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JJ309: Fluid Mechanics
2.0 Fluid Static
1. If a fluid is within a container then the depth of an object placed in that fluid can
be measured. The deeper the object is placed in the fluid, the more pressure it
experiences
The formula that gives the pressure, p on an object submerged in a fluid is:
p = ρgh
Where,
ρ (rho) - the density of the fluid,
g- the acceleration of gravity
h - the height of the fluid above the object
2. Example Problems:
a. A barometer shows the reading 750mm merkury. Determine;
i.
Atmosphere pressure in unit SI
ii.
The head of water for that pressure
(100 kN/m2,10.2m)
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JJ309: Fluid Mechanics
b. What is the pressure experienced at a point on the bottom of a swimming
pool 9 meters in depth? The density of water is 1.00 x 103
kg/m3.(88.3kN/m2)
Assume standard atmospheric conditions. Determine the pressure in kN/m2
for the pressure below:
i.
depth 6m below under free space water.
ii.
At the 9m under surface of oil with specific gravity 0.75.
(58.86kN/m2,66.22 kN/m2)
c.
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JJ309: Fluid Mechanics
d. Find the height of water column, h which is equivalent to the pressure , p of
20 N/m2 . Take into consideration specific weight of water , ω is 1000 kg/m2
x 9.81 m/s2
(2.03x10-3m)
e. A fluid in piezometer increased 1.5 m high from point A in a pipeline system .
What is the value of pressure in point A in N/m2 if the fluid is :
i. Mercury with specific gravity 13.6
ii. Salted water with specific gravity 1.24
A
(200.1240x103N/m2,18.24 x103N/m2)
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JJ309: Fluid Mechanics
f. Find the head, h of water corresponding to an intensity of pressure, p of 340 000
N/m2. Take into consideration that the mass density, ρ of water is 100kg/m3
(h=34.65m)
g. A Bourdon pressure gauge attached to a boiler located at sea level shows a
reading pressure 10 bar . If atmospheric pressure is 1.01 bar , determine :
i. The absolute pressure in kN/m2
ii. The pressure head of water , h
(1101 kN/m2, 112.2m)
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JJ309: Fluid Mechanics
3.
Pascal’s Law and Hyraulic Jack
i. State the Pascal’s Law
ii.
Describe hydraulic Jack
4. Example :
a. A force, F of 900 N is applied to the smaller cylinder of an hydraulic jack. The
area, a of a small piston is 22 cm2 and the area A of a larger piston is 250
cm2. What load, W can be lifted on the larger piston if :
i.
the pistons are at the same level.
ii.
the large piston is 0.8 m below the smaller piston.
Consider the mass density ρ of the liquid in the jack is 103 kg/m3
(10.227 kN,10.423kN)
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JJ309: Fluid Mechanics
b. Two cylinders with pistons are connected by a pipe containing water. Their
diameters are 75 mm and 600 mm respectively and the face of the smaller piston
is 6 m above the larger. What force on the smaller piston is required to maintain
a load of 3500 kg on the larger piston?(275.91 N)
c. A force, F of 650 N is applied to applied to a smaller cylinder of hydraulic jack.
The area of small piston is 15cm2 and area of the larger pispon is 150cm2. Mass
density of the liquid in the jack 103 kg/ m3 Sketh each situation below and
calculate the load if, (6500N, 6595.6N, 6441.14N)
i. The piston are the same level
ii. The large piston is 0.65 m below the smaller piston
iii. The small piston is 0.40m below the large piston
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JJ309: Fluid Mechanics
d. A diameter of big piston in hydraulic jack is three times bigger than the diameter
of small piston. The small diameter is 630 mm and is used to support a weight of
40 kN. Find the force which is needed to rise up the big piston 2 m above the
small piston. Given the specific gravity of oil is 0.85. (313.23kN)
e. A force , F = 500 N is applied to the smaller cylinder of hydraulic jack . The area,
a of a small piston is 20 cm2 while the area, A of a large piston is 200 cm2 . What
mass can be lifted on the larger piston.
(509.68 kg)
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JJ309: Fluid Mechanics
f. A hydraulic press has a diameter ratio between the two pistons of 8:1 . The
diameter of the larger piston is 600 mm and it is required to support a mass of
3500 kg . the press is filled with a hydraulic fluid of specific gravity 0.8 . Calculate
the force required on the smaller piston to provide the required force ;
i. When the two pistons are at same level
ii.
When the smaller piston is 2.6 m below the larger piston.
(536.48 N, 627.92 N)
g. A hydraulic jack has diameter cylinder 5 cm and 18 cm. A force has put on small
cylinder to lift the load 1100 kg at bigger cylinder. Determine force F for lift the
both cylinders.
(832.6N)
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JJ309: Fluid Mechanics
h. A area of big piston in hydraulic jack is three times bigger than the area of small
piston. The small diameter is 630 mm and is used to support a weight of 40 KN.
Find the force which is needed to rise up the big piston 2 m above the small
piston. Given the specific gravity of oil is 0.85 (104.4kN)
i. The diameter of plunger and ram of a hydraulic press are 30 mm and 200 mm
respectively. Find the weight lifted by the hydraulic press when the force applied
at the plunger is 400N and the difference level between plunger and ram is 0.5
m. Given ρ fluids is 1065 kg/m3 ( 17929.9N)
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JJ309: Fluid Mechanics
5. Concept of manometer
i.Manometer Simple
ii.Manometer U tube
iii.Manometer Differential
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JJ309: Fluid Mechanics
6.Example
a. Assume that Patm= 101.3 kN/m2 water flow in pipe and in merkuri in manometer
a= 1m h=0.4 m. Determine the absolute pressure. As figure a (38.1kPa)
Figure a
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JJ309: Fluid Mechanics
b. A U tube manometer is used to measure the pressure of oil (s= 0.8)
flowing in a pipeline as in figure b. Its right limb is open to the atmosphere
and the left limb is connected to the pipe. The centre of the pipe is 9 cm
below the level of mercury in the right limb. If the difference of mercury
level in the two limbs is 15 cm, determine the gauge pressure of the oil in
the pipe in KPa. (19.541 KPa)
9 cm
15 cm
s merkury 13.6
Fig. b
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JJ309: Fluid Mechanics
c. Determine absolute pressure at A if Patm = 101.3 kN/m2, h1=20cm,h2= 40 cm as
fig c (45.971kPa)
water
merkury
figure c.
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JJ309: Fluid Mechanics
d. For a gauge pressure in pipe is 5kN/m2, determine the specific gravity
of the liquid B in the figure given below. (6.54)
water
12cm
Liquid B
e. Find the level of h if P1 is absolute pressure 150kN/m2, ρm= 13.6 x103
kg/m2 and in pipe is water in fig. e. (0.401m)
500mm
h
Fig. e
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JJ309: Fluid Mechanics
f. One end of a manometer contain mercury is open to atmosphere, while
the other end of the tube is connected to pipe in which a fluid of specific
gravity 0.85 is flowing. Find the gauge pressure the fluid flowing in pipe.
(26.271kN/m2)
Fig.f
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JJ309: Fluid Mechanics
g.
A U tube manometer measures the pressure difference between two
points A and B in a fluid as shown in Figure d. The U tube contains
mercury. Calculate the difference in pressure at pipe A and B if h1 = 160
cm, h2 = 50 cm and h3 = 80 cm. The liquid at A and B is water ρ =
1000kg/m3 and the specific gravity of mercury is 13.6.1 (53955N/m2)
Figure g
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JJ309: Fluid Mechanics
h.
The figure e below shown a U tube manometer . The specific gravity of mercury is
13.6 . If the pressure difference between point B and A is 47 kN/m2 , h = 12cm
and a = 43 cm , determine the height of b .(3.71m)
water
a
b
merkury
Figure h
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JJ309: Fluid Mechanics
i. A manometer U tube is using to measure between A and B in pipe has water and in
manometer has mercury. Determine the differential pressure between pipe A and B, if
a =150 cm, b = 70 cm and c = 45 cm. Figure f (47.77kN/m2)
Figure i
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JJ309: Fluid Mechanics
j. Figure g shown U tube manometer. If the differential of pressure between X andY is
50KN/m2 , h=2m and a=0.85m determine b (0.4719m)
Figure j
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JJ309: Fluid Mechanics
s
k. Figure k shows a d
differential manometer connected at two points A nd B. At
r
d
2
A air pressure is 10
00kN/m . Find the abso
olute pressure at B
Figure k
(84.28kPa)
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JJ309: Fluid Mechanics
l. A U-tube manometer is connected to a closed tank containing air and water as
shown in Figure h. At the closed end of the manometer the absolute air
pressure is 140kPa. Determine the reading on the pressure gage for a
differential reading of 1.5-m on the manometer. Express your answer in gauge
pressure value. Assume standard atmospheric pressure and neglect the
weight of the air columns in the manometer. (64.5 kPa)
Figure l
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JJ309: Fluid Mechanics
m. A U-tube manometer contains oil, mercury, and water as shown in Figure i.
For the column heights indicated what is the pressure differential between
pipes A and B? (-15.1kPa )
Figure m
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JJ309: Fluid Mechanics
n.
A U-tube manometer is connected to a closed tank as shown in Figure j. The
air pressure in the tank is 120 Pa and the liquid in the tank is oil (γ = 12000
3
N/m ). The absolute pressure at point A is 20 kPa. Determine: (a) the depth of
oil, z, and (b) the differential reading, h, on the manometer. Patm = 101.3 kPa
(z = 1.66 m, h = 1.33 m )
Figure n
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JJ309: Fluid Mechanics
o. The inverted U-tube manometer of Figure k contains oil (SG = 0.9) and water as
shown. The pressure differential between pipes A and B, p − p , is −5 kPa. Determine
A
the differential reading, h. (0.46 mm )
Fig.o
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B
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JJ309: Fluid Mechanics
j.
In the figure below, fluid Q is water and fluid P is oil (specific gravity = 0.9). If h
= 69 cm and z = 23 cm, what is the difference in pressure in kN/m2 between A
and B?(-1.579kN/m2)
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JJ309: Fluid Mechanics
k. Figure m belows shows a u-tube manometer that used to measure the pressure
difference between pipe P and pipe Q that contains water. If the fluid in u-tube is
oil with specific gravity 0f 0.9, calculate the pressure difference between these
two pipes in kN/m3 . Given M =80 cm and
N = 25 cm.(1667.7 Pa)
Figure p
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JJ309: Fluid Mechanics
r. For the inclined-tube manometer of Figure n, the pressure in pipe A is 8 kPa. The
fluid in both pipes A and B is water, and the gage fluid in the manometer has a
specific gravity of 2.6. What is the pressure in pipe B corresponding to the
differential reading shown?(5.51kPa )
fig.r
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JJ309: Fluid Mechanics
2
s. A piston having a cross-sectional area of 0.07 m is located in a cylinder containing
water as shown in Figure o. An open U-tube manometer is connected to the cylinder
as shown. For h = 60 mm and h = 100 mm, what is the value of the applied force, P,
1
acting on the piston? The weight of the piston is negligible (892.7 N)
Fig. s
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JJ309: Fluid Mechanics
1. Pressure Measurement
Piezometer, Barometer
Bourdon gauge
Sketch important parts of bourdon gauge
Explain mechanism of a bourdon gauge
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JJ309: Fluid Mechanics
2. Buoyancy
Define Buoyancy Force
R1
R 1 = R2
ρ1 g1 v1 = ρ2 g2 v2
R2
Buoyancy is the upward force that an object feels from the water and when compared to
the weight of the object
Buoyant Force=Weight of Displaced Fluid
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JJ309: Fluid Mechanics
3. Example Question
a. A rectangular pontoon has a width B of 6 m, a length l of 12 m, and a draught D of
1.5 m in fresh water (density 1000 kg/m3). Calculate :
a) the weight of the pontoon
b) its draught in sea water (density 1025 kg/m3)
c) the load (in kiloNewtons) that can be supported by the pontoon in fresh
water if the maximum draught permissible is 2 m.
(1059.5kN, 1.46m, 14126kN,353.1kN)
b.
8 cm side cube weighing 4N is immersed in a liquid of relative density 0.8
contained in a rectangular tank of cross- sectional area 12cm x 12cm. If the tank
contained liquid to a height of 6.4 cm before the immersion determine the levels of
the bottom of the cube and the liquid surface. (x =0.063m)
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