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7/29/2019 Note Cc303 - Fluid Pressure Politeknik
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BY: MYZATUL BINTI MANSOR
JKA, PTSB
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Hydrostatics is the study of pressures throughout a fluid atrest and the pressure forces on finite surfaces.
As the fluid is at rest, there are no shear stresses in it.
Hence the pressure at a point on a plane surface always
acts normal to the surface, and all forces are independent
of viscosity.
The pressure variation is due only to the weight of the fluid.
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Pressure is the force per unit area, where the force is
perpendicular to the area
Acts perpendicular to ALL surfaces
(like a Normal force)
Pressure unit:
o Pascal ( 1 Pa = 1 N/m2)
P=A m2Nm
-2
(Pa)
NF
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A liquid is subjected to pressure due to its own weight,
this pressure increases as the depth of the liquid
increases.
Depends on depth
P = gh
o = density of fluid
o g = gravity
o h = depth beneath the water
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Unit Definition or
Relationship
1 pascal (Pa) 1 kg m-1 s-2
1 bar 1 x 105 Pa
1 atmosphere (atm) 101,325 Pa
1 torr 1 / 760 atm
760 mm Hg 1 atm
14.696 pounds per
sq. in. (psi)
1 atm
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Example 1
Find the pressure represented by a column of
i. 10 cm of water
ii. 5 cm of oil of specific gravity 0.75iii. 2 cm of mercury
Solution:P = gh
i. For water column : P = 1000 x 9.81 x 0.1 = 981 N/m2
ii. For the oil column: P = 0.75 x1000 x 9.81 x0.05=367.88 N/m2iii. For the mercury column: P = 13.6 x1000x9.81x0.02
= 2668.32 N/m2
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ABSOLUTE PRESSURE
is defined as the pressure which is measured with
reference to absolute vacuum pressure
GAUGE PRESSUREis defined as the pressure which is measured with the help
of a pressure measuring instrument, in which the atmospheric
pressure is taken a datum. The atmospheric pressure on the
scale is marked as zero.
VACUUM PRESSURE
is defined as the pressure below the atmospheric pressure
(negative Gauge Pressure)
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P abs = Patm + Pgage
Note:
i) The Patm at sea level at 15C= 101.3 kPa
ii) The atmospheric pressure
head = 760 mm of mercury
or 10.33 m of water
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EXAMPLE 2:
Express a pressure of 155 kPa (gage) as an absolute
pressure. The local atmospheric pressure is 98 kPa(abs).
Solution:
P abs = 98 kPa+ 155 kPa = 253 kPa
EXAMPLE 3:
Express a pressure of 225 kPa (abs) as a gage pressure. The
local atmospheric pressure is 101 kPa(abs).
P abs = Patm + Pgage
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EXAMPLE 4:
Calculate the change in water pressure from the surface to a
depth of 5m.
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EXAMPLE 5:
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For a liquid, usually the position is measured as
distance from the free surface, or depth h, which is
positive downward as illustrated in Fig. 2.3. Hence,
p2p1 = g(h2h1) = (h2h1)
p = g h = h Note:P abs = Patm + PgageP abs = Patm + PgageAt free surface, Patm = 0
P abs = 0+ PgageP abs = Pgage
So;
P = Po + gh
P = Po + h
P = h
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Example 6:
A 6 m deep tank contains 4 m of water and 2 m of oil of
relative density 0.88. Determine the pressure at bottom of the
tank.
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Solution:At top tank surface :P1 = 0 kPa ( Patm)At the oil water interface :P2 = P1 + pressure due to 2 m of oil
= 0+ (0.88 x 1000x 9.81 x 2)
= 17265.6 N/m2
At the bottom tank :P3 = P2 + pressure due to 4 m of water
= 17265.6 + ( 1000 x 9.81 x 4)
=56505.6 N/m2 = 56.506 kN/m2
FORMULA:
P = Po + gh
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Example 7:
An open tank contains water to a depth 2.5 m and an oil of
specific gravity 1.25 to a depth of 1.5m.
(a) Draw the pressure distribution diagram acting on the tank
wall
(b) Determine the pressure
i. At the water surface
ii. At the oil-water interfaceiii.At a depth of 3.5 m below the free surface
iv.At the bottom of the tank
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Barometer
Piezometer
U tube manometer
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A barometer is used to measure
the pressure of the atmosphere.
The simplest type of barometer
consists of a column of fluid (mercury).
P2 - P1 = gh
Pa = gh
Patmalso expressed as mm of mercury = h
At sea level, Patm = 101.3 kPa, mercury = 133.1 kN/m3,
barometric height, h = 761 mm Hg.
If water used as barometric fluid, barometric height h = 10.36 m.
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The piezometer is used for measuring gauge pressures. One
end of this piezometer is connected to the point where
pressure is to be measured and other end is open to the
atmosphere. The rise of liquid gives the pressure head at
that point.
If at a point A, the height of liquid (water) is h in piezometer
tube, then pressure at A;
PA= g h
Fig 2.1:
Piezometer
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Manometer are defined as devices used for measuring the
pressure at a point in a fluid by balancing the column of
fluid by the same or another column of the fluid. It
classified as:
(a) Simple manometers
(b) Differential manometers
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This device consists of a glass tube bent in U-shape, one
end of which is connected to a point at which pressure is to
be measured and other end remains open to the
atmosphere as shown in Figure 2.1
Positive pressure Negative pressure
(vacuum pressure)
Figure 2.1
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This device is used to measure the difference in pressure
between two points in a pipe, or in two different pipes.
In its simplest form a differential manometer consists of a
U-tube, containing a heavy liquid, whose two ends are
connected to a points, whose difference of pressures is
required to be find out.
The most commonly used :
i. U-tube differential manometer
ii. Inversed U-tube differentia manometer
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(a) U-tube differential manometer
=
+ = + +
+
1
+ =
+
2
+
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(a) Inverted U-tube differential manometer
=
= 1 = 2
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