An inward flow reaction turbine has the following data:

Head available = 25 m

Velocity of flow = 2.5 m/s (constant)

Guide blade angle = 10°

Runner vanes are radial at the inlet and discharge at the outlet is radial. What will be the approximate hydraulic efficiency of the turbine? [ given, $tan 1 0^{\circ} = 0.176$ , g = 10 m/s²]

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This question was previously asked in

SJVN ET Mechanical 2019 Official Paper

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Answer 1

Concept:

Hydraulic efficiency for a reaction turbine is given by:

$ \eta_h = \frac{V_{w1} \cdot u_1}{gH} $

Given:

$ H = 25~m,~V_f = 2.5~m/s,~\alpha = 10^\circ \Rightarrow \tan \alpha = 0.176,~g = 10~m/s^2 $

Step 1: Whirl Velocity

$ V_{w1} = \frac{V_f}{\tan \alpha} = \frac{2.5}{0.176} \approx 14.2~m/s $

Step 2: Tangential Velocity

$ u_1 = V_{w1} = 14.2~m/s $ (since radial vanes, no losses assumed)

Step 3: Hydraulic Efficiency

$ \eta_h = \frac{14.2 \times 14.2}{10 \times 25} = \frac{201.64}{250} = 0.8163 = 81.63\% $