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**ใช้ Francis turbine อธิบาย Theory Rotodynamic machine**

Reaction Turbines ใช้ Francis turbine อธิบาย Theory Rotodynamic machine

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**Francis Turbine (Radial Flow)**

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**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

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**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

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

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Axial Flow Turbine

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**Runners of Axial Flow Turbines**

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Mixed Flow Turbine

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