Mapua Institute of Technology School of Civil Engineering Environmental Environmental and Sanitary Engineering Hydraulics Laboratory
Experiment No.: 1 Title:FALLING SPHERE VISCOMETE VISC OMETER R
Name:DEL ROSARIO, Johndem F. Student #: 2007180011 Program & Year: CE-3 Course code & Sec: CE140-OP / B2 (Fluid mechanics) Group #: 10 Group Members: Members: SANTOS, Emil Carl Carl D. / FELICIA, Timothy Daniel Daniel DJ Date Performed:10/14/10 Date Submitted: 10/28/10
Rating
Engr. Fibor J. Tan Instructor
EXPERIMENT NO. 1 FALLING SPHERE VISCOMETER
Commercial Falling Sphere viscometers are non-available. One type of which is shown on the sketch. The one available is not of the commercial type this viscometer makes use of the principles in case of flow around a small sphere. For laminar flow vd/2 1in which d is the diameter of the sphere. The friction or the deformation drag Fd of the sphere moving at a constant velocity V through a fluid of infinite extend is given by Stokes Law with the following assumptions: 1. The particle must be a sphere. 2. The surface of the particle must be smooth. 3. The resistance to fall or drag force F d is due to the viscosity of the fluid. 4. The terminal velocity must be constant.
------------------------------------------------ (1)
A free body diagram of the sphere after it has acquired constant velocity or terminal velocity is shown on the sketch where W is the weight of the sphere. Fb is the buoyant force and Fd is the deformation drag.
Or
(2)
(3)
(4)
Solving for :
18V
Equation (4) has to be corrected in actual practice because the extent of the fluid is not infinite and the influence of the boundary proximity on the sphere is large. The correction is usually affected by multiplying the observed velocity of fall VS by a certain constant K which is a function of d/Dm the diameter of the sphere and medium ratio, such that V = VS K
(5)
Where K =
2
1 + 9d/ 4 Dm ÷ (9d/4 Dm)
The equation for viscosity then becomes
= d2(S L) / 18VSK for which the viscosity can be computed.
OBJECTIVE:
The purpose of this experiment is to determine the viscosity of a certain fluid. APPARATUS:
Viscometer
stopwatch
Hydrometer
thermometer
caliper
steel balls
2 LABORATORY PROCEDURE:
Determine the temperature and specific gravity of the liquid whose viscosity is desired. Drop cautiously one of the spheres noting whether the sphere is guided correctly or is off center. Determine the time required for the sphere to travel a certain distance. Repeat the procedure for each sphere. REPORT:
From the data obtained in the laboratory, compute for each run
1. (a) Ratio of sphere diameter to diameter of med ium, d/Dm (b) Correction constant, K (c) The observed velocity of fall, VS (d) Dynamic Viscosity, 2.
Using
the computed value of dynamic viscosity , compute for the Kinematic Viscosity
v. v = / L 3. Plot VS versus d/Dm
FINAL DATA SHEET
NAME: DEL ROSARIO, Johndem F.
DATE:10/14/10
SUBJECT & SECTION: CE140-0P / B2
GROUP NO.10
SEAT NO.
EXPERIMENT NO. 1 FALLING SPHERE VISCOMETER
GROUP NO.
TRIAL NO.
Y (m)
t (sec)
VS (m/s)
d (m)
Dm (m)
d/Dm
k
V (m/s)
(Pa-s)
v 2 (m /s)
1
1
7.32
0.14
0.00476
0.09285
0.05
1.13
0.16
0.47
3.7x10
2
1
26.50
0.04
0.00241
0.09285
0.03
1.06
0.042
0.45
3.5x10
3
1
3.39
0.29
0.00792
0.09285
0.09
1.23
0.357
0.58
4.5x10
4
1
-4
-4
1 -4
FINAL SAMPLE COMPUTATION
TRIAL NO. 1 Y 1m Vs = = = 0.14 m/s t 7.32 s
d
=
Dm
0.00476 m = 0.05 0.09285 m
9d
K=1+
K=1+
+
4Dm
2
9d
4Dm
9(0.00476) 4(0.09285)
+
9(0.00476) 2 4(0.09285)
= 1.13
V = (Vs)(K) = (0.14 m/s)(1.13) = 0.16 m/s
s= (s)(g) = (7350 kg/m3)(9.81) = 72103.5 KN/m3
L= (L)(g) = (1280 kg/m3)(9.81) = 12,556.8 KN/m3 2
=
d (s-L)
= 18(Vs)(K)
2
(0.00476) (72103.5 12556.8) 18(0.14)(1.13) = 0.47 Pa-s
= (V)(L)
0.47
L
V= =
-4
2
=3.7x10 m /s
RESULTS AND DISCUSSION
When objects are placed within or on the area of the fluid, it experiences a feeling of deflection, oscillation or resistance and therefore, its velocity may be controlled or reduced.From the experiment, the absolute viscosity was determined with correction formula due to some factors like the size of the sphere, the diameter of its opening and the varying velocity of the sphere. The objective of the experiment was to determine the value of the corrected absolute viscosity of glycerin. Different steel ball with different diameter is used in the classic experiment to improve the accuracy of the calculation.
To apply the experimental formula for viscosity of glycerin derived from the principles of Stoke¶s Law. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. Stokes's law is the
basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube.
Errors always occur on an experiment. Sources of errors may have been the values that have been gathered by measuring, like the diameter of the sphere or the opening, or rounding off digits that may have made the required value stray. By understanding accurately the procedures specifying additional data and specific instruction, the so urce of error would be minimal.
PLOTTED VS versus d/Dm
Vs versus d/Dm 0.35 0.3
Vs
0.25 0.2 Vs versus d/Dm
0.15 0.1 0.05 0 0.03
0.05
0.09
d/Dm
CONCLUSION
Viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them.If a specific layer of a liquid is taken, the layer below it moving with lesser velocity tries to decrease the velocity of upper layer due to cohesive forces between the molecules of adjacent layers. In turn the upper layer which is moving with greater velocity tries to increase the velocity of the lower layer. So between parallel, successive layers of a liquid in motion, opposing force comes into play tending to decrease the relative velocity between the layers. Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction.
Furthermore, this resistance acts against the motion of any solid object through the fluid and also against motion of the fluid itself past stationary obstacles. Viscosity also acts internally on the fluid between slower and faster m oving adjacent layers.
Weve seen how viscosity acts as a frictional brake on the rate at which water flows through a pipe; let us now examine its frictional effect on an object falling through a viscous medium. To make it simple, we take a sphere. If we use a very viscous liquid, such as glycerin, and a small sphere, for example a ball bearing of radius a millimetre or so, it turns out experimentally that the liquid flows smoothly around the ball as it falls.
APPENDIX PRELIMINARY DATA SHEET
REFERENCE
http://en.wikipedia.org/wiki/Viscometer
Munson, B.; Okiishi, T.; Young, D. (2006). Fundamentals of Fluid th
Mechanics, 5 Edition USA: John Wiley and Sons, Inc.
