Question 15.P.15: A centrifugal pump running at 900 rpm has an impeller diamet......
A centrifugal pump running at 900 rpm has an impeller diameter of 500 mm and eye diameter of 200 mm. The blade angle at outlet is 35° with the tangent. Determine assuming zero whirl at inlet, the inlet blade angle. Also calculate the absolute velocity at outlet and its angle with the tangent. The flow velocity is constant at 3 m/s. Also calculate the manometric head.
The velocity diagrams are as shown.
Consider inlet
u_{1}={\frac{\pi\times0.2\times900}{60}}=9.42\;\mathrm{m/s} \\ V_{f1} = 3\ {\rm m/s}
Blade angle at inlet
\tan\,{\beta}_{1}={\frac{V_{f1}}{u_{1}}}={\frac{3}{9.42}}
∴ β_{1} = 17.66°
Considering outlet
u_{2}={\frac{\pi\times0.5\times900}{60}}=23.56\ {\mathrm{m/s}} \\ V_{u2}=u_{2}-\frac{V_{f2}}{\tan35}=23.56-\frac{3}{\tan35}=19.28~\mathrm{m/s}\tan\;\alpha_{2}={\frac{3}{19.28}}
∴ α_{2} = 8.85°
V_{2}=\sqrt{3^{2}+19.28^{2}}\ =19.51\ \mathrm{m/s}
The outlet velocity is 19.51 m/s at an angle of 8.85° to the tangent. (taken in the opposite direction of u).
Manometric head ={\frac{23.56\times19.28}{9.81}}=46.3\ \mathrm{m}
