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Prepared By:
Prof. S. G. Taji
Civil Engineering Department
Sanjivani College of Engineering, Kopargaon
Turbine
Revision of Basics
(Fluid Mechanics)
Continuity Eq A1V1 = A2V2
Bernoulli’s Eq
(P1/ρg)+ (V12 /2g) + Z1= [P2/ρg] + (V22 /2g) + Z2 +hf
Mass Flow Rate
MFR=Mass of fluid flowing / sec
We know, ρ = Mass/Volume  mass = ρ x Volume
Mass/sec = (ρ x volume)/sec -but, volm/sec (m3/s)= Q
Therefore, MFR = M/s = ρ x Q = ρ A V
Fluid Mechanics – Basics
Relative Velocity = Final Velocity – Initial velocity
If initial vel = u and final vel. = V
then Relative Velocity = V – u
Impulse – Momentum Principle
It states, force exerted by jet of water on plate will be
equal to rate of change of momentum in the dirn of
motion
Fx = Rate of change of momentum (in the direction of force)
Fluid Mechanics – Basics
Impulse – Momentum Principle
oWe know, Momentum = Mass x Velocity = M x V
oNow, Change in momentum = Initial momentum – final momntm
oChange in momentum = M1V1– M2V2 --- but, M1=M2 = M
oTherefore, Change in momentum = M(V1–V2 )
oNow, Rate of Change of Momentum = (Change in Momntm)/sec
oTherefore, Rate of Change of Momentum = M(V1–V2 ) / sec
= (M/sec) x (V1–V2)
= ρ A V1 x (V1–V2)
Fluid Mechanics – Basics
Gross Head (Hg)= Total head available at reservoir
Net Head (H)= Hg – Hf  where, Hf = Head loss
oHf = 4 f L V2/ 2 g D  Darcy – Weisbach Eq.
Theorotical Velocity = Vth = √2gH
Actual Velocity = Vact = Cv √2gH  Cv = Coeff. Of Vel.
Work Done/s = Force (in direction of motion) x Velocity
Power = Work done / sec ----- N-m/sec or watt
= ρ x g x Q x H watt or g x Q x H KW
Fluid Mechanics – Basics
Kinetic Energy (KE) = ½ M V2
KE/sec = ½ M V2 / sec = ½ (M/sec) (√2gH)2
= ½ (ρ A V) (√2gH)2
= ρ Q g H N-m/sec or watt  Power
Fluid Mechanics – Basics
Velocity Vector Diagram at Inlet and Outlet
α
V1Sin α = Vf1
V1Cos α = Vw1
α Ɵ
V1
Vr1 Vf1
u1
u2
Ɵ
ϕ
ϕ β
Vw2
Vw1
u1
u2
Vr2 V2 Vf2
V1
Relative velocity = jet vel – plate velocity
= V1Cos α – u1
= Vw1 – u1
THANK YOU….!!!!!

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Basics of Turbine

  • 1. Prepared By: Prof. S. G. Taji Civil Engineering Department Sanjivani College of Engineering, Kopargaon Turbine Revision of Basics (Fluid Mechanics)
  • 2. Continuity Eq A1V1 = A2V2 Bernoulli’s Eq (P1/ρg)+ (V12 /2g) + Z1= [P2/ρg] + (V22 /2g) + Z2 +hf Mass Flow Rate MFR=Mass of fluid flowing / sec We know, ρ = Mass/Volume  mass = ρ x Volume Mass/sec = (ρ x volume)/sec -but, volm/sec (m3/s)= Q Therefore, MFR = M/s = ρ x Q = ρ A V Fluid Mechanics – Basics
  • 3. Relative Velocity = Final Velocity – Initial velocity If initial vel = u and final vel. = V then Relative Velocity = V – u Impulse – Momentum Principle It states, force exerted by jet of water on plate will be equal to rate of change of momentum in the dirn of motion Fx = Rate of change of momentum (in the direction of force) Fluid Mechanics – Basics
  • 4. Impulse – Momentum Principle oWe know, Momentum = Mass x Velocity = M x V oNow, Change in momentum = Initial momentum – final momntm oChange in momentum = M1V1– M2V2 --- but, M1=M2 = M oTherefore, Change in momentum = M(V1–V2 ) oNow, Rate of Change of Momentum = (Change in Momntm)/sec oTherefore, Rate of Change of Momentum = M(V1–V2 ) / sec = (M/sec) x (V1–V2) = ρ A V1 x (V1–V2) Fluid Mechanics – Basics
  • 5. Gross Head (Hg)= Total head available at reservoir Net Head (H)= Hg – Hf  where, Hf = Head loss oHf = 4 f L V2/ 2 g D  Darcy – Weisbach Eq. Theorotical Velocity = Vth = √2gH Actual Velocity = Vact = Cv √2gH  Cv = Coeff. Of Vel. Work Done/s = Force (in direction of motion) x Velocity Power = Work done / sec ----- N-m/sec or watt = ρ x g x Q x H watt or g x Q x H KW Fluid Mechanics – Basics
  • 6. Kinetic Energy (KE) = ½ M V2 KE/sec = ½ M V2 / sec = ½ (M/sec) (√2gH)2 = ½ (ρ A V) (√2gH)2 = ρ Q g H N-m/sec or watt  Power Fluid Mechanics – Basics
  • 7. Velocity Vector Diagram at Inlet and Outlet α V1Sin α = Vf1 V1Cos α = Vw1 α Ɵ V1 Vr1 Vf1 u1 u2 Ɵ ϕ ϕ β Vw2 Vw1 u1 u2 Vr2 V2 Vf2 V1 Relative velocity = jet vel – plate velocity = V1Cos α – u1 = Vw1 – u1