soil with 125 cc of Calgon solution and allow to soak for at least 16 hours. 3. Using distilled water, transfer the soil-water-slurry completely into a mixing cup. The cup shall be more than half full. Stir it with a mixer for a period of 1 minute. 4. Using distilled water, transfer the dispersed soil-water-slurry completely into a 1000 cc hydrometer cylinder A to its 1000 cc mark exa ctly. 5. In another 1000 cc cylinder B, take 875 cc of distilled water and 125 cc of Calgon solution. Read the temperature of the solution. Insert the hydrometer into the solution and read it at the top of the meniscus as R z (zero correction), and also observe the meniscus correction R m. 6. For the cylinder A prepared in Step 4, using the palm of the hand over the open end of the cylinder (or with a rubber stopper), turn the cylinder upside down and back for 1 minute to complete the agitation of the slurry. At the end of 1 minute (t = 0), place it on a flat table and insert the hydrometer immediately. Read the hydrometer (at the top of meniscus) as R at 0.25, 0.5, 1, and 2 minutes. After the 2 minutes reading remove the hydrometer gently and place it in cylinder B. 6
7. About 30 seconds before 4 minutes reading, inert the hydrometer gently into the soil-water suspension. Take a reading exactly at 4 minutes after the initial time (t=0). Remove the hydrometer gently and place it in cylinder B. 8. Repeat Step 7 for the elapsed times at approximately 8, 16, 30 minutes, 1, 2, 4, 8, 24 hours from the initial time. Record the exact times and the hydrometer readings. Record the temperatures in cylinder B occasionally. 9. Thoroughly clean the tools and the testing area. Report: .Test procedures. .Computation of hydrometer test data .Grain size distribution curve Theory: It assumes that the soil particles are spheres and individual particles settle in the water solution with the velocity v given by Stokes' law; v =
γs - γ w 18 η
D
2
Eq.(1)
where γs is the unit weight of solid (=Gs γw) , γw is the unit weight of water, η is the viscosity of -5 2 o water (which is equal to 1.0197 x 10 g sec/cm at 20 C and varies with the temperature) and D is the diameter of falling soil particle. When a hydrometer is suspended in the water, it measures the specific gravity of the water-soil suspension at a depth L as seen in Fig. 1. Therefore, the average velocity v of the particle with D diameter can be determined from a fallen distance L at a time t from the beginning of the test as; ( γs - γ w ) (g/ cm3) D (mm) 2 v (cm/sec) = = [ ] t (min) x 60 18 η (g sec/ cm2 ) 10 L(cm)
Eq.(2)
and by solving Eq. (2) for D,
D (mm) =
30 η
L (cm)
γs - γ w
t (min)
= A
L (cm) t (min)
Eq. (3)
where the parameter A is a function of the viscosity of water (hence the temperature) and Gs , o and given in Table 1. The ASTM 152-H hydrometer is calibrated at 20 C for Gs = 2.65 particles and those relationships between L and the reading R are given in Fig. 2. A hydrometer reading of, say 30 at a time t means that 30 g of soil solids (with Gs = 2.65) in suspension are at the depth o L of 1000 cc of soil-water mixture at 20 C. Therefore, the percent finer of a soil can be calculated based on those measured values with the corresponding particle diameter D a s; 7
Percent finer by weight (%) =
R cP M soil
x 100 Eq. (4)
where Msoil is oven-dry mass of soil in a total test sample and α ={Gs x 1.65}/{(Gs -1) x 2.65} is the correction for specific gravity for other than Gs = 2.65, and R cP = R + R T - R z (corrected hydrometer reading for percent finer computation). R T , and R z corrections are given in the following additional corrections. Corrections: o Since the ASTM 152-H hydrometer was calibrated at 20 C for Gs = 2.65 particles, the following corrections are needed. Temperature correction (positive or negative), R T = -4.85 + 0.25T, where T is the average test o temperature ( C). Meniscus correction R m (always positive) is the difference in upper and lower meniscus of the suspension. This correction is needed since the readings will be done at the upper meniscus. Zero correction R z (positive or negative) is needed since the deflocculating agent is added to the solution (not pure water). Computations:
Description of soil:________________________ Sample No.:____________ Depth:__________ Gs:____________________, Hydrometer type: ASTM 152-H or others____ o Dry weight of soil Wsoil :______________, Average temperature of test_____________ C Meniscus correction, R m :____________, Zero correction, R z :_______________ Temperature correction, R T:___________ (1) (2) (3) Time Hydrometer R cP t (min) reading, R
(4) (5) Percent finer R cL (%)
(6) L (cm)
Create your own spreadsheet here. __________________________________ Columns (1) and (2): readings during tests Column (3): R cP = R + R T - R z Column (4): from Eq. (4) Column (5): R cL = R + R m , correction for L determination Column (6): from the values in Column (5) and Fig. 2 Column (7): from Table 1 Column (8): from Eq. (3)
8
(7) A
(8) D (mm)
Table 1 "A" values in Eq. (3) as a function of Gs and Temperature
Fig. 2 Length L as a function of hydrometer reading (ASTM 152-H) 9
Soils Lab #2 Liquid Limit and Plastic Limit Test Purpose: To determine the liquid limit (LL) and plastic limit (PL) of Atterberg Limits (LL, and PL and shrinkage limit) of a fine grained soil. References: .ASTM D4318 Standard Test Method for Liquid Limit, Plastic Limit, and Plasticity Index of Soils. Specimens: Air-dried fine soils, passed No. 40 Sieve (0.425 mm) Equipment and tools: .Balance .Mixing cup .Spatula .Distilled water .Glass plate .Liquid limit device .Disposable aluminum cans for moisture content determination Procedures:
1. Prepare several (say 8) moisture content cans (mark can ID # and measure tare weight). Liquid Limit: 2. Mix about 250 g of soil and distilled water to make a uniform paste in the mixing cup. 3. Fill the portion of the liquid limit cup with the paste. Make a smooth surface with a spatula and its maximum depth is about 8 mm. 4. Cut the groove along the center line of the fill with the grooving tool. When grooving keep the grooving tool position normal to the inner surface of the cup. 5. Turn the crank at the rate of about 2 turns per second until the opening of the groove closes for 1/2 inch (12.7 mm) length. Record that number of turns at the 1/2" groove closing as the number of blow, N. 6. Take a part of the mix at the end of each blow test for moisture content determination using previously prepared cans. 7. Bring the soil back to the mixing cup and add a small amount of distilled water and re-mix the specimen thoroughly. 8. Repeat Steps 3 through 7. The targeted initial number of blow N is between 30 and 40 and the smallest N shall be around 20 or less. Take moisture contents only for those N va lues. 9. Plot log N versus moisture content (w) relations (flow curve). Read the w value corresponding to N = 25 from the flow curve to determine Liquid Limit, which is always expressed as a percentage of the moisture content. 10
Plastic Limit: 10. Mix about 20 g of the specimen with a small amount of water in the mixing cup to make rather hard paste. 11. Make the past into a small ball by hand and mix thoroughly. Then make it to a long thread by rolling on a glass plate with your palm. If you can roll it into a less than 1/8 inch (3.13 mm) diameter thread without any break, that moisture content is still higher than the plastic limit. 12. With a drier or by rolling the whole specimen in your hand for a while, make the specimen with less moisture content than the previous try. Then repeat Step 11. When you can barely roll into a 1/8" thread with several breaks (i.e., crumbled thread with 1/8" diameter), collect those crumbled specimen for the moisture content determination. That moisture content is defined as Liquid Limit, which is also expressed as a percentage of moisture content.
13. Thoroughly clean the tools and the testing area. Report: . Test procedures . Liquid limit and plastic limit . Plasticity index Note: Moisture content (water content) determination
moisture content, w = weight of water / weight of solid Computation Table
Can ID No._________________ (1) marked at beginning of the test Wt. of wet in can____________ (2) measured immediately after the test Wt. of oven dry in can________ (3) measured after 24 hours of oven dry Wt. of can__________________ (4) measured at beginning of the test Wt. of water________________ (5) = (2)-(3) Wt. of solid ________________ (6) = (3)-(4) m.c., w(%)__________________ (7) = (5)/(6) x 100
11
Soils Lab #3 Compaction Test Purpose: To determine the maximum dry density of a soil and its optimum water content under a standard compaction energy. References: .ASTM D698 Standard Method for Laboratory Compaction Characteristics of Soil Using 3 3 Standard Effort (12,400 ft-lbf/ft (600 kN-m/m )) Specimens: Air dried soil specimen, passing No.4 (4.75 mm) sieve Equipment and tools: .Mixing pan .Scoop .Compaction mold .Compaction hammer (or automatic compaction machine) .Steel straight edge .Specimen ejection jack .Balance .Moisture content determination cans Procedures: 1. Prepare several (4) moisture content cans (mark can ID # and measure tare weight). 2. Weigh the compaction mold + base but without the extension collar as W1. 3. Obtain about 6 lb of air dried specimen without lumps (passing No.4 sieve) in a mixing pan. 4. Add about 5 % water to the soil and mix them thoroughly. 5. Pour the mixed soil into the mold with an extended collar in three equal layers. Each layer is compacted with 25 drops of the hammer (5.5 lb weight and 12" drop). The final height of the specimen shall be slightly above the top edge of the mold without the collar. 6. Remove the extended collar carefully from the mold. Using a steel straight edge, level the surface of the soil along the top of the mold, so that the volume of the specimen is exactly 3 equal to the internal volume of the mold (1/30 ft ). Weigh the compacted soil + mold + base with the balance as W2 . 7. Eject the compacted soil from the mold by a jack, and take representative specimen for moister content determination. 8. Bring the soil back into the mixing pan and break the soil lumps. 9. Add additional 2 % water to the soil and mix it thoroughly. 10. Repeat Steps 5 through 9 until the water content exceeds its optimum water content (o.w.c.). When you push the surface of compacted soils with the thumb, it will be very hard below or at o.w.c. It become spongy and water starts to bleed out at higher than o.w.c.. 11. Thoroughly clean the tools and the testing area. 12
Report: . Test procedures . Compaction curve (water content versus dry density of soil) . Maximum dry density . Optimum water content . Zero-air-void curve in the compaction curve Notes: Compaction Energy = (Weight of Hummer) x (Height of Hammer Drop) x (Number of Drops) x (Number of Layers) / (Volume of Mold)
for Standard (Proctor) Compaction 3 3 Compaction Energy = 5.5 lb x 1 ft x 25 drops x 3 layers / (1/30 ft ) = 12400 ft-lbf/ft Wet density of soil,
Dry (computed) density of soil , Zero-air-void curve ,
3
γwet = Wwet /V = (W2 -W1 )/ (1/30 ft ) γdry = γwet /(1 + w) γzav = Gs γwat /(1 + wGs )
where W1 and W2 are measured during the test, γwat is the unit weight of water (62.4 pcf) , w is the measured water content, Gs is the specific gravity of solid, and γzav is the (computed) dry density of soil for zero-air-void (fully saturated) for a given water content and a specific gravity of solid.
13
Soils Lab #4 Consolidation Test Purpose: Students will observe a demonstration of a complete laboratory one-dimensional consolidation test and a set of actual lab data will be given. Students will analyze the data to determine consolidation parameters (coefficient of consolidation, e-log P curve, preconsolidation pressure, etc.). References: .ASTM D-2435 Standard Test Method for One-Dimensional Consolidation Properties of Soils .Text book (Chapter 9. Settlements) and class notes Specimens: Undisturbed cohesive soil in sampling tube Equipment and tools: .One-dimensional consolidation device - consolidation ring, loading unit, weights .Porous stones and filter paper .Wire saw .Balance .Water content cans .Stopwatch Procedures: 1. Measure the inner diameter and height of a clean dry consolidation ring and weigh it. 2. Eject the specimen from the sampling tube and trim it to fit exactly into the inside dimension of the consolidation ring. Weigh the specimen in the ring. Take a small quantity of remaining soil in a can for an auxiliary initial water content determination. 3. Place the ring with the specimen in the consolidation device. 4. Put the loading plate and loading piston in position. 5. Make the loading arm in balance by adjusting the counter weight of the arm. 6. Set the vertical dial gage at zero and be ready for loading. 7. Carefully put the initial load at the zero time and record the vertical dial gage at the time intervals of 0.1, 0.25, 0.5, 1, 2, 4, 8, 15, 30 min., and 1, 2, 4, 8, 24 hours. 8. At the end of approximately 24 hours, read the final dial gage reading for that load application, and increase the load to the next level at the new zero time. Record the vertical dial gage at the same (similar) time intervals. 9. Usually before the second load application, or sometimes during the middle of the first load application, the water is poured into the device to fill above the top of the ring and it is kept at that level until the end of the test. 10. Repeat Step 8 until the maximum pressure is attained. A typical sequence of consolidation 2 pressure is 0.25, 0.5, 1, 2, 4, 8, (16) kgf/cm (24, 48, 98, 196, 391, 792, (1584) kPa). 11. After the final reading is completed under the maximum load, the specimen is reloading. The 2 load is reduced with several steps (typically 4, 1, 0.25 kgf/cm ). During each unloading step, the 14
initial dial gage (just before the unloading) and the final reading (typically after one to two hours after the unloading) are needed to measure the rebounds. Therefore, this entire unloading process usually takes one day. 12. At the end of the unloading process, remove the specimen in the ring and weigh it. The specimen in the ring is then placed in the oven for water content determination. 13. Thoroughly clean the tools and the testing area. Report: .Test procedures .Computation of consolidation data .Plot of log (t) vs. δ curve for t50 and Cv determination by log t method .Plot of root (t) vs. δ curve for t90 and Cv determination by root t method .Plot of e-lop p curve .Determination of preconsolidation pressure Pc by Casagrande method .Determination of compression index Cc Note: e-log p curve computation table
Description of Soil________________________, Location______________________________ Specimen diameter D,__________________, Initial specimen height Ho ,_____________________ Water contents: beginning of test (whole specimen)_________________ beginning of test (auxiliary specimen)_______________ end of test (whole specimen)______________________ Weight of dry specimen Ws _________________ , Height of solid Hs ,____________________ (1) pressure
pi
(2) final dial reading δi
(3) change in specimen height Δδi
(4) final specime n height Htf,i
(5) heigh t of void Hv,i
lb/ft2
inch
inch
inch
inch
(6) final void ratio e
(7) avg. specimen ht. during test Htavg,i inch
(8) fitting time t50
t90
t50
t90
sec
sec
in2/s
in2/s
Create your own spreadsheet here. 2 Height of solid Hs =Ws /(γwat Gs ASpecimen )= Ws /(γwat Gs πD /4) C.1: Applied consolidation pressure C.2: Final vertical dial reading for the end of each pressure pi C.3: Δδi = δi - δi-1 (positive number for loading and negative number for unloading) C.4: Htf,i = Htf,i-1 - Δδi C.5: Hv,i = Htf,i - Hs C.6: e = Hv,i / Hs C.7: Htavg,i = (Htf,i-1 + Htf,i )/2 C.8: fitting times determined by log t and root t methods 2 2 C.9: Cv = (T50 Htavg, i )/(4t50) and Cv = (T90 Htavg, i )/(4t90) 15
(9) Cv from
Soils Lab #5 Direct Shear Test Purpose: To determine the angle of internal friction of granular soils by using a direct shear device. References: .ASTM D 3080 Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions. .Text book (Chapter 11. Shear strength of soils) and class notes. Specimens: Air-dried granular soil Equipment and tools: .Direct shear device, .Balance, .Caliper Procedures: 1. Measure the dimensions of shear box components. 2. Weigh the desired amount of dry granular soil. 3. Assemble the shear boxes. The upper and lower shear boxes are tighten together by two bolts. At this stage the four corner bolts (with Teflon on the tips) are lowered as to just touch the surface of the lower shear box. 4. Pore the entire amount of soil into the space in the shear box. Compact as directed. 5. Place the top loading plate and apply the desired vertical stress by loading piston. 6. Measure the specimen height. 7. Remove two tightened bolts from the shear boxes and turn the four corner bolts clockwise with about a quarter turn to separate the upper and lower boxes. 8. Place the vertical and horizontal dial gages and adjust those to zero positions. 9. Start the shearing with a constant shearing speed. Record time, vertical and horizontal dial gages, and shear force at time intervals as directed. 10. Stop the test after attaining the desired shear deformation. 11. Remove the vertical load. 12. Thoroughly clean the tools and the testing area. Report: .Test procedures .Density of the specimen .Shear force and shear deformation curve a nd determination of shear strength .Plot of vertical deformation versus shear deformation to see the volumetric behavior .Plot of shear strength versus normal stress to determine the angle of internal friction (exchange data with other groups to draw this τf versus σ N curve)
16
Soils Lab #6 Unconfined Compression Test Purpose: To determine undrained strength of undisturbed cohesive soil by the unconfined compression test. References: .ASTM D-2166 Standard Test Method for Unconfined Compression Strength of Cohesive Soil .Text book (Chapter 11. Shear Strength of soils) and class notes Specimens: Undisturbed cohesive soil Equipment and tools: .Specimen trimming device .Wire saw .Balance .Water content cans .Caliper (and Pi-tape) .Unconfined compression loader Procedures: 1. Trim an undisturbed specimen into a cylindrical specimen of a desired dimension. Make sure that the bottom and top surfaces shall be perpendicular to the specimen axis. The height to the diameter ratio shall be about 2 or more. 2. Take a small quantity of remaining soil for water content determination. 3. Measure the diameter and height of the specimen and weigh it. 4. Place the specimen in the unconfined compression loader and bring the loading plate to just contact with the specimen. Set the vertical deformation gage reading to the zero position.. 5. Load the loader with a constant speed as directed until the specimen fails. Record the vertical dial gage reading and vertical load at time intervals as directed. 6. Observe and sketch the shape at failure. If the failure planes are observed, measure those angles with a protractor. 6. Remove the specimen and place it in the oven for water content determination. 7. Thoroughly clean the tools and the testing area. Report: .Test procedures .Stress versus strain curve .Determination of unconfined compression strength qu .Computation of cohesion as Cu = qu /2
17
Note: Corrected specimen area
Since this is an undrained test (no volume change during the test), the specimen area shall be corrected by assuming a constant volume during shear; (Initial volume) Ho x Ao = H x A (during shear) = (Ho - ΔH) x A = constant. Therefore, A = (Ho x A o)/(Ho - ΔH) = Ao /(1- ΔH/Ho) = A o /(1-εv ), where Ho is the initial specimen height, H is specimen height during the test, Ao is the initial specimen area, A is corrected specimen area, ΔH is the vertical deformation, and ΔH/Ho (=εv ) is the
18
HYDRAULICS LAB #1 REYNOLDS EXPERIMENT PURPOSE To determine the Reynolds number at which flow through a smooth pipe changes from laminar to transitional flow and also from transitional flow to turbulent flow. APPARATUS Reynolds apparatus, consisting of head tank, 10 mm internal diameter glass tubing and valves to control the flow rate of the water and dye. PROCEDURE After observing the various components of the apparatus and how to control the flow rate of the water and dye, the following should done:
1. Fill the tank up to overflow pipe. 2. Open the tank outlet valve and adjust the inlet valve so as to maintain a constant head at overflow. 3. Open the dye needle valve and readjust discharge valve (outlet valve) and dye valve until a thin line of dye is observed flowing in the glass tube. This is laminar flow. Since this is a very low flow rate, measure the flow rate using a graduated cylinder and stopwatch. 4. Increase the flow by adjusting the outlet valve until the dye starts to waver. This is the beginning of transition and occurs at the critical Reynolds number. Measure the flow rate using the collection method (by collecting water in the hydraulic bench, using a stopwatch). Judgment must be made to decide when the dye line begins to oscillate. 5. Increase the flow until a more pronounced wavering occurs. This is the middle of the transition. Measure the flow rate. 6. Increase the flow until the dye starts to break u p at the tube entrance. The flow is now at the beginning of the turbulent region. Measure the flow rate using the collection method. 7. Increase flow until full turbulence is observed (dye is completely mixed). Measure the flow rate. 8. Decrease flow in an opposite manner to the above, again measuring the flow rate when turbulence just changes to transition and transition chan ges to laminar. 9. Shut off dye, inlet and outlet valves. 10. Record the temperature of water. ANALYSIS
1. Sketch the appearance of the dye line in the tube, when the flow is in the laminar, transitional and turbulent region. 2. Calculate the Reynolds number for each of the flow measurements taken. The Reynolds number is given by the expression: ℝ=
Vd v
OR 19
ℝ
4Q =
d v
3. Define the three flow regimes based on the experimental values of the Reynolds number. Make a comparison with the textbook definition of these flow regimes. DATA
Internal Diameter of the flow visualization pipe, d = ______mm Temperature of the water = ______ ° C 2 Kinematic viscosity of water, = _________ m /s Visual dye condition
Volume of water collected (ml)
Time taken (sec)
20
Q (m3/s)
Reynolds No. =4Q/(πd
HYDRAULICS LAB #2 VENTURI AS A FLOW MEASUREMENT DEVICE OBJECTIVES The main objectives of this experiment are to study the axial distributions of pressure and velocity of a fluid flowing through a venturi meter and to determine the discharge coefficient of the venturi meter. INTRODUCTION A venturi is a converging-diverging nozzle of circular cross section. When connected to a flow passage, a venturi can be used as a flow measurement device.1 Clemens Herchel, a hydraulic engineer, described the first practical venturi meter in a paper (ref. 3) in 1887. The principle of the venturi meter is that when a fluid flows through the venturi meter, it accelerates in the convergent section and decelerates in the divergent section, resulting in a drop in the static pressure followed by a pressure recovery in the flow direction. By measuring the difference in the pressures at an axial station upstream of con vergent section and at the throat, the volumetric flow rate can be established. Bernoulli’s equation can be written between sections 1, 2 and any section n as
z1 h1
V12 2g
z2 h 2
V22 2g
zn h n
Vn2 2g
(1)
Where h1, h2 and hn are pressure heads, V1, V2, and Vn are the average velocities at sections 1, 2, and any other section n. As the axis of the venturi is the same level at all the sections above the datum, it implies z1=z2=zn. By rearranging equation 1, the velocity at any section n can be calculated when the velocity at section one is known and the pressure heads are known at various points n along the pipe, as follows:
Vn
2 g (h1 hn ) (V 1 ) 2
(2)
Since, from the continuity equation, V1 A1 = V2 A2
(3)
where A1 and A2 are the cross sectional areas at the two sections, equation 1 can be rewritten as
h1
h2
V 22
2g
A 2 1 2 A1
1 Other obstruction-type flow measurement devices are described in references 1 and 2. 21
(4)
The ideal volumetric flow rate, Q can be calculated from the flowing equation:
Q
V 2 A2
h2 ) A2 2 1 A1 2 g ( h1
A2
(5)
As a result of friction, the actual volumetric flow rate is less than that predicted by equation 5. The actual volumetric flow rate can be calculated from the ideal volumetric flow rate by introducing a correction factor, discharge coefficient cv, which is defined as: cv
QACTUAL
(6)
Q
Therefore, Q ACTUAL = cv A2
h2 ) A2 2 1 A1 2 g ( h1
(7)
In general, the discharge coefficient of a venturi meter is a function of the flow Reynolds number and the venturi geometry, and has to be determined before the venturi meter can be used to measure volumetric flow rate accurately. In this experiment, the axial distribution of pressure and velocity of water flowing through a venturi meter are to be studied. From the measurements of pressure heads and flow rate of the water through the venturi meter, the discharge coefficient as a function of the flow Reynolds number is to be determined. Note: From Eq. 1, you can find the ideal pressure distribution. But for the purpose of calculation and comparison of experimental results, it is convenient to express (hn-h1) as a fraction of the velocity head at the throat (section 2): hn
h1
V 22 2 g
V 12
V 22
V n2
2
A 2 A 2 A1 A n
22
2
(8)
APPARATUS The test apparatus is shown in Fig 1. A venturi meter is set up on a hydraulic bench, which not only supplies water to flow through the venturi meter but also measures the volumetric flow rate. Pressure taps are installed on the ven turi mater at a number of axial sections. Each tap is connected to a piezometer tube to measure the local static pressure. All the piezometer tubes are connected at their upper ends to a common manifold; thus, all pressures are measured with respect to the pressure in the manifold. The manifold pressure is adjusted during the experiment to control the mean levels of water in the piezometer tubes. The water flow rate is controlled with an inlet valve and an exit valve. PROCEDURE 1. Level the test apparatus. 2. With the two control valves wide open, allow water to flow through the venturi meter at maximum flow rate by switching on the pump. 3. Adjust the two control valves alternately until a meniscus is visible in each of the piezometer tubes. Adjust the manifold pressure if necessary. 4. Remove air bubbles in the piezometer tubes by tapping the tubes. 5. Adjust the two control valves such that a maximum difference between the static heads at the first measurement section and at the throat measurable with the piezometer tubes is attained. 6. Record the height of the water columns in all the piezometer tubes. 7. Measure the time required to collect several volumes of water in the collection tank of the hydraulic bench. 8. Reduce the water flow rate such that the static heads at the first measurement section and at the throat differ by approximately 20 mm (0.8 in) less than that which was observed in the previous run. 9. Record the height of the water columns in the piezometer tubes at the first measurement section and at the throat. 10. Measure the flow rate. 11. Repeat steps 8 through 10 five times. 12. Record the water temperature. 13. Switch off the pump and drain water from the venturi meter. REPORT 1. Calculate the average flow velocity at the first measurement section for each of the six runs using the relationship between the flow rate a nd the average velocity of a fluid flowing through a given cross section (Q = VA). 2. By applying the Bernoulli equation (equation 2) between the first measurement section and each of the other sections, determine the average flow velocity at each of the other measurement sections for each run. 3. Compare the average flow velocities calculated in the last step to those found using the flow rate - average flow velocity relationship. 4. Calculate the theoretical pressure distribution relative to the velocity head at the throat (section 2), using equation 8. 5. For the data obtained during the first run and last runs, calculate the actual pressure distribution relative to the velocity head at the throat. 23
6. Using the data from the first run, tabulate the theoretical pressure (from step 4) and velocities (from step 2) at each of the measurement sections. 7. Using the data from the first run, sketch the venturi meter to scale (lengths and diameters) on a linear graph, and plot the theoretical and actual (for maximum and minimum flowrates) pressure distribution relative to the velocity head at the throat (from steps 4 and 5). Connect the points of each series with lines. 8. Using the data from the first run, sketch the venturi meter to scale (lengths and diameters) on a linear graph, and plot the velocities (from steps 1 and 2) as functions of the distance along the venturi meter on the sketch. Connect the points of each series with lines. 9. Calculate the flow rate and the discharge coefficient for each run. 10. Calculate the flow Reynolds number for each run based on the flow rate and the diameter at the first measurement section. 11. Plot the discharge coefficient as a function of the Reynolds number on a linear graph, and show the best-fit curve. 12. Compare the results with those available in literature. 13. Discuss the results and the error sources. REFERENCES rd 1. Holman J.P., Experimental Methods for Engineers, 3 edition, McGraw Hill Book Company, Inc. 1978, pp 216-229. 2. Munson, Young and Okiishi, Fundamentals of Fluid Mechanics, Third Edition, John Wiley and Sons, Inc., 1998. 3. Herchel, C. The Venturi Water Meter: An Instrument Making Use of a New Method of Gauging Water: Applicable to the Cases of Very Large Tubes and of a Small Valve Only, of the Liquid to be Gauged, Transactions of ASCE, 17 (1887), pp 228-258.
24
Total head 2
2
V1 /2g
Vn /2g
2
V2 /2g h1
hn h2
Direction of flow z1
z2
zn Datum
n
2
1
Fig. 1 Ideal conditions in a Venturi meter A
B
C
D
E
F
G
H
J
K
L
(1) (2)
Direction of flow
8
All dimensions in mm
7
22
22
34
37
54
52 67 82 102
Fig. 2 Dimensions of Venturi meter and positions of piezometer tubes
REF DIA (mm)
A 26.0
B 23.2
C 18.4
D 16
E 16.8
F 18.47
G 20.16
H 21.84
J 23.53
K 25.24
DATA RECORDED
Sample
A
B
PIEZOMETER READINGS (mm) C D E F G H J K
# 1 2 3 4 5 6
Temperature of the water = ______ ° C Kinematic viscosity of water, = _________
2
m /s 25
L
TIME (Secs) 5 1 2 3 L 5 5 5 L L L
Q (avg) L/S
Q (avg) 3 M /S
L 26.0
THEORETICAL CALCULATIONS
Sample # Piez.
1 hn
Vn (Q/A)
2 Vn Bernoulli
hn
Vn (Q/A)
3 Vn Bernoulli
hn
Vn (Q/A)
Vn Bernoulli
A (1) B C D (2) E F G H J K L Sample # Piez
4 hn
Vn (Q/A)
5 Vn Bernoulli
hn
Vn (Q/A)
A (1) B C D (2) E F G H J K L
26
6 Vn Bernoulli
hn
Vn (Q/A)
Vn Bernoulli
Theoretical Pressure Distribution Dia (mm) PIEZOMETER
d 2
a2 an
d n
A (1) B C D (2) E F G H I J K
27
2
2
a2 a2 a1 an
2
For highest flowrate
For lowest flowrate
Q = _________m /s V22 2g ________m Observed Actual Pr head distributions hn h1 hn hn - h1 2 V 2 2 g
Q = _________m /s V22 2g ________m Observed Actual Pr head distributions hn h1 hn hn - h1 2 V 2 2 g
3
PIEZOMETER
3
A (1) B C D (2) E F G H I J K L Discharge Coefficient of the Venturi Meter: Sample #
Piez A (m)
Piez D (m)
Q Eq 5 3 (m /s)
QACTUAL 3 (m /s)
1 2 3 4 5 6
28
CV Eq 6
V1 (m/s)
R= V1D1/
HYDRAULICS LAB #3 FLOW OVER SHARP CRESTED WEIR INTRODUCTION The sharp-crested weir is frequently used as a device for measuring discharge in a channel. It is simple to install, and provided that it conforms to prescribed requirements, it may be used with confidence in conjunction with standard calibration data. In this experiment we establish the relationship between head over the weir and discharge. EQUIPMENT Sharp crested weir with air vent, dial vernier depth gauge, steel rule. THEORY The flow is illustrated in Fig 1. The height of the crest above the channel bed is “a”, and the height of the water surface above the crest is “h”. Considering a typical streamline from a point in the plane of the weir, we note that on the assumption of uniform velocity V in the upstream flow, the specific energy E is given b y
a h
V 2
(1)
2g
and this specific energy is constant over the cross-section. Suppose that the velocity along a typical streamline in the plane of weir is V, and the height of the streamline above the weir crest is z. Then if there is no loss of head along the streamline, and the pressure in the plane of the weir is atmospheric, Bernoulli’s equation is
ah
2
V
2g
a z
2
V
(2)
2g
2
Ignoring the velocity head V /2g in the approach channel, equation 2 gives velocity over weir as V
2 g (h
z)
(3)
The element of discharge Q through an element of height z and width B is then Q
V B z
or Q
2 g (h z ) B dz
29
(4)
Fig.1 Flow over a sharp crested weir Provided that V is horizontal, the total discharge Q may then be obtained, ignoring the contraction of the jet in the plane of the weir, as h
Q
2 g (h z ) Bdz
(5)
o
Performing the integration, Q
2 3
3
(6)
B 2g h 2
It is now necessary to introduce a dimensionless discharge coefficient C into the equation to allow for the many assumptions made in the derivation, giving the following as the weir equation: 3
2 Q C B 2g h 2 3
(7)
In the experiment we aim to verify the power-law dependence of Q on h, and to establish the value of C. Although the theory has been derived specifically for a sharp-crested weir, a similar treatment clearly applies to spillways with rounded crests, although the value of C will vary from case to case.
30
PROCEDURE The channel is first set horizontal, as indicated by the linear and circular scales, by use of the screw jack. The height of the weir is measured by steel rule. It is then placed vertically in the channel, approximately 0.5m upstream of the outlet. With the point of the dial vernier depth gauge resting on the weir crest, the gauge scale is set to zero, so that subsequent measurement of water level is referred to zero at the weir crest.
Water is then admitted to the channel by opening the control valve steadily, until a convenient maximum flow is obtained. (This maximum depends on the available depth of flow in the channel). The discharge is then measured by timing the collection of a known weight of water. During the timed interval, the head over the weir is measured using the dial vernier depth gauge at a distance of 0.3m upstream of the weir. To obtain a good accuracy, it is desirable to measure the head several times over the interval and to record the mean value. The flow is then reduced in stages, and at each stage both the discharge and the head are measured. It is important that at all times during the measurements, the underside of the jet issuing from the weir should spring clear of the downstream face of the weir plate, and a vent pipe is provided to assist the separation of the jet by admitting air into this region. From time to time, and particularly at low heads, it is necessary to blow a little air along this pipe to maintain the separation of the jet from the weir plate. The approximate range of heads over which readings may be taken is from 50mm to 25mm; measurements should cease when it is no longer possible to ensure separation of the jet from the weir plate.
ANALYSIS 1. Calculate C from Equation 7 for each measurement. Prepare a table listing h, Q, C and h/a values. Does C remain a constant? 3/2 2. Plot Q as a function of h and interpret your plot with reference to Equation 7. 3. Plot C as a function of h/a and investigate if C varies with h/a. 4. Plot Q as a function of h. The curve to be obtained will be the discharge-head curve for the sharp-crested weir used.
31
DATA RECORDED
a = ________ mm = ________ m B = ________ mm = ________ m Sample No 1 2 3 4 5 6
h (mm)
h (m)
Q1 (kg/s)
Q2 (kg/s)
Q3 (kg/s)
QAV (kg/s)
Sample Calculations QAV = (Q1 + Q2 + Q3) / 3 = _____________ kg/s 3 3 Q = _____________ m /s ……………..[for water 1000 kg = 1.0 m ]
THEORETICAL CALCULATIONS
3
Sample No
h (m)
2 QT B 2 g h 2 3 3 (m /s)
QACTUAL 3 (m /s)
1 2 3 4 5 6 Sample Calculations QT = C= h/a =
32
C= QAC/QT
h/a
Q 3 (m /s)
WEIGHING TECHNIQUE The precision weighing unit of the TecQuipment Hydraulic Bench, which has a 3:1 ratio, is designed for accurate measurement of relatively large quantities of water up to a maximum of 36 kg.
Before proceeding with any experimental work on the bench, students should familiarize themselves with the following technique: (a) Close the bench supply valve and direct the supply hose into the weigh tank via center of the bench top. (b) Slide the weigh beam stop out of line of the beam and lift the beam for 10-15 seconds to ensure the weigh tank is empty. (c) The weigh beam will be in its lower position with only the weight carrier on (fig 2a). Slide the weigh beam stop above the weigh beam. (d) Switch on the pump. (e) Open the bench supply valve. (f) Start timing the instant the weigh beam comes horizontal and place selected mass immediately on to the weight hanger. (See figs 2b and 2c). (g) When the mass of water collected balances the mass of the weight hanger, the beam will rise again to the horizontal position (Fig 2d). At this instant, stop the timer and record the timing interval. Note: The mass of water collected is three times the mass used on the weight hanger. (h) Close supply valve or switch off the pump. (i) To drain the weigh tank, depress weigh beam above weight hanger and slide weigh beam stop away. Gently let weigh beam rise until it stops aga inst the sump tank. Remove weights and tank will continue draining. As the weigh beam returns to the horizontal, lift it for 10-15 seconds to drain final amount from weigh tank (fig 2e).
33
Weigh Beam Stop
(a) (i) Stop positioned over beam (ii) Start pump (iii) Drain valve closed Closed
(b) (i) Beam moves to horizontal (ii) Start clock Closed
(c) (i) Add required weights
Closed
(d) (i) Beam moves to horizontal (ii) Stop clock Closed
A
(e) (i) Drain (ii) Press down on A (iii) Slide stop away (iv) Release arm gently; remove weights (v) Lift at B to complete draining for 10-15s
B
Open
Fig. 2
34
HYDRAULICS LAB #4 ENERGY HEAD LOSS DUE TO A HYDRAULIC JUMP OBJECTIVE: The objective of this experiment is to study the formation of a hydraulic jump and determine the energy head loss due to a free hydraulic jump in a horizontal, rectangular channel. APPARATUS: 1- Five-Meter Flow Channel 2- Sluice gate 3- Dial vernier depth gauge 4- Stop watch THEORY: Hydraulic jump occurs when the flow changes from rapid to tranquil in an open channel. Flow is
rapid or supercritical when the Froude number, F, defined as
√
, is greater than 1 and is
tranquil or subcritical when F is less than 1. A hydraulic jump is highly turbulent, with complex internal flow patterns, and it is accompanied by considerable energy loss. Hydraulic jumps are caused by changes in the channel bed slope, the presence of a sluice gate or a downstream obstacle at the foot of a spillway. Application of Momentum equation to the jump leads to a relationship between the depths (h1 and h2) as follows (for a rectangular channel) :
1
Where h1: flow depth just upstream of the jump h2: flow depth just downstream of the jump q: discharge per unit width (Q/B)
Figure 1: A hydraulic jump in a channel flow. 35
We can manipulate Equation (1) mathematically to obtain:
1 8 1
(2)
Where: Fr 2: Froude number at section 2.
Equation (2) is useful to calculate the flow depth just upstream of the jump if the flow conditions are known downstream. Once we determine the flow depths upstream and downstream of the hydraulic jump, we can use the energy equation to calculate the head loss due to the jump as
(3)
This equation can be manipulated to obtain
(4)
In this experiment we are trying to form the hydraulic jump and find out the head loss due to the jump. PROCEDURE: A. Data to collect
1. Measure and record the flow depths h1 (just upstream of the jump) and h2 (Just downstream of the jump) 2. Measure and record channel width 3. Measure and record flow rate(Q) using weighting technique B. Test procedure 1. Adjust the channel to a horizontal position. 2. Measure the channel width. 3. Turn the pump on and adjust the flow control valve to achieve flow depth of about half of the channel’s height. 4. Place the sluice gate vertically in the channel at a distance of two meters downstream from the flow source to generate a hydraulic jump. Make sure that the sluice gate is not placed too low in the channel to avoid water back up over the channel walls. 5. Wait about a minute after installing the sluice g ate to have a stable flow depth. 6. Using the dial verneir depth gauge, measure and record the flow depths just upstream and downstream of the jump labeled as h1 and h2, respectively. 7. Measure the flow rate using the weighting technique. 36
ANALYSIS
1. 2. 3. 4.
Determine the flow velocity just before and after the jump. Compute the Froude number for section one and two as shown in figure 1. Compute Head Loss due to the jump Draw the water surface profile for the jump
DATA RECORDED
B = ________ mm = ________ m Sample No 1 2 3 4 5 6
h1 (m)
h2 (m)
Q1 (kg/s)
Q2 (kg/s)
Q3 (kg/s)
Sample Calculations QAV = (Q1 + Q2 + Q3) / 3 = _____________ kg/s 3 3 Q = _____________ m /s ……………..[for water 1000 kg = 1.0 m ]
37
QAV (kg/s)
Q 3 (m /s)
HYDRAULICS LAB #5 IMPACT OF JET ON VANES
INTRODUCTION One way of producing mechanical work from fluid under pressure is to use the pressure to accelerate the fluid to a high velocity in a jet. The jet is directed onto the vanes of a turbine wheel, which is rotated by the force generated on the vanes due to momentum change or impulse, which takes pace as the jet strikes the vanes. Water turbines working on this impulse principle have been constructed with outputs of the order 100 megawatts and with efficiencies greater than 90%.
In this experiment, you are going to determine the force generated by a jet as it strikes a flat plate and a hemispherical cup and compare it with the momentum flow rate in the jet. DESCRIPTION OF APPARATUS The jet impact apparatus is shown in Fig. 1. The vane is supported by a lever, which carries a jockey weight and is restrained by a light spring. THEORY Consider a vane symmetrical about the x-axis as shown in Fig. 2. A jet of fluid flowing at the rate of W kg/s along the x-axis with velocity u0 m/s strikes the vane and is deflected by it through an angle β, so that the fluid leaves the vane with the velocity u1 m/s inclined at an angle β to the x-axis. Changes in elevation and in piezometric pressure in the jet from striking the vane to leaving it are neglected.
The rate which momentum is entering the system shown is 2 = Wu0 (kg m/s ) in the direction of x and the rate at which momentum is leaving the system is 2 = Wu1 cos β (kg m/s ) in the direction of x The force in the direction of x on the jet, being equal to the rate of momentum change, is therefore: 2 = (Wu1 cos β – Wu0) kg m/s or =
(Wu1 cos β – Wu0)
Newton
The force, F, on the vane in the direction of x is equal and opposite to this, so that: F
=
W( u0 – u1 cos β )
Newton
38
For the case of the flat plate, we may assume that β = 90 , so that cos β = 0 and ˚
F p = Wu0 Newton Note: This value is irrespective of u1 For the case of hemispherical cup, we assume that β = 180 , so that cos β = -1 and ˚
Fc = W ( u0 + u1) Newton Since changes in piezometric pressure and elevations are neglected, the maximum value of u1 will be u0 (when there is no energy loss) so that the maximum possible value of the force on the hemispherical cup is: Fc max = 2 Wu0 Newton i.e. twice the force on the plate. PROCEDURE 1. Level the apparatus. 2. Flat plate and Cover plate are to be supported by the lever. Then set the lever to the balanced position (as indicated by the tally) with the jockey weight at its zero position, by adjusting the nut above the spring. 3. Set the flow control valve of the hydraulic bench at its maximum and start the pump. 4. Record the position of the jockey weight, y, which restores the lever to the balanced position. Measure the discharge in volumetric tank. 5. For a series of decreasing flowrates for which the experiment is conducted, discharge is to be measured and jockey weight position to be noted. 6. Repeat steps 2 to 5 for hemispherical cup. ANALYSIS 1. Calculate the velocity, u0, for each discharge. For this, the jet velocity, u, at the exit of the nozzle is calculated from the discharge measured and the cross-sectional area of the nozzle. The velocity, u0, as it strikes the vane is less than the velocity, u, at the exit from the nozzle, because of the deceleration due to gravity, and may be calculated from the expression: 2
2
u0 = u – 2 g s where s is the distance between the vane and the nozzle.
39
2. Compute theoretical F p and Fc max for each discharge (refer to equations given in the theory portion). 3. Compute the actual force, F’ p and F’c for each discharge by taking the moments about the pivot. Note: The jockey weighs (0.6kg x g) Newton. When it is moved a distance, y (meters), from its zero position, the corresponding force, F’ (Newtons), on the vane is obtained by taking moments about the pivot, as: F’ x D = (jockey weight in kg) x g x y Where D = distance from center of vane to pivot of level and g = acceleration due to gravity. 4. Plot force on vane (Newtons) (F and F’) and Rate of delivery of momentum Wu0 (Newton) for both flat plate and hemispherical cup. 5. Discuss your results.
40
FOR THE FLAT PLATE: DATA
Jockey mass Nozzle dia Vane/Pivot centers Vane above nozzle
y (mm)
5L (secs)
=
grams =
mm
= =
mm mm
TIME
TO
COLLECT
15 L (secs)
25 L (secs)
35 L (secs)
QAV (L /s)
W (kg/s)
u (m/s)
uo (m/s)
Wuo (Newton)
F p (Newton)
F’ p (Newton)
CALCULATIONS
W (kg/s)
y (m)
41
FOR THE HEMISPHERICAL CUP: DATA
TIME y (mm)
5L (secs)
TO
COLLECT
15 L (secs)
25 L (secs)
35 L (secs)
QAV (L /s)
W (kg/s)
u (m/s)
uo (m/s)
Wuo (Newton)
Fc (Newton)
F’ c (Newton)
CALCULATIONS
W (kg/s)
y (m)
42
HYDRAULICS LAB #6 STEADY AXISYMMETRIC UNCONFINED FLOW INTRODUCTION The purpose of this experiment is to investigate steady unconfined groundwater flow in the vicinity of wells. Also, transient states of cone of depression and the process of groundwater recovery will be demonstrated. THEORY
Figure 1 shows steady axisymmetric flow to a well in an u nconfined aquifer. The aquifer is fed by a constant rate of accretion N reaching the water table. At steady state the discharge entering the storage should be equal to discharge leaving it in any portion of the aquifer. Hence, for a cylindrical portion of the aquifer that has a radius r, (see Fig. 2)
Q W
Q leakage
Q leakage
Q aquifer
r r N 2
2 w
h r
Qaquifer A x V , A 2 rh, V K
h Qw (r 2 r w2 ) N 2 r h K r 43
(1)
Where Qw is the well discharge, r w is the well radius, K is the hydraulic conductivity, and h is the water table elevation. The first group of terms on the right hand side represents the recharge due to accretion N, and the last group of terms represents the flow from the remaining portion of the aquifer. Equation 1 assumes that flow lines are horizontal and there is flow only in the redial direction. Integrating Eq. 1 between r = r 1, h = h1 and r = r 2, h = h2 one obtains, 2 1
h
h
2 2
r 1 N 2 r w2 N r 1 2 ln r 1 r 2 ln 2 K K r 2 K r 2 Qw
(2)
where h1 and h2 are the water table elevations at distances r 1 and r 2 from the well, respectively. The well radius is very small, and it can be neglected. Hence, Eq. 2 can be written as K
1 2
h1
h22
Qw r 1 N 2 2 ln r 1 r 2 r 2 2
(3)
EQUIPMENT Hydrology apparatus. PROCEDURE 1. Place the portholes on the weirs at the upstream and downstream ends of the catchment. 2. Set the apparatus horizontal. 3. Determine and record the locations of wells A and B with respect to the piezometers. 4. Start the pump, and feed water to the overhead spray. Adjust the pump discharge such that the rotameter reading is about 3 1/min. 5. Wait until the water table rises to an elevation of about 130 mm. Then quickly open the valve that drains the well A to the weir. Observe the changes in the piezometer water levels. 6. Wait until steady state is reached. Measure the well discharge by observing the water level in the flowrate measuring weir box, and rea ding the corresponding discharge from the weir calibration curve. 7. Record the water levels in piezometers 7 and 8. 8. Quickly close the valve that drains the well A. Observe the changes in the piezometer water levels. 9. Reduce the pump discharge slightly, and open the valve that drains the well B into the weir. Wait until steady state is reached. Then measure the well discharge using the flowrate measuring weir box, and record the water levels in all the piezometers.
44
ANALYSIS 1. Determine the rate of accretion N. Note that the surface area of the catchment is 1m x 2m. 2. Using the water levels in piezometers 7 and 8 recorded when well A was discharging, calculate the hydraulic conductivity K from Eq. 3. 3. Calculate the theoretical water table using Eq. 2 when well B is discharging. Assume r w = 0. To calculate the water table elevations to the right of the well, use the distance of piezometer 15 from the well and the water level in that piezometer as r 2 and h2, respectively. To calculate the theoretical water table elevations to left of the well, use piezometer 14 for the same purpose. 4. Plot the theoretical and observed water tables when the well B is discharging. Compare. 5. Explain the transient states of the water table observed when the valves draining the wells are opened and closed (see procedure 5 and 8). 6. Discuss your results.
DATA RECORDED
(i)
For Determination of Hydraulic Conductivity K 3
Discharge from well A, Qw = _______________________ m /s 3
Rate of accretion, N = ____________________________m/s = For Piezometer 7,
r 1 = ___________________________ m h1 = __________________________ m
For Piezometer 8,
r 2 = ___________________________ m h2 = __________________________ m
CALCULATION Use Eq 3 to find K
45
Rotameter reading ( m / s ) Surface area of the catchment
(ii)
For Determination of Water Table 3
Discharge from well B, Qw = _________________ m /s Hydraulic Conductivity K = __________________ m/s (Note: Use the value obtained for K above)
PIEZOMETER
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
OBSERVED h (m)
x (m)
0.00 0.20 0.40 0.50 0.60 0.66 0.74 0.80 0.88 0.96 1.04 1.12 1.20 1.26 1.34 1.40 1.50 1.60 1.80 2.00
46
r (m) w.r.t WELL AT B
THEORETICAL h (m) (use Eq 2)
Use observed head at 14 as h2 0.26 0.18 0.10 0.04 0.04 0.10 0.20 0.30
Use observed head at 15 as h2
Key F,G,I,II - Valves 1,2 - Wells 19 mm diameter - Piezometer Tappings (Numbered 1 to 20) 60 - Space of 60 mm between Piezometer Tappings 3 - Board with 20 Piezometer Tubes Mounted 4 - Tilt Mechanism
1
40 200
4
1
200 2
4
5 6
40
40
100 100 60 3
2
3
60 80 80 80 80 80 60 7 8
9
40 60 100 100
10 11 12 13 14 15 16
17
18
200
200 19
20
F G
II
I
Pump
Figure 3: Apparatus layout showing Wells and Piezometer only
47
