Note Cc303 - Fluid Pressure Politeknik

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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Note Cc303 - Fluid Pressure Politeknik