1. MECHANICAL ENGINEERING โ FLUIDMECHANICS
2
Pressure (P):
โข If F be the normal force acting on a surface of area A in contact with liquid,then
pressure exerted by liquid on this surface is: P =F / A
โข Units : N /m2 or Pascal (S.I.) and Dyne/cm2 (C.G.S.)
โข Dimension
:
[P] =
[F]
[A]
=
[MLT 2 ]
[L2 ]
=[ML-1T -2
]
โข Atmospheric pressure:Its value on the surface of the earth at sea level is nearly
1.01*10 5N/ m2 or Pascal in S.I. other practical units of pressure are atmosphere,
bar and torr (mm of Hg)
โข 1atm = 1.01 *10 5Pa = 1.01bar = 760 torr
โข Fluid Pressure at aPoint:
Density ( ฯ):
dp=
dF
dA
โข In a fluid, at a point, density ฯ is defined as: Mass/volume
โข In case of homogenous isotropic substance, it has no directional properties, so is
a scalar.
โข It has dimensions [ML-3] and S.I. unit kg/m3 while C.G.S. unit g/ccwith
1g / cc = 10 3kg / m 3
โข Density of body = Density of substance
โข Relative density or specific gravity which is defined
as:
RD
Densit
Density
of body
of water
Specific Weight ( w):
โข It is defined as the weight per unit volume.
โข Specific weight =
Weight
=
m.g
Volume Volume
Specific Gravity or Relative Density(s):
โข It is the ratio of specific weight of fluid to the specific weight of a standard fluid.
Standard fluid is water in case of liquid and H2 or air in case of gas.
Specific gravity=
๐ท๐๐๐ ๐๐ก๐ฆ ๐๐ ๐น๐๐ข๐๐
๐ท๐๐๐ ๐๐ก๐ฆ ๐๐ ๐ ๐ก๐๐๐๐๐๐ ๐น๐๐ข๐๐
or
๐พ
๐พ๐ค
or
๐
๐๐ค
Where, ๐พ Specific weight , and ๐
Density of water specific
2. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Specific Volume ( v):
โข Specific volume of liquid is defined as volume per unit mass. It is also defined as the
reciprocal of specific density.
โข Specific volume =1/Density
Newtonโs Law of viscosity
โข ๐ = ๐
๐๐ข
๐๐ฆ
Where ๐ = Shear Stress, ๐= Co-efficient of viscosity or absolute viscosity
๐๐ข
๐๐ฆ
= Rate of angular deformation or rate of change of shear strain
Dynamic Viscosity and kinematic viscosity
โข Dynamic Viscosity- Resistance offered by fluid to flow
โข Units are Ns/m2
or Kg/ms
โข 1 poise= 0.1 Ns/m2
โข Kinematic Viscosity =
๐ท๐ฆ๐๐๐๐๐ ๐๐๐ ๐๐๐ ๐๐ก๐ฆ(๐)
๐๐๐ ๐ ๐ท๐๐๐ ๐๐ก๐ฆ (๐)
โข 1 Stoke= c.m2
/s = 10-4
m2
/s
Bulk Modulus
โข Bulk modulus K=
dP
โdV
V
โข Compressibility (ฮฒ) =
1
K = โdV
VdP
= dฯ
ฯdP
Where K= Bulk modulus of elasticity, ฯ= Density and V= Specific volume
Surface Tension
โข The cohesive forces between liquid molecules are responsible for the phenomenon known as surface
tension
โข Unit N/m
โข Pressure inside drop P =
4ฯ
d
โข Pressure inside bubble P =
8ฯ
d
โข Pressure inside jet P =
2ฯ
d
Where d= Diameter of drop, P= Gauge pressure and ฯ= Surface tension
3. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Capillary Action
โข Height of water in capillary tube- ๐ =
๐๐๐ช๐๐๐ฝ
๐๐๐
โ=rise in capillary ๐= Surface tension of water
D= Diameter of tube
๐=Angle of contact between liquid and material
๐=<90o for water and glass and >90o for mercury and glass
Absolute Pressure
Hydrostatic law
๐ ๐ท
๐ ๐
= ๐๐
๐๐ก๐๐ซ๐ ๐ = ๐๐๐ง๐ฌ๐ข๐ญ๐ฒ ๐๐ง๐ ๐ = ๐๐๐๐๐ฅ๐๐ซ๐๐ญ๐ข๐จ๐ง ๐๐ฎ๐ ๐ญ๐จ ๐ ๐ซ๐๐ฏ๐ข๐ญ๐ฒ
Manometers
โข Piezometers
A
p gh
๏ฒ
=
abs atm gauge
abs atm vac
P P P
P P P
= +
= โ
4. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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โข U-Tube Manometer
1 1 2 2
A m B
P s gh s gh h gs P
+ โ โ =
Where s1,s2 and sm are density of fluids in
manometer
Hydrostatic Forces on submerged bodies
โข Vertical Planes
Total Force ๐ = ๐๐ ๐๐ก
ฬ
โข Center of Pressure
๐โ
=
๐ฐ๐
๐จ๐
ฬ
+ ๐
ฬ
โข Horizontal Surface
Total Force ๐ = ๐๐ ๐๐ก
ฬ
โข Center of Pressure
๐โ
= ๐
ฬ
5. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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โข Forces on Inclined surface .
total C G
F gh A
๏ฒ
= ๏ด
โข Centre of pressure
๐โ
=
๐ฐ๐๐บ๐๐๐
๐ฝ
๐จ๐๐ช.๐ฎ
+ ๐๐ช.๐ฎ
โข Curved Surface โ
2 2
tan
R h v
v
h
F F F
F
F
๏ฑ
= +
=
Vertical component of force Fv
Weight of the liquid supported by
the curved surface over it up to the
free liquid surface
Horizontal component of force
Fh
Total pressure force on the vertical
projected area of the curved
surface
Completely submerged and floating at the interface of two liquids
1 1 2 2
B
F gV gV
๏ฒ ๏ฒ
= +
Where 1
V and 2
V are volumes
Body floating in a liquid
2
2
B
F V
๏ท
=
6. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Principal of floatation
โข If the body weight is equal to the buoyant force, the body will float
B
Mg W F gV
๏ฒ
= = =
Condition of stability
โข Fully submerged body
Stable Equilibrium: G below B
Unstable Equilibrium: G above B
Neutral Equilibrium: G coincides with B
โข Floating body
Stable Equilibrium: M above G
Unstable Equilibrium: M below G
Neutral Equilibrium: M coincides with G
Metacentric height (GM)
โข Metacentre radius (BM)
I
BM
V
=
โข Metacentric Height (GM)
GM BM BG
I
GM BG
V
= โ
= โ
7. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Where I= Second moment area about body surface vertical axis
V = Volume of water displaced
Time period of transverse oscillation of floating body
โข 2 G
K
T
gGM
๏ฐ
= KG= Least radius of gyration, GM=Meta- Centric Height
Continuity Equation
โข ฯ1A1V1 = ฯ2A2V2
Where A,V are cross-section area of the flow and Velocity of flow respectively
For incompressible flow ฯ=constant so
A1V1 = A2V2
Generalized differential Continuity Equation
โข
๐๐
๐๐ก
+
๐(๐๐ข)
๐๐ฅ
+
๐(๐๐ฃ)
๐๐ฆ
+
๐(๐๐ค)
๐๐ง
= 0
Where u,v and w are the velocities in x,y,and z direction respectively
For steady incompressible two dimensional flow, ฯ=constant and
๐๐
๐๐ก
= 0
๐๐ข
๐๐ฅ
+
๐๐ฃ
๐๐ฆ
= 0
Velocity and Acceleration of Fluid Particle
โข Velo = ui
โ + vj
โ + wk
โโ
โข Acceleration in X-direction ๐๐ฅ =
๐๐ข
๐๐ก
= ๐ข
๐๐ข
๐๐ฅ
+ ๐ฃ
๐๐ข
๐๐ฆ
+ ๐ค
๐๐ข
๐๐ง
+
๐๐ข
๐๐ก
Acceleration in Y-direction ๐๐ฆ =
๐๐ฃ
๐๐ก
= ๐ข
๐๐ฃ
๐๐ฅ
+ ๐ฃ
๐๐ฃ
๐๐ฆ
+ ๐ค
๐๐ฃ
๐๐ง
+
๐๐ฃ
๐๐ก
Acceleration in Y-direction ๐๐ง =
๐๐ค
๐๐ก
= ๐ข
๐๐ค
๐๐ฅ
+ ๐ฃ
๐๐ค
๐๐ฆ
+ ๐ค
๐๐ค
๐๐ง
+
๐๐ค
๐๐ก
For steady flow
๐๐ข
๐๐ก
=
๐๐ฃ
๐๐ก
=
๐๐ค
๐๐ก
= 0
๐ = โ๐๐ฅ
2 + ๐๐ฆ
2 + ๐๐ค
2
Note- Local Acceleration due to increase in rate of velocity with respect to time at a point and
convective acceleration due to rate of change of position (
๐๐ข
๐๐ก
=
๐๐ฃ
๐๐ก
=
๐๐ค
๐๐ก
= 0)
8. MECHANICAL ENGINEERING โ FLUIDMECHANICS
9
Rotational fluid
ฯz =
1
2
(
โV
โx
โ
โU
โy
)
Vortex flow
โข Free Vortex V*r=Constant
โข Forced Vortex V=r ฯ and ๐ป =
๐2๐2
2๐
Velocity potential
โข If โ is the velocity function, then
๐ข = โ
๐โ
๐๐ฅ
, v=โ
๐โ
๐๐ฆ
, ๐ค = โ
๐โ
๐๐ง
โข Polar direction
๐ข๐ = โ
๐โ
๐๐
,๐ข๐ = โ
1
๐
๐โ
๐๐
Stream Function
โข If ๏น is the Stream function , then
๐ข = โ
๐๏น
๐๐ฆ
, v=
๐๏น
๐๐ฅ
Equipotential line
โข Condition for Equipotential line ๐โ = 0
So
๐๐ฆ
๐๐ฅ
= โ
๐ข
๐ฃ
Line of constant stream function
โข Condition for constant stream function 0
d๏น =
๐๐ฆ
๐๐ฅ
=
๐ฃ
๐ข
Relation between stream function and velocity potential function
โข
โโ
โx
=
โ๏น
โy
,
โโ
โy
= โ
โ๏น
โx
Equation of motion
โข ๐น
๐ฅ = ๐น
๐ + ๐น๐ + ๐น
๐พ + ๐น๐ก + ๐น๐ถ
Where,
Gravity force ๐น
๐
9. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Pressure force ๐น๐
Viscosity force ๐น
๐พ
Turbulance force ๐น๐ก
Compressibility force ๐น๐ถ
โข When Compressibility force ๐น๐ถ is negligible
๐น
๐ฅ = ๐น
๐ + ๐น๐ + ๐น
๐พ + ๐น๐ก is Reynoldโs equation of motion
โข ๐น๐ก is negligible
๐น
๐ฅ = ๐น
๐ + ๐น๐ + ๐น
๐พ is Navier- Stokes equation of motion
โข When flow is assumed to be ideal, ๐น
๐พ = 0
๐น
๐ฅ = ๐น
๐ + ๐น๐ is Eulerโs equation of motion
Eulerโs equation of motion
โข
๐๐
๐
+ ๐๐๐ง + ๐ฃ๐๐ฃ = 0
Bernoulliโs equation
โข ๐ + ๐๐๐ง +
๐๐2
2
= 0
โข
P
ฯg
+ z +
V2
2g
= 0
Where,
P
ฯg
= Pressure head
Z = Potential head
V2
2g
= Kinetic head
Application of Bernoulliโs theorem
โข Venturimeter
Qact = Cd
a1a2โ2gh
โa1
2 โ a2
2
Where,
Cd=Co-efficient of venturimeter which is <1
a1, a2= Area of cross section, h= Head
โข Orifice meter
Vena contracta ๐ถ๐ =
Area of vena contracta
Area of orific
10. MECHANICAL ENGINEERING โ FLUIDMECHANICS
11
Discharge ๐ถ๐ = ๐ถ๐
โ1โ(
ao
a1
)
2
โ1โ(
ao
a1
)
2
๐๐
2
where,
a1= area of cross section before vena contracta
ao=Area of orifice
โข Pitot Tube
๐๐๐๐ญ = ๐๐ฏโ๐๐ (๐๐ญ๐๐ ๐ง๐๐ญ๐ข๐จ๐ง ๐ก๐๐๐ โ ๐๐ญ๐๐ญ๐ข๐ ๐ก๐๐๐)
Where ๐๐ฏ is co-efficient of velocity
Value of ๐๐ given by differential
โข ๐๐ = ๐(
๐บ๐
๐บ
โ ๐) where ๐บ๐ > ๐บ
โข ๐๐ = ๐(๐ โ
๐บ๐
๐บ
) where S > ๐บ๐
๐บ๐, ๐บ are realtive density of
manometric fluid and fluid flowing
Momentum Equation
โข F.dt= d(mv) known as impulse- momentum equation
Force exerted on flowing fluid by a bend pipe
โข If ๐1 = ๐2 then net force acting on a fluid
โข ๐1๐ด1 โ ๐1๐ด1๐ถ๐๐ ๐ โ ๐น
๐ฅ =
Change in velocity in horizontal โ mass of fluid
โข Fy = ฯQ(change in velocity vertically) โ P2A2Sinฮธ
โข Resultant force = โFx
๐ + Fx
๐
Viscous flow
โข To be viscous flow Reynold number should be less than 2000
๐ ๐ =
๐ผ๐๐๐๐ก๐๐ ๐๐๐๐๐
๐๐๐ ๐๐๐ข๐ ๐๐๐๐๐
=
๐๐๐ท
๐
<2000
Where, v=velocity of flow, ๐= viscosity of flow, D= Diameter of piper and ๐= Density of fluid
โข Flow of viscous fluid through circular pipe
11. MECHANICAL ENGINEERING โ FLUIDMECHANICS
12
โข Velocity u =
1
4ฮผ
(โ
โP
โx
) [R2
โ r2]
โข Shear stress ๐ = (โ
โP
โx
)
r
2
โข Ratio of maximum to average velocity
Maximum Velocity
Average Velocity
= 2
โข Drop of pressure in given length
P1 โ P2
ฯg
= hf =
32u
ฬ ฮผL
ฯgD2
Also called Hagen Poiseuille Equation
Here u
ฬ =average velocity, P1, P2 = Pressure at two different points in the pipe
โข Flow of viscous fluid between two parallel plates
โข Velocity u =
1
2ฮผ
(โ
โP
โx
) [ty โ y2]
โข Shear Stress ๐ =
1
2
(โ
โP
โx
) [t โ 2y]
โข Ratio of maximum to average velocity
Maximum Velocity
Average Velocity
=
3
2
โข Drop of pressure in given length
P1โP2
ฯg
= hf =
12u
ฬ ฮผL
ฯgt2
Kinetic energy correction factor
ฮฑ =
K.E
sec
based on actual velocity
K.E
sec
based on average velocity
For laminar flow ฮฑ=2 and for turbulent flow ฮฑ=1.33
Momentum correction factor
ฮฒ =
Momentum
sec
based on actual velocity
Momentum
sec
based on average velocity
For laminar flow ฮฒ=1.33 and for turbulent flow ฮฒ=1.20
Loss of head due to friction in viscous flow
hf =
4flV2
2Dg
Where t is the thickness
12. MECHANICAL ENGINEERING โ FLUIDMECHANICS
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Where f= friction co-efficient
For laminar flow ๐ =
16
๐ ๐
where Re is Reynoldโs number
For turbulent flow, coefficient of friction f =
0.079
Re
1
4
Chezyโs Formula
V = Cโmi , C = Chezy Constant = โ
ฯg
f
i = Loss of head per unit length of pipe=
โ๐
๐ฟ
(hydraulic slope tan ฮธ)
m = Hydraulic mean depth
Mean velocity of flow m =
Area (A)
Wetted Perimeter(P)
Minor losses in pipe
โข Loss of head due to sudden enlargement
he =
(V1 โ V1)2
2g
โข Loss of head due to sudden contraction
he =
V2
2g
(
1
Cc
โ 1)
2
or he = 0.5
V2
2g
when Cc=0.65
โข Loss of head due to entrance
๐๐๐๐๐๐๐๐๐ = 0.5
V2
2g
โข Loss due to exit pipe
=
๐ฝ๐
๐๐
โข Loss due to obstruction
=
V2
2g
(
A
Cc(Aโa)
โ 1)
2
โข Losses due to bend
= K
๐ฝ๐
๐๐
where k depends on bending of pipe
Hydraulic gradient and Total Energy line
โข H.G.L=Pressure head+datum head
โข T.G.L= Pressure head+datum head+Kinetic Head
13. MECHANICAL ENGINEERING โ FLUIDMECHANICS
14
Flow through pipes in series or compound pipes
Major loss = Head loss due to friction in each pipe
While, minor loss = Entrance loss + Expansion loss +
Contraction loss + Exit loss
Flow will remain constant
Equivalent pipe in series pipe
๐ฟ
๐5
=
๐ฟ1
๐1
5 +
๐ฟ2
๐2
5 +
๐ฟ3
๐3
5
Power Transmission through pipes
โข P =
ฯgAV
1000
(H โ hf)
hf = loss due to friction
โข Efficency of power transmission
๏จ =
๐๐๐ค๐๐ ๐๐ฃ๐๐๐๐๐๐๐ ๐๐ก ๐๐ข๐ก๐๐๐ก
๐๐๐ค๐๐ ๐ ๐ข๐๐๐๐๐๐
=
๐ปโโ๐
๐ป
โข Condition for maximum transmission of power
๐ป = 3โ๐ and ๏จ = 66%
Dimensional analysis:
Quantity Symbol Dimensio
ns
Mass m M
Length l L
Time t T
Temperature T ฮธ
Velocity u LT -1
14. MECHANICAL ENGINEERING โ FLUIDMECHANICS
15
Acceleration a LT -2
Momentum/Impulse mv MLT -1
Force F MLT -2
Energy - Work W ML 2T -2
Power P ML 2T -3
Moment of Force M ML 2T -2
Angular momentum - ML 2T -1
Angle ฮท M 0L 0T 0
Angular Velocity ฯ T -1
Angular acceleration ฮฑ T -2
Area A L 2
Volume V L 3
First Moment of Area Ar L 3
Second Moment of Area I L 4
Density ฯ ML -3
Specific heat-
Constant
Pressure
C p L 2 T -2 ฮธ -1
Elastic Modulus E ML -1T -2
Flexural Rigidity EI ML 3T -2
Shear Modulus G ML -1T -2
Torsional rigidity GJ ML 3T -2
Stiffness k MT -2
Angular stiffness T/ฮท ML 2
T -2
Flexibiity 1/k M -1
T 2
Vorticity - T -1
Circulation - L 2
T -1
Viscosity ฮผ ML -1
T -1
Kinematic Viscosity ฯ L 2
T -1
Diffusivity - L 2
T -1
Friction coefficient f /ฮผ M 0
L 0
T 0
Restitution coefficient M 0
L 0
T 0
Specific heat-
Constant volume
C v
L 2
T-2
ฮธ -1
15. MECHANICAL ENGINEERING โ FLUIDMECHANICS
16
Dimensionless number
โข Reynoldโs number (Re)
๐ ๐ =
๐ผ๐๐๐๐ก๐๐๐ ๐น๐๐๐๐
๐๐๐ ๐๐๐ข๐ ๐น๐๐๐๐
=
๐๐๐ท
๐
โข Froudeโs Number (Fe)
Fe = โ
Inertia Force
Gravity Force
=
๐
โ๐ฟ๐
โข Eulerโs Equation (Eu)
๐ธ๐ข = โ
๐ผ๐๐๐๐ก๐๐ ๐น๐๐๐๐
๐๐๐๐ ๐ ๐ข๐๐ ๐น๐๐๐๐
=
๐
โ๐
๐
โ
โข Weberโs number (We)
๐๐ =
๐ผ๐๐๐๐ก๐๐ ๐น๐๐๐๐
๐๐ข๐๐๐๐๐ ๐น๐๐๐๐
=
๐
โ๐
๐๐ฟ
โ
โข Mach number (M)
๐ =
๐ผ๐๐๐๐ก๐๐
๐ธ๐๐๐ ๐ก๐๐ ๐น๐๐๐๐
=
๐
๐ถ
Velocity distribution for turbulent flow in pipe
v = vmax + 2.5Vโ
loge (
Y
R
)
Where Vโ
=โ
๐๐
๐
Shear or friction velocity, Y=distance from pipe wall, ๐=Density
Displacement Thickness (๐ โ
)
๐ โ
= โซ {1 โ
๐ข
๐
} ๐๐ฆ
๐ฟ
0
U=Stream Velocity, u=Velocity of fluid at the element, ฮด= boundary layer thickness
Momentum Thickness (ฮธ)
ฮธ = โซ
๐ข
๐
{1 โ
๐ข
๐
} ๐๐ฆ
๐ฟ
0
Energy Thickness (๐ โโ
)
๐ โโ
= โซ
๐ข
๐
{1 โ
๐ข2
๐2
} ๐๐ฆ
๐ฟ
0
16. MECHANICAL ENGINEERING โ FLUIDMECHANICS
17
Drag force on a flat plate due to boundary layer
ฯo
ฯU2
=
โฮธ
โx
Know as Von Karman momentum integral equation
Drag force on plate obtained by ๐น๐ท = โซ โ๐น = โซ ๐๐
๐ฟ
0
๐๐๐ฅ where, b if thickness of plate
Local (๐๐
โ
)and average (๐๐) co-efficient of drag
CD
โ
=
ฯ0
ฯU2
2
โ
, CD =
ฯ0
ฯAU2
2
โ
Boundary condition for the velocity profile
โข At y=0, u=0
โข At y=๐ฟ, u=U
๐๐ข
๐๐ฆ
= 0
17. MECHANICAL ENGINEERING โ FLUIDMECHANICS
18
Saparation of boundary layer
Force exerted by jet on plate
โข Force exerted by jet = mass of fluid striking per sec *
change in velocity =
ฯa(V)*(V โ 0)
=ฯa(V)2
Force exerted by jet on inclined plate
โข Fn=ฯa(V)2 Sinฮธ
โข Force component in X-direction = Fn Sinฮธ
โข Force component in Y-direction = Fn Cosฮธ
Force exerted by jet on curved plate
โข Fx=ฯaV(V+V cosฮธ)
โข Fy=ฯaV(0-V sinฮธ)
Force exerted by jet on curved plate , moving with some velocity
โข Fx=ฯa(V-u)( (V-u)+ (V-u) cosฮธ)
โข Fy=ฯa(V-u)(0-(V-u) sinฮธ)
19. MECHANICAL ENGINEERING โ FLUIDMECHANICS
20
Work done by Pelton turbine
โข Work ๐ = ๐๐๐1[๐๐1 โ ๐๐2]๐ข where ๐๐1, ๐๐2are whirl velocity
Hydraulic Efficiency
โข Hydraulic Efficiency =
๐[๐๐๐ยฑ๐๐๐]๐ฎ
๐๐
๐
โข When blade velocity= (inlet velocity of jet)/2 then,
Maximum efficiency
๐+๐ช๐๐โ
๐
Degree of reaction
R =
Change of pressure energy inside the runner
Change in total energy
Specific Speed
โข For turbine ๐๐ =
๐โ๐
๐ป
5
4
โ
where P= power, H= head and N= number of rotation
โข Dimensionless Specific speed ๐๐ =
๐โ๐
(๐๐ป)
5
4
โ
Turbine Specific Speed
(S.I)
Specific Speed
(M.K.S)
Pelton 8.5 to 30 10 to 35
Pelton with two jets 30 to 51 35 to 60
Francis 51 to 255 60 to 300
Kaplan and propeller 255 to 860 300 to 1000
For Pumps, ๐๐ =
๐โ๐
๐ป
3
4
โ
where Q is discharge
Unit quantities
โข Unit speed (Nu): N = NuโH
โข Unit Power (Pu): P = Pu โ H
3
2
โ
โข Unit discharge (Qu): Q = QuโH
Model laws of turbine
โข
๐
๐๐ท3 = ๐๐๐๐ ๐ก๐๐๐ก
โข
๐
โ๐ป๐ท2 = ๐๐๐๐ ๐ก๐๐๐ก
20. MECHANICAL ENGINEERING โ FLUIDMECHANICS
21
โข
๐ป
๐2๐ท2 = ๐๐๐๐ ๐ก๐๐๐ก
โข
๐
๐3๐ท5 = ๐๐๐๐ ๐ก๐๐๐ก
โข
๐
๐ป
3
2
โ ๐ท2
= ๐๐๐๐ ๐ก๐๐๐ก
Net Positive suction Head in pump
โข NPSH= Pressure head + Static head - Vapor pressure head of your product โ Friction head loss