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A Pelton wheel works under a head of 400 m. Friction loss through the pipe flow is limited to 10%. The coefficient of velocity for the jet is 0.98. What is the velocity of the jet’? Take g = 10 m/s2.
1. 83 m/s
2. 71 m/s
3. 65 m/s
4. 46 m/s

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Correct Answer - Option 1 : 83 m/s

Concept:

The velocity of water jet through a nozzle at inlet in case of a Pelton wheel is given by,

\({\rm{V}} = {\rm{\;}}{{\rm{C}}_{\rm{v}}}\sqrt {2{\rm{g}}{{\rm{H}}_{{\rm{net}}}}} \)

Where, V is the velocity of the water jet, \({{\rm{C}}_{\rm{v}}}\) is the coefficient velocity, \({{\rm{H}}_{{\rm{net}}}}\) is the net head available after accounting for all losses and g is acceleration due to gravity.

Calculation:

Given, \({\rm{coefficient\;velocity\;}},{\rm{\;}}{{\rm{C}}_{\rm{v}}} = 0.98\)

Working head = 400 m and frictional losses is 10%.

\(\therefore {\rm{\;Net\;head\;available}},{\rm{\;}}{{\rm{H}}_{{\rm{net}}}} = 400 \times 0.9 = 360{\rm{m}}.\)

Acceleration due to gravity = g = 10 m/s2.

\(\therefore {\rm{V}} = {\rm{\;}}{{\rm{C}}_{\rm{v}}}\sqrt {2{\rm{g}}{{\rm{H}}_{{\rm{net}}}}} = 0.98 \times \sqrt {2 \times 10 \times 360} = 83.2{\rm{\;m}}/{\rm{s}}\)

∴ The velocity of the jet is 83 m/s.

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