This document discusses different types of manometers used to measure pressure, including mercury barometers, U-tube manometers, inclined-tube manometers, and differential manometers. It defines key terms like absolute pressure and gauge pressure. Different manometers are used to measure pressure in various engineering applications like HVAC systems, construction, and measuring blood pressure. The document also discusses units of measurement for pressure and viscosity.

1. Dr. Eng. Ezzat El-Sayed G. Saleh
Civil Engineering Dept.
Minia University
Lec (2-3)
Fluid Statics ”Manometers”

3. A Life ruled by time, a
life powered by new
opportunities

4. Pressure
Pressure: is defined as the amount of force exerted
on a unit area of a substance. This can be stated by
the equation:
A
F
P 

5. Direction of Fluid Pressure on
Boundaries
Closed Duct
Pipe
Dam

6. Mercury Barometer

7. Barometer
Apparatus used to measure pressure; derived from the Greek “baros”
meaning, “weight”. Created by Evangelista Torricelli in 1646 who
inverted a tube filled with mercury (Hg) into a dish until the force of the
Hg inside the tube balanced the force of the atmosphere on the surface
of the liquid outside the tube.

8. The two points “o”, and “a” are in the same
elevation, then

Po = Pvap. + mer. g y
Po = Pa = Patm
Patm = mer. g y
Pvap. Can be neglected

9. Comparison between Absolute and Gage Pressures
Absolute Zero
Pressure
Absolute
Pressure (2)
Absolute
Pressure (1)


Vacuum or Negative
gage pressure (2)
gage
pressure (1)
Atmospheric
Pressure

10. Absolute and Gage Pressure
 A simple equation relates the two pressure measuring
systems:
where
Pabs Absolute pressure
Pgage Gage pressure
Patm Atmospheric pressure
.
P
P
P atm
gage
abs 


11.  A perfect vacuum is the lowest possible pressure.
Therefore, an absolute pressure will always be positive.
 A gage pressure above atmospheric pressure is
positive.
 A gage pressure below atmospheric pressure is
negative, sometimes called vacuum.
 Gage pressure will be indicated in the units of Pa (gage)
or psi (g).

12.  Absolute pressure will be indicated in the units of Pa
(abs) or p s i(a).
 At sea level, the standard atmospheric pressure is
101.3 kpa (abs), or 14.70 psia.
 Unless the prevailing atmosphere pressure is given,
we will assume it to be
101 kpa(abs), or 14.7 psi.

14. Gage pressure: is commonly measured by a Bourdon gage.
Difference in pressure is measured by a manometers.
Local atmospheric pressure: (i.e. the absolute pressure of the
atmosphere at a place) is measured by a mercury barometer.
The local atmospheric pressure varies with the elevation above mean
see level and local meteorological conditions.
For engineering application, a standard atmospheric pressure at
mean sea level at 15oC is often used. The value of this standard
atmospheric pressure (called 1 atmosphere) is:
1 atm. = 760 mm of mercury =10.34 m of water
= 101.33 KPa = 101.33 m bar

15. A manometer is one of the earliest and simplest devices used
for measurement of gauge pressure and differential pressures.
Manometer has myriad uses in different fields. (
‫عدد‬
‫ال‬
‫حيىص‬
‫من‬
‫تخدامات‬‫الاس‬
)
 Used in the maintenance of heating, ventilation, and air
conditioning (HVAC) systems, low pressure pneumatic
(
‫ايئ‬‫و‬‫ه‬
) or gas systems.
 Construction of bridges, installing swimming pools and other
engineering applications.
 Climate forecasting.
 Clinical applications like measuring blood pressure and in
physiotherapy.
 Piezometers are used to measure the pressure in pipes where
the liquid is in motion.

16. Manometers

17. Piezometer
As shown in the figure, one end of the piezometer is open to
atmospheric pressure, and the other end is connected to the
point A, where pressure is to be measured.

19. Two photos showing how to measure the head in a gated pipe system.
The head is the distance between the water level in the tube and the
center of the pipe.

21. It consists of a glass tube bent
like the letter 'U'. In this type of
manometer, balancing a column
of liquid is done by another
column of same or other liquid.
One end of the U-tube is attached
to the point where pressure is to
be measured, while the other end
is open to atmospheric pressure.
U-Tube Manometer

22. U- tube- Manometer

24. 2
m
atm
1
w
water h
g
P
h
g
P 




B
A P
P 
Since the pressures
at equal elevations
in a continuous
mass of fluid at rest
must be the same,
)
gage
0
P
(
h
g
h
g
P .
atm
1
w
2
m
water 





A U-tube Manometer

25. PA= -ve PA= +ve
x
.
g
y
.
g
P
P
P m
A
A
Q
P 




 x
.
g
y
.
g
P
P
P m
A
A
Q
P 





A U-tube Manometer for Measurements of
Positive and Negative Pressures
The indicated Liquid B, in this case, is mercury

26. A U-tube Manometer for Measurements of
Positive and Negative Pressures
P1= P2
PA+ L g hL+ I g hi = Patm 
PA = + ve
PA = - ve
 Patm
 Patm
P1=P2
 PA+ L g (hL+ hi) = Patm+  ig hi

27. Inverted U-tube Differential Manometer
U- tube Differential Manometer

28. Digital Manometer
A digital manometer uses a microprocessor and pressure
transducer to sense slight changes in pressure. It gives
the pressure readout on a digital screen. It measures
differential pressure across two inputs. An analog/digital
output in proportion to the instantaneous pressure can be
obtained.
Digital manometers report positive, negative, or
differential measurements between pressures.

29. A Differential Manometer is connected to a pipe at two
Points to measure the pressure difference
P3 = P4 & P1 +L g (h + hi ) = P2 + L g ((Z2 – Z1) + h ) + i
g hi

30. The well-type or cistern
manometer, is similar to a U-tube
manometer but one half of the
tube is made very large so that it
forms a well.
The change in the level of the
well as the measured pressure
varies is negligible. Therefore,
the liquid level in only one tube
has to be measured, which
makes the instrument much
easier to use than the U-tube
manometer.
Well - Type
Manometer

33. A Differential Manometer is connected to a pipe at
two points to measure the pressure difference
P1 = P2 + L g { h + h (d/D)2 }

34. 
l
PA = i g (l sin )
Analysis of Inclined-Tube Manometer:
An Inclined Differential Manometer is connected to a pipe at two points
to measure the pressure difference.

35.  The fact that the shear stress in the fluid is directly
proportional to the velocity gradient can be stated
mathematically as











dy
dV
where the constant of proportionality µ (the Greek
letter eta) is called the dynamic viscosity of the fluid.
……………….. (1)
Dynamic Viscosity

36.  The definition of dynamic viscosity can be derived by
solving for µ
 






 


dy
dV
The units of µ can be derived by substituting the
SI units into Eq. (2) as follows
……………….. (2)
2
2
m
S
.
N
s
m
m
m
N




The dimensions of force multiplied by time divided by
length squared are evident.
Units of Dynamic Viscosity

37. International System  N.s / m2, Pa.s, or kg
/(m.s)
B.G System  Ib.s / ft2 or Slug/ (ft.s)
c.g.s System Poise = dyne.s /cm2 =g / (cm.s) = 0.1
Pa.s
Dynamic Viscosity Units in the three most widely used systems

38.  Because Pa is another name of N / m2
 
s
.
Pa


In terms of kg rather than N
……………….. (3)
s
.
m
kg
m
s
s
m
.
kg
m
s
N 2
2
2






Units of Dynamic Viscosity

41. 41#
Any Questions???

43. h
h
g
P 

A
h
g
A
P
F 



 h
A
I
h
h
cg
cp



Forces on a Sluice Gate
h

44. Radial Gate

47. This propeller meter is installed inside a pipe section.

49. Siphon