This presentation includes the revision of basics principles and equations of fluid mechanics used while studying the turbines. These basics include the continuity equation, mass flow rate, Bernoulli's equation, velocity vector diagram at inlet and outlet of the unsymmetrical vane, when the jet of water striking tangentially, etc. Watch Video of this presentation on Link: https://youtu.be/CLMAkxk0hNI For notes/articles, Visit my blog (link is given below). For Video, Visit our YouTube Channel (link is given below). Any Suggestions/doubts/reactions, please leave in the comment box. Follow Us on YouTube: https://www.youtube.com/channel/UCVPftVoKZoIxVH_gh09bMkw/ Blog: https://e-gyaankosh.blogspot.com/ Facebook: https://www.facebook.com/egyaankosh/

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

8. THANK YOU….!!!!!