fluid mechanics

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
!!!