There is a simplest explaination of fluid mechanics

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

2. 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. Torricelli used Mercury instead of Water

8. We use the “barometer” to
measure changes in atmospheric
pressure to help predict weather
changes.

10. 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.

11. 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

12. Comparison between Absolute and Gage Pressures

13. 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 


14.  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).

15.  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.

16. Manometers

17. 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.
 Used in the maintenance of heating, ventilation, and air
conditioning (HVAC) systems, low pressure pneumatic 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.

18. 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.

20. 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

22. 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

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 manometer, is similar
to a U- tube manometer but one half
of the tube is made very large so that
is 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

31. Difference between U- type and Well – type Manometer

32. Difference between “Raised well manometer” and
“Raised Well inclined 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 construction of a bourdon tube gauge, construction
elements are made of brass.

36.  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

37.  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

38. The Dynamic Viscosity Units in the three most widely used systems
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

39.  Because Pa is another name of N l 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

40. 40#
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41. h
h
g
P 

A
h
g
A
P
F 



 h
A
I
h
h
cg
cp



Forces on a Sluice Gate
h

42. Radial Gate

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