At the inlet of an axial impulse turbine rotor, the blade

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At the inlet of an axial impulse turbine rotor, the blade linear speed is 25 m/s, the magnitude of absolute velocity is 100 m/s and the angle between them is 25°. The relative velocity and the axial component of velocity remain the same between the inlet and outlet of the blades. The blade inlet and outlet velocity triangles are shown in figure. Assuming no losses, the specific work (in J/kg) is _______.

1. 3277.84
2. 3277.94
3. 3277.89
4. 3277

Correct Option: A

Given α = 25º
V_r₁ sin β₁ =V₁ sinα
∴ 78 sin β₁ = 100 sin 25º
∴ β₁ = 32.81º
∵ V_r₁ = V_r₂
∴ β₁ = β₂ = 32.81º
Now ∴ ∆V_w = V_r₁ cosβ₁ + V_r₂ cosβ₂
= 2V_r₁ cosβ₁
= 2 × 78 × cos32.81°
∴ ∆V_w = 131.1136 m/sec
∴ Sp. power = ∆V_w . u = 131.1136 × 25
= 3277.84 J/kg.