1. ใช้ Francis turbine อธิบาย Theory Rotodynamic machine
Reaction Turbines
ใช้ Francis turbine อธิบาย
Theory
Rotodynamic machine

2. Francis Turbine (Radial Flow)

3. Free Vortex Theory V1 cos a1 –U1=Vr1 cot β1 B b1 α1 Vrel1 U1 V1 Vrel1
Best Efficiency V1
V1 cos a1
Vr1 R1 R2 V2
T =ρQ (V1 r1 cos a1 – V2 r2 cos) a1
T ≈ ρQV1 r1 cos a1
Q= (2πR1 B) Vr1 = (2πR2 B) Vr2

4. V1 cos a1 –U1=Vr1 cot β1 Q= (2πR1 B) Vr1 α1 = 17.4o
Example 8.9 Roberson et al
A Francis turbine is to be operated at a speed of 600 rpm
and with the discharge 4.0 m3/s.
If r1 = 0.60 m, β1 = 110o, and
the blade height is 10 cm,
what should be the guide vane angle α1
for a non-separating flow condition at the runner entrance?
V1 cos a1 –U1=Vr1 cot β1
Q= (2πR1 B) Vr1
U1 = ωR1 = 37.7 s
α1 = 17.4o

5. Find Torque
T ≈ ρQV1 r1 cos a1
T = 81.2 kN-m
Find Power
P=Tω
P = 5100 kw
(Assume no loss ? Friction)

6. Axial Flow Turbine

7. Runners of Axial Flow Turbines

8. Mixed Flow Turbine