Watch Video of this presentation on Link: https://youtu.be/nt9-q5SDaqk 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. Francis Turbine
Main Components
Velocity Triangle
Efficiencies
Design Aspects
Satish G. Taji
Assistant Professor
Civil Engineering Department
SRES’s Sanjivani College of Engineering, Kopargaon1
Hydraulic Turbines
1

2. Francis Turbine – Main Components
Prepared By Prof. S. G. Taji
Image Courtesy: Wikipedia (Google); gmdu.net (Google); pinterest (Google), learnengineering.org

3. Francis Turbine – Velocity Triangle
 R1, R2= Radius of wheel at the inlet and outlet of vanes
 V1, V2 = Absolute velocities of the jet at the inlet and
outlet respectively,
 u1, u2 = Peripheral velocities of the vane at the inlet
and outlet respectively,
 Vr1, Vr2 = Relative velocities at the inlet and outlet
respectively,
 Vf1, Vf2 = Velocities of the flow at the inlet and outlet
respectively,
 Vw1, Vw2 = Velocities of the whirl at inlet and outlet
 θ, φ = Tip angles at the inlet and outlet respectively,
 α, β = Angles made by absolute velocities at the inlet
and outlet
Prepared By Prof. S. G. Taji

4. Francis Turbine – Velocity Triangle
β < 90o
Prepared By Prof. S. G. Taji
Wheel
Tangent
at outlet
Tangent
at inlet
1
2
2
1
1
2

5. Francis Turbine – Velocity Triangle
β =90o
Prepared By Prof. S. G. Taji
Wheel
Tangent
at outlet
Tangent
at inlet

6. Francis Turbine – Velocity Triangle
β > 90o
Prepared By Prof. S. G. Taji
Wheel
Tangent
at outlet
Tangent
at inlet

7. Francis Turbine – Velocity Triangle
 Uniform velocity at inlet and outlet Tip (vane)
 u1 = π D1 N / 60
 u2 = π D2 N / 60
where, D1 =Dia. Of Wheel at the inlet
D2 =Dia. Of Wheel at the outlet;
N= Speed in rpm = 60f/p
 Force exerted by Jet on the Bucket (β<90O )
 Force exerted in the direction of motion
 Fx = Rate of Change of Momentum in the same dirn
But, in this case, momentum is angular momentum
∴ Fx= Mass of water striking the vane per second ×
(Initial angular momentum – final angular momentum)
Prepared By Prof. S. G. Taji
m
R
VM = m x v
Angular momentum
= (m x v) x R

8. Francis Turbine – Velocity Triangle
 Force exerted by Jet on the Bucket (β<90O )
 Now, Angular Momentum = Momentum x Radius
i. momentum /sec at the inlet = (mass/sec) x (velocity
component in tangential dirn)
= (ρ a V1) x [Vw1]
ii. momentum /sec at the outlet= (mass/sec) x (velocity
component in tangential dirn)
= (ρ a V1) x [-Vw2]
iii. Angular momentum at inlet = (ρ a V1) x [Vw1] x R1
iv. Angular momentum at outlet = (ρ a V1) x [-Vw2] x R2
Prepared By Prof. S. G. Taji

9. Francis Turbine – Velocity Triangle
 Force exerted by Jet on the Bucket (β<90O )
∴ Fx= Mass of water striking the vane per second ×
(Initial angular momentum – final angular momentum)
Fx = (ρ a V1) x [Vw1 R1] - (ρ a V1) x [-Vw2] x R2
= (ρ a V1) [Vw1 R1 + Vw2 R2]
 When, β > 90o  Fx (ρ a V1) [Vw1 R1 - Vw2 R2]
 In general,
Fx = = (ρ a V1) [Vw1 R1 ± Vw2 R2]
 When, β = 90o (Radial discharge at outlet )
Fx = = (ρ a V1) [Vw1 R1]
Prepared By Prof. S. G. Taji

10. Francis Turbine – Velocity Triangle
 Work Done by Jet on the runner / sec
Work Done /sec = Fx x Angular Velocity (ω)
= (ρ a V1) x [Vw1 R1 ± Vw2R2] x ω
= (ρ a V1) x [Vw1 ω R1 ± Vw2 ω R2]
but, u1 = ωR1 & u2 = ωR2
Work Done /sec = (ρ a V1) x [Vw1 u1 ± Vw2 u2] N-m/s
Power = (ρ a V1) x [Vw1 u1 ± Vw2 u2] N-m/s or watts
 When, β = 90o (Radial discharge at outlet )
Work Done /sec = (ρ a V1) x [Vw1 u1]
Prepared By Prof. S. G. Taji

11. Francis Turbine – Efficiencies
 Hydraulic Efficiency (ήh)
 ήh = (WD/sec) / (KE/sec) OR RP / WP
Prepared By Prof. S. G. Taji

12. Francis Turbine – Efficiencies
 Mechanical Efficiency (ήm)
 ήm = (Shaft Power) / (WD/sec) OR SP / RP
 Overall Efficiency (ή0)
Prepared By Prof. S. G. Taji

13. Francis Turbine – Design Aspects
1. Discharge through reaction Turbine
Prepared By Prof. S. G. Taji

14. Francis Turbine – Design Aspects
2. Speed Ratio (Ku):
3. Flow Ratio (Kf):
4. Ratio of Width to Diameter (n)
Prepared By Prof. S. G. Taji