Question 6.12: The moving and fixed blades are identical in shape in a reac......
The moving and fixed blades are identical in shape in a reaction turbine. The absolute velocity of steam leaving the fixed blade is 105 m/s, and the blade velocity is 40 m/s. The nozzle angle is 20°. Assume axial velocity is constant through the stage. Determine the horsepower developed if the steam flow rate is 2 kg/s.
For 50% reaction turbine Fig. 6.29, α_1 = β_2, and α_2 = β_1.
From the velocity triangle ACD,
C_{w1} = C_1 \cosα_1 = 105 cos 20° = 98.67 m/s
Applying cosine rule to the Triangle ABC:
V^2_1 = C^2_1 + U^2 – 2C_1U\cosα_1
so:
V_1 = \sqrt{105^2 + 40^2 – (2) \times (105) \times (40) \times \cos 20°} = 68.79 m/s
Now,
BD = C_{w1} – U = V_1 \cosβ_1 = 98.67 – 40 = 58.67
Hence,
\cosβ_1 = \frac{58.67 }{68.79} = 0.853, and β_1 = 31.47°
Change in the velocity of whirl is:
ΔC_w = C_{w1} + C_{w2} = 98.67 + 58.67 = 157.34 m/s
Horsepower developed is:
P = \dot{m}UΔC_w = \frac{(2) × (157.34) × (40)} {(0.746) × (1000)} = 16.87 hp
