Nama
: Mufti Ghazali M
NIM
: 060045
Tugas
: Mekanika Fluida
Dosen
: Yanasari. ssi
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
1
Chapter Forces on submerged plane areas 1.
If
a triangle of height d and d and b is vertical and submerged in liquid with
its vertex at the liquid surface (see figure below), derive an expression to its center of pressure
2. A
circular area of diameter d is vertical in a liquid.
Its
upper edge is
coincident with the liquid surface (see figure below), derive an expression for it¶s of pressure
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
3.
A
vertical semicircular area of diameter d and radius r is submerged
and has its diameter in liquid surface (see figure below), derive an expression for the depth to its center of pressure.
4.
A
vertical, rectangular gate with water on one side is shown in figure
below, determine the total resultant force acting on the gate and location of the center of pressure
2
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
5.
An
inclined, rectangular gate with water on one side is shown in figure
below, determine the total resultant force and location of center of pressure
6.
A
vertical triangular gate with water on one side is shown in figure
below, determine the total resultant force and location of center of pressure
3
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
4
7. Freshly poured concrete approximates a fluid with s.g. =
2.40
like the
figures below, calculate the forces in four bolt.
8. Gate AB in figure below is 1 m long and 0.9 m wide, calculate force F on the gate and the position of its center of pressure
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
9.
Calculate
the resultant force on triangular window ABC in figure below
and locate the center of pressure
10. Isosceles triangular gate AB in figure below is hinged at A compute the horizontal force P required at point B for equilibrium, neglecting the weight of gate
5
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
Chapter Buoyancy and floatation 1.
A
cube of timber 1.25 ft on each side float in water as shown on figure
below, the specific gravity of the timber is 0.60. find the submerged depth of cube
2. A
concrete cube 10.0 in on each side is to be held in equilibrium under
water by attaching a lightweight foam buoy to it, as shown in figure below (in theory, the attached foam buoy and concrete cube, when placed under water, will nighters nighters rise nor sink.) if specific we ight of concrete and foam are 150 lb/ft 3 and 5 lb/ft 3, respectively, what minimum volume of foam required.
6
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
7
Forces acting in this problem were W f f and W c c are respectively weight of the foam and concrete, and F bf and F bc are the respectively buoyant forces on the foam and concrete.
3.
A
barge is loaded with 150 ton of coal, weight of empty inn air is 35
ton, if barge is 18 ft wide, 52 ft long, and 9 ft height, what is the draft.
4.
Determine
the submerged depth of a cube of steel 0.30 m on each side
floating in mercury, specific gravity of steel and mercury are 7.8 and 13.6
5.
A
pieces of wood of s.g. o.651 in 3 in square and 5 ft long. How many
pounds of lead weighting fastened at one end of the stick so that it will float upright with 1ft out of water?
6.
A
rectangular open box
25
ft by 10 ft in plan and 1 2 ft deep weight 40
ton and is launched in fresh water. (a) How deep will it sink? (b)if the water is 12 ft deep, what weight of stone placed in the box will cause it rest on the bottom?
(a) (b)
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
7.
A
8
ship, with vertical sides near water line, weight 4000 ton and draws
22
ft in salt water ( K = 64 lb/ft 3) see figure below.
of water ballast decrease the draft to
21
Discharge
of 200 ton
ft what would the draft d in
fresh water?
Because the shape of underwater section of ship is not known, best to solve this problem on the basis of volume displaces. draft was caused by a reduction of weight of 64[(1)(A)]= 22
ft and
200(2000)
21
A
200
1ft decrease in
tons, or KVd =
where V d epresent the volume between draft d R epresent
ft, and [(1)( A)]( 200)(2000)/64=6250 ft 3, F b= weight of
displaced liquid KV d / K K in figure upside the vertical crosshatch d , V d d =F b volume is the difference in displaced in fresh water and sea water. This difference in volume can be express as W K Fresh / K
H2O
- W K salt / K
H2O,
or
3 (400-200)(2000)/62.4-(4000- 200)/64, since V d d = 6250 ft /ft depth, the
vertically crosshatch volume can also be expressed as 6 250y. 50 y. Hence, 6250y 50y =(4000=(4000-200)(2000)/62.4-(4000-200)( 2000)/64,
y =0.49 =0.49
ft;
d =21+0.49=21.49 ft.
8.
A
cube
2.2
ft on edge has its lower half of s.g. =1.6 and upper half s.g.
=0.7. Is rest in a two layer fluids, with lower s.g. =1.4 and upper s.g. = 0.8.
Determine
the height h of the top of the cube above the
interface see figure below.
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
9
9.
With
how many pounds of concrete ( K! 25 kN/m) must be beam of
volume of 0.2 m 3 and s.g.=0.67 be coated to insure that it sinks in water?
10.
What
is the weight of the loaded barge in figure below? The barge is
7m in width
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
10
Chapter Hydraulics and energy grade lines 1.
A
pipeline with a pump leads to a nozzle as shown on figure below.
Find the flow rate when the pump develops a head of 80 ft. assume that the head loss in the 6 in diameter pipe may may be expressed by
, while the head loss in the 4-in diameter pipe is
, sketch the energy line and hydraulics grade line, and find the
pressure head at the suction of the pump.
Select the datum as the elevation of the water surface in the reservoir.
Note from continuity that
where
V3
is the jet velocity.
and
Writing
,
an energy equation from the
surface of the reservoir jet,
fps;
.
Head
loss
,
V3=29.7
in
suction
. the energy line and hydraulics grade line are drawn on the figure
to scale. Inspection on that figure shows that the pressure head on the
suction side of the pump is P b /K!ft. likewise, the pressure head at any point in the pipe may be found if the figure is scale.
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
2. A
11
pump lifts water at the rate of 180 cfs to a height of 375 ft, at a pipe
friction loss of 27 ft. find the power required if the pump efficiency is 88%. Sketch the energy grade line and hydraulics grade line.
, energy and hydraulic grade lines are
sketched in figure below.
3. The diameter of the suction and discharge pipes of the pump are 6 in and 4 in, respectively. The discharge pressure is read by a gage at a point 5 ft above the centerline of the pump, and the suction pressure is read by a gage
2
ft below the centerline . If the pressure gage reads
20
psi and the suction gage read a vacuum of 10 inHg when a fluid of specific gravity 0.79 is pumped at the rate of 2.0cfs, find the power delivered to the fluid. Sketch the energy grade line and the hydraulics grade line.
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
12
The energy and hydraulics grade lines are sketched in figure below
4.
A
pump with a shaft of 7.5 k W and an efficiency of 70% is connected
in a water line carrying 0.1m 3 /s. the pump has a 150-mm diameter suction line and a 1 20-mm-diameter discharge line. The suction lines enter the pump 1m below the discharge line. For a suction pressureof 70kN/m3, calculate the pressure at the discharge flange and the rise in the hydraulics grade line across the pump.
The energy added per unit weight of water, E, is given by
,
, applying the energy equation from
suction flange to discharge flange gives
in which the subscripts s and d refer to the suction and
discharge conditions, respectively. From the continuity equation, .
kPa. The rise in hydraulic grade line is
Solving
for pd =89.6 =89.6
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
5.
Determine
13
the elevation of hydraulic and energy grade line at point
A,B,C,D,E of the figure below(z=10ft)
Solving for the velocity head is accomplished by applying the energy
equation from the reservoir to E,
. From the continuity equation,
V E V. after simplifying, E=4 and
. hence, the hydraulic grade at
The energy grade line for
A
is
B,
A
is
for for
and
The energy grade line is at 62.19+1.66=63.85 ft
Across
the valve the hydraulic grade line drop by
or 16.6 ft.
hence, at C the energy and hydraulic grade lines are at 47. 25 and 45.59, respectively.
At
point D,
and
With
the energy grade line at 37.6+1.66=39.26 ft.
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
At
14
point E the hydraulic grade line is 10 ft, and the energy grade line is
6. The head extracted by turbine CR in figure below is pressure at T is 72.7 psi. For losses of
200
ft and the
between W and R and
between C and T , determine (a) how much water is flowing and
(b) the pressure head at R. draw the energy line.
Because the energy line is at T is at elevation
and well above the elevation at W , the water flow into the reservoir W . At
(a)
T
Substituting
T to
C
R to W Hr
and solving
at W
or
then
(b)
Using
R to W , datum R
and
the reader may check this pressure head by
applying the Bernoulli equation between T and R.
To plot the energy line in the figure, evaluate the energy at four sections indicated: Elevation of energy line at
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
Elevation of energy at Elevation of energy at Elevation of energy at
15
7. Sketch the hydraulic and energy grid lines for figure below ( H=10m) H=10m)
Friction losses are
try
try
. Minor losses are
the hydraulic and energy grade lines are sketched in
figure below [further checking (not shown) of the
assumed value of f 1 and f 2 are acceptable]
R eynolds eynolds
number indicates that the
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
8.
Determine
16
the slope of the hydraulic grade line for flow of the atmospheric air
through a rectangular
21-in
by 7-in in galvanized iron conduit ( V=25 fps)
Slope of the hydraulic grade line
From figure of R eynolds eynolds number. Slope of the hydraulic grade line
9.
What
size square conduit is needed to convey 375 L/s of water at 15
of the hydraulic grade line of 0.002 ? Let d=side of conduit
=0.022. Assume f =0.0
From figure of R eynolds eynolds number
0
C
with a slope
Tugas Mekanika Fluida pengganti absensi Mufti Ghazali 060045
17
10. Neglecting minor losses other than valve, sketch the hydraulic grade lines for figure below. The globe valve has a loss coefficient of K =4.5. =4.5.
Try f =0.013. =0.013.
The hydraulic grade line is sketched in figure below. [further checking (not shown)
of the
eynolds R eynolds
number indicates that the assumed value of f is acceptable.]
