Fluid Mechanics
Dr Farid Khan
1
Analytical method for finding metacentric height
b/2
b/2
a
M
i
G
o
h
W
G
W
g
B
B
B1
f
FB
b
c
d
e
FB
w vol. of t he w edge hoi
1 b
ih length of ship
2 2
1 b b
tan L
2 2 2
Lb2
8
tan
2
Analytical method for finding metacent
Fluid Mechanics
Dr Farid Khan
1
Viscosity
Resistance to flow
Resistance to shear stresses
Viscosity is due to:
1. Cohesion between atoms/molecules, and
2. Interaction between atoms/molecules
Cohesion = Attraction force b/w similar atoms/molecules
Inter
Fluid Mechanics
Dr Farid Khan
1
Pascals Law
Statement: When a fluid is at rest, the pressure at a
point is same in all directions
Proof: P P2 P
1
3
Assume
Wedge shaped differential element of fluid
Thickness of this differential element is unity dz = 1
Fluid Mechanics
Dr Farid Khan
1
Barometer
Device used to measure atmospheric
pressure
Vacuum
Why we used mercury not water?
Patm @ mean sea level = 101.3 kN/m2
= 1.013 bar
= 760 mm of Hg
= 10.3 m of H2O
2
Barometer
Vacuum
Device used to measure atmospheri
Fluid Mechanics
Dr Farid Khan
1
Manometer
Used to measure pressure of fluids (liquids or gases)
in a reservoirs (tanks, pipes, pressure vessels)
Measuring liquid (manometer liquid) is used
Liquids with high density or specific weights are used
as measu
Fluid Mechanics
Dr Farid Khan
1
Single-tube Manometer
A y a h
ah
y
A
B
Sp. Gr. S1
h
y
Original level
P B ( y y ) 2 (h y ) 0
B
ah
ah
P 2 (h
) B( y
)
B
A
A
y
Sp. Gr. S2
2
Single-tube Manometer
ah
ah
P w S2 ( h
) w SB ( y
)
B
A
A
a
if A a t hen
0
A
B
P
Fluid Mechanics
Dr Farid Khan
1
Hydrostatic forces on surfaces
Hydrostatic force on:
- Horizontal plane
- Vertical plane
- Inclined plane
- Curved plane
2
Hydrostatic force on horizontal plane
A = Total area of plane surface
G = Centroid of plane
hG = de
Fluid Mechanics
Dr Farid Khan
1
Hydrostatic force on curved surface
Liquid above curved surface KL
O
O
dF hdA
dF dF cos
V
hdA cos
h
J
dFH dF sin
hdAsin
K
dF
L
dA
2
Hydrostatic force on curved surface
Vertical projection of area dA
dA dA sin
V
O
O
H
Fluid Mechanics
Dr Farid Khan
1
Bouyancy and floatation
Cruise Ships
Power boats
2
Bouyancy and floatation
Aircraft carrier
Submarine
3
Bouyancy and floatation
Why a needle or stone sinks while ship
(weighing thousands of tons) floats?
4
Bouyancy and floa
MtE-204
Fluid Mechanics
Dr Farid Khan
1
Dr. Farid Khan
Assistant Professor in UET Peshawar since 1997
B.Sc Mechanical Engineering 1997
M.Sc Mechanical Engineering Design 2005
PhD MicroElectroMechanical Systems (MEMS) 2011
[email protected]
2
Cours
Fluid Mechanics
Dr Farid Khan
1
Head Loses in pipes
Major loss
- Head loss due to friction
Minor losses
-Head loss due to sudden enlargement
-Head loss due to sudden contraction
-Head loss at the entry
-Head loss at the exit
-Head loss due to obstructio
Fluid Mechanics
Dr Farid Khan
1
Types of flow
Steady flow
Unsteady flow
Uniform flow
Non-Uniform flow
Laminar flow
Turbulent flow
2
Steady flow
A steady flow is one in which the characteristics (velocity, pressure
and temperature) may differ from point t
Fluid Mechanics
Dr Farid Khan
1
Eulers equation
Stream line
Applying Newtons second law
F m a
2
dS
on liquid differential element
along the stream line
P+(dP/ds)ds
P
1
dw = dSdA
Z
Datum line
dp
PdA P
ds dA dsdA cos dsdAat
ds
at= Tangential acceleration
2
Fluid Mechanics
Dr Farid Khan
1
Bernoullis equation
V2
z
constant
2g
p
p1
2
1
Bernoullis eq.
2
V
p2
V2
z1
z2
2g
2g
Assumptions made:
1.
The fluid is ideal and incompressible
2.
The flow is steady and continuous
3.
The flow is along steam line i.e. on
Fluid Mechanics
Dr Farid Khan
1
Pitot tube
Is used to measure the local
velocity of flowing liquid
h
Ps/
Po/
Vo
2
po
Tip
2
Vo
ps
Vs
zo
zs
2g
2g
po
2
Vo
ps
2g
Vo
2 gh
2
Vo
ps
po
h
2g
2
Pitot tube
Is used to measure the local
velocity of flowing liquid
Fluid Mechanics
Dr Farid Khan
1
Orifice meter
Is used for the measurement of discharge in pipes
Venacontracta (minimum area/dia of jet)
Flange
Orifice
Flow
d1
d
X
2
Orifice meter
d1
d
d2
X
3
Orifice meter
Is used for the measurement of discharge in pipe
Fluid Mechanics
Dr Farid Khan
1
Flow nozzle
Is used for the measurement of discharge in pipes
2
Flow nozzle
3
Flow nozzle
4
Flow nozzle
Is used for the measurement of discharge in pipes
5
Flow nozzle
2
p1
2
V
p
V
z1 1 2 z2 2
2g
2g
2
1
p1
2
V
p2 V2
2g
2
Fluid Mechanics
Dr Farid Khan
1
Notch
Is used for the measurement of discharge in tanks/reservoirs
An opening in one side of a tank or a reservoir, with the liquid level
below the top edge of the opening
The bottom edge, over which the liquid flows, is
Fluid Mechanics
Dr Farid Khan
1
Flow through pipes
Pipes uses?
2
Flow through pipes
Pipes are used for:
Transportation
- Oil
- Gas
- Water
- steam
Power transmission through pipes
3
Flow through pipes
Pipes
materials?
4
Flow through pipes
Pipe Materia