This document discusses several topics related to fluid mechanics including: 1. Definitions of specific gravity, density, and atmospheric pressure. 2. Explanations of absolute and gauge pressure. 3. Descriptions of viscosity, surface tension, manometers, and different types of fluid flow. 4. Explanations of the equation of continuity, Bernoulli's equation, and their applications. 5. Discussions of venturi meters, orifices, pumps, hydroelectric power plants, and pump-storage systems.

2. FLUID MECHANICS
3
m
kg
V
m
=ρ
kg
m
m
V
=
3
υ
3
m
KN
1000
g
1000V
mg
V
W
=
ρ
==γ

3. Its specific gravity (relative density) is equal to the ratio
of its density to that of water at standard temperature and pressure.
W
=
γ
γL
W
L
L
ρ
ρ
=S
Its specific gravity (relative density) is equal to the ratio
of its density to that of either air or hydrogen at some specified
temperature and pressure.
ah
G
γ
γ
=
ah
G
G
ρ
ρ
=S
where: At standard
condition
W = 1000 kg/m3
W = 9.81 KN/m3

4. Atmospheric pressure: The pressure exerted by the
atmosphere.
At sea level
condition:
Pa = 101.325 KPa
= .101325 Mpa
= 1.01325Bar
= 760 mm Hg
= 10.33 m H2O
= 1.133 kg/cm2
= 14.7 psi
= 29.921 in Hg
= 33.878 ft H2O
Absolute and Gage Pressure
Absolute Pressure: is the pressure measured referred to absolute zero
and using absolute zero as the base.
Gage Pressure: is the pressure measured referred to atmospheric
pressure, and using atmospheric pressure as the base

5. Atmospheric Pressure
 Atmospheric pressure is normally about
100,000 Pa
 Differences in atmospheric pressure
cause winds to blow
 Low atmospheric pressure inside a
hurricane’s eye contributes to the
severe winds and the development of
the storm surge

6. x dx
v+dv
v
moving plate
Fixed plate
v
S dv/dx
S = (dv/dx)
S = (v/x)
= S/(v/x)
where:
- absolute or dynamic
viscosity
in Pa-sec
S - shearing stress in Pascal
v - velocity in m/sec
x -distance in meters

7. r h
Where:
- surface tension, N/m
- specific weight of liquid, N/m3
r – radius, m
h – capillary rise, m
C
0 0.0756
10 0.0742
20 0.0728
30 0.0712
40 0.0696
60 0.0662
80 0.0626
100 0.0589
Surface Tension of Water
r
cos2
h
γ
θσ

8. MANOMETERS
Manometer is an instrument used in measuring gage pressure in length of
some liquid
column.
 Open Type Manometer : It has an atmospheric surface and is capable
in measuring
gage pressure.
 Differential Type Manometer : It has no atmospheric surface and is
capable in
measuring differences of pressure.
Pressure Head:
where:
p - pressure in KPa
- specific weight of a fluid,
KN/m3
h - pressure head in meters of
fluid
h
P
γ

9. In steady flow the velocity of the fluid particles at any point is constant
as time passes.
Unsteady flow exists whenever the velocity of the fluid particles at a
point changes as time passes.
Turbulent flow is an extreme kind of unsteady flow in which the velocity
of the fluid particles at a point change erratically in both magnitude and
direction.
Types of flowing fluids:

10. More types of fluid flow
 Fluid flow can be compressible or
incompressible.
 Most liquids are nearly incompressible.
 Fluid flow can be viscous or
nonviscous.

11. When the flow is steady, streamlines are often used to represent
the trajectories of the fluid particles.

12. 222
2
vA
t
m
111
1
vA
t
m
Vm
The Equation of Continuity

distance
tvA

13. 222111 vAvA
EQUATION OF CONTINUITY
The mass flow rate has the same value at every position along a
tube that has a single entry and a single exit for fluid flow.
SI Unit of Mass Flow Rate: kg/s

14. Open Type Manometer
Open
Manometer Fluid
Fluid A
Differential Type Manometer
Fluid B
Manometer Fluid
Fluid A

15. Determination of S using a U - Tube
x
y
Open Open
Fluid A
Fluid B
SAx = SBy

16. Energy and Head
Bernoullis Energy
equation:
Reference Datum (Datum Line)
1
2
z1
Z2
HL = U - Q

17.  BERNOULLI’S EQUATION
 In steady flow of a nonviscous,
incompressible fluid, the pressure, the
 fluid speed, and the elevation at two
points are related by:

18. 1. Without Energy head added or given up by the fluid (No
work done by
the system or on the system:
L2
2
22
t1
2
11
H+Z+
2g
v
+
γ
P
=h+Z+
2g
v
+
γ
P
L2
2
22
1
2
11
H+Z+
2g
v
+
γ
P
=Z+
2g
v
+
γ
P
h+H+Z+
2g
v
+
γ
P
=+Z+
2g
v
+
γ
P
L2
2
22
1
2
11
2. With Energy head added to the Fluid: (Work done on the system
3. With Energy head added given up by the Fluid: (Work done by the
Where:
P – pressure, KPa - specific weight,
KN/m3
v – velocity in m/sec g – gravitational
acceleration
Z – elevation, meters m/sec2
+ if above datum H – head loss, meters
- if below datum

19. Ventury Meter
A. Without considering Head loss
flowltheoreticaQ
vAvAQ
Z
g2
vP
Z
g2
vP
2211
2
2
22
1
2
11
γγ
Manometer
1
2
B. Considering Head loss
flowactual'Q
vAvA'Q
HZ
g2
vP
Z
g2
vP
2211
L2
2
22
1
2
11
γγ
Meter Coefficient
Q
'Q
C

20. Orifice: An orifice is an any opening with a closed perimeter
Without considering Head Loss
1
2
a
a
Vena Contractah
By applying Bernoulli's Energy theorem:
2
2
22
1
2
11
Z
g2
vP
Z
g2
vP
But P1 = P2 = Pa and v1is negligible, then
21
2
2
ZZ
g2
v
and from figure: Z1 - Z2 = h,
therefore
h
g2
v
2
2
gh2v2
Let v2 = vt
gh2vt
where:
vt - theoretical velocity, m/sec
h - head producing the flow, meters
g - gravitational acceleration, m/sec2

21. velocityltheoretica
velocityactual
v
C
t
v
v'
Cv
orificetheofarea
contractavena@jetofarea
Cc
A
a
Cc
dischargeltheoretica
dischargeactual
v
C
Q
Q'
Cd
vcd CCC
where:
v' - actual velocity
vt - theoretical velocity
a - area of jet at vena
contracta
A - area of orifice
Q' - actual flow
Q - theoretical flow
Cv - coefficient of velocity
Cc - coefficient of contraction
Cd - coefficient of discharge

22. Lower
Reservoir
Upper
Reservoir
Suction Gauge Discharge Gauge
Gate Valve
Gate
Valve

23. metersHZZ
2g
vvPP
H L12
2
1
2
212
t
γ
Q = Asvs = Advd m3/sec
WP = Q Ht KW
KW
60,000
TN2
BP
π

24. HYDRO ELECTRIC POWER PLANT
Headrace
Tailrace
Y – Gross Head
Penstock turbine
1
2

25. Headrace
Tailrace
Y – Gross Head
Penstock
ZB
1
2
Draft Tube
B
Generator
B – turbine inlet

26. Pump-Storage Hydroelectric power plant: During power generation the turbine-pump acts
as a turbine and
during off-peak period it acts as a pump, pumping water from the lower pool (tailrace)
back to the upper
pool (headrace).
Turbine-Pump

27. THANK YOU
!!!