Correct Answer - Option 3 : 4.57 m/s
Concept:
Tangential velocity at inlet \({u_1} = \frac{{\pi {D_1}N}}{{60}}\)
\(\left( {\tan \theta } \right) = \frac{{{V_{f1}}}}{{{u_1}}}\)
Calculation:
Given:
N = 1200 rpm, Inner Diameter = 200 mm = 0.2 m, Outer Diameter = 250 mm
Now,
Tangential velocity at inlet \({u_1} = \frac{{\pi {D_1}N}}{{60}}\)
\(= \frac{{\pi × 0.2 × 1200}}{{60}} = 12.56\;{m}/{s}\)
Now,
∴ Vane angle at inlet \(\left( {\tan \theta } \right) = \frac{{{V_{f1}}}}{{{u_1}}} = \frac{{V_{f1}}}{{10.47}}\)
∴ tan 20° × 12.56 = Vf1
∴ Vf1= 4.57 m/s