The blade and fluid velocities for an axial turbine are

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The blade and fluid velocities for an axial turbine are as shown in the figure.

The magnitude of absolute velocity at entry is 300 m/s at an angle of 65° to the axial direction, while the magnitude of the absolute velocity at exit is 150 m/s. The exit velocity vector has a component in the downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific work (in kJ/kg) is___________ .

1. 52.88
2. 51.88
3. 52.81
4. 52

Correct Option: C

Given: V₁ = 300 m/sec
u =150 m/sec
V_f1 = V_f2
(α = 25°)
V₂ = 150 m/sec

Specific work = [V_w1 + V_w2]. u
V_w1 = V₁ cos 25°
V_w2 = 300 cos 25°
= 271.89 m/s
V_f1 = V_f2 = V₁ sin 25
V_f2 = 300 sin 25
= 126.78 m/s
V_w2 = √V_f1² - V_f2²
= √150² - 126.78² = √6426.83
V_w2 = 80.16 m/s
Specific work = [V_w1 + V_w2]. u
= [271.89 + 80.76] × 150
= 52807.5 J/kg
= 52.81 kJ/kg