Chapter 2 - Fluid Pressure Concept & Measurement
Chapter 2 - Fluid Pressure Concept & Measurement
Chapter 2 - Fluid Pressure Concept & Measurement
(DAC 21003)
CHAPTER 2
PRESSURE MEASUREMENT
TYPES OF PRESSURE
Atmospheric Pressure
Surface of the earth depends upon head of air above the surface.
At sea level (101.3 kN/m2) = 10.35 m of water or 760 mm of Hg
Vacuum
Pressure is zero (perfectly empty in space).
Gauge Pressure.
Measured above or below atmospheric pressure.
Absolute Pressure.
Pressure
Atmospheric Pressure
P = 0 k Pa Gauge or
P = 101 kPa Absolute
Absolute Pressure
Vacuum Pressure or
Negative Pressure Gauge
Absolute Zero Pressure
SOLUTION:
Given:-
Gauge pressure, Pgage = 60 kPa
Atmospheric pressure, Patm = 740 mmHg
Mercury specific gravity, S.gmercury = 13.6
SOLUTION .... Cont ‘
Known that,
Patm = mgh (m = mercury density)
Patm = (13.6)(1000)(9.81)(740/1000)
Hence,
Pabs = Pgage + Patm
Pabs = 60 + 98.73
Where:
F
P …………….. ( 2.1 )
A
F = Force (N)
A = Area (m2)
PASCAL LAW
P3 z
B
q
P1
x
A C
W
P2
P2 = P3 (iv)
From equation (ii) and (iv), it was found that;
P1 = P2 = P3
SOLUTION:
Given:-
Depth of water, h = 25 m
Specific weight of water, w = 9.81 kN/m3
Hence,
P = h
P = (9.81)(25)
P = 245.25 kN/m2
PRESSURE HEAD
Container
h
P h ............................ ( 2.2 )
where,
h = Fluid height in cylinder
= Specific weight
h
(specific weight = )
A B
Water 2.5 m
Mercury 0.4 m
SOLUTION:
Given:-
Patm = 101.3 kPa
Pabs = 231.3 kPa
Pm = (sgm)(ρw) (g)(h)
Pm= (13.56)(1000)(9.81)(0.4) = 53209.4 Pa
Known that,
sgolive = 1.4
PRESSURE MEASUREMENT
Device :-
i. Piezometer
ii. Manometer
iii. Bourdon Gauge
iv. Tansducer
PIEZOMETER
Example type of manometer.
To measure pressure in pipe.
Suitable for measuring moderate pressure of fluids.
Fluid in pipe is same in piezometer tube.
Tube diameter should at least 0.5 inch or 12 mm avoid
capillary error.
h h
P h
Pitot tube
2.1 m
B
4.8 m
ater
w
8m
A
6m
Datum
SOLUTION:
PA
hA
g
PA
6 4.8
(1000)(9.81)
PA 105948 Pa 105.95 kPa
PB
hA
g
PB
8 2.1
(1000)(9.81)
PB 99081 Pa 99.08 kPa
MANOMETER
Types of manometers :-
Differential Manometers
Inverted Manometers
SIMPLE U-TUBE MANOMETERS
PB
PA B
A
h1
h2
x x
Px-left = Px-right
where,
Px-left = PA + A gh2
A
h1
PA + A gh2 = B g(h1+h2) x
h2
x
PA = B g(h1+h2) - A gh2
EXAMPLE 2.5
Calculate pressure at A in kN/m2 if h1 = 50 cm,
h2 = 120 cm, A = 1000 kg/m3 and
B = 13560 kg/m3
w
(water) B
h1
A
h2
x x
m
(mercury)
SOLUTION:
Consider left and right side of manometers,
Px-left = Px-right
where,
Px left PA w gh 2
Px left PA (1000)(9.81)(0.12)
Px left PA 1177.2
PA 1177.2 0 22614.012
PA 21436.8 N/m2 21.44 kN/m2
DIFFERENTIAL MANOMETERS
A
B
Px-left = Px-right
where,
Px-left = PA + A gh2
hence,
Water
(s.g = 1.0) B
1.6 m
A
Mercury
h (s.g = 13.6)
x x
SOLUTION:
Consider left and right side of manometers,
Remenber:
Px-left = Px-right x
where, s.g x
w
Px left PA w g(h a h )
Px left PA (1000)(9.81)(h a h )
Px left PA 9810h a 9810h
Px right PB m gh w g(ha hb )
Px right PB s.g m . w gh w g(ha hb )
Px right PB (13.6)(1000)(9.81)(h ) (1000)(9.81)(ha 1.6)
Px right PB 133416h 9810ha 15696
SOLUTION .... Cont ‘
air
x x
h1
h2
PA
A
h3
PB
B
a
Px-left = Px-right
where,
Px-left = PA - a gh2 – air gh1 (neglect air)
h2
PA
h3
PA - PB = agh2 - ag (h3 + h1) A
PB
B
a
EXAMPLE 2.7
Figure below show inverted manometers used to
measure pressure inside a pipe. Find the pressure
difference of PA – PB.
Fluid X
(s.g = 0.9)
x x
0.25 m
1.625 m
0.5 m
A Water
(s.g = 1.0)
SOLUTION:
Consider left and right side of manometers,
Px-left = Px-right
where,
Px left PA w g(h a )
Px left PA (1000)(9.81)(1.625)
Px left PA 15941.25
Px right PB x gh b w gh c
Px right PB s.g x . w gh b w gh c
Px right PB (0.9)(1000)(9.81)(0.25) (1000)(9.81)(1.625 0.25 0.5)
Px right PB 2207.25 8583.75
Px right PB 10791
SOLUTION .... Cont ‘
PA 15941.25 PB 10791
PA PB 5150.25 kN/m2
BOURDON GAUGE
Commonly measure gauge pressures or vacuum.
A curved tube of elliptical cross section tend to straighten if
subjected to higher pressure.
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