# If the overall efficiency of a Pelton Turbine is 65% and its Mechanical efficiency is 80%, then its Hydraulic efficiency would be?

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If the overall efficiency of a Pelton Turbine is 65% and its Mechanical efficiency is 80%, then its Hydraulic efficiency would be?
1. 81.25%
2. 55.25%
3. 75.25%
4. 85.25%

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Correct Answer - Option 1 : 81.25%

Concept:

The overall efficiency ηo of turbine = volumetric efficiency (ηv) × hydraulic efficiency (ηh) × mechanical efficiency (ηm)

${η _o} = {η _v} × {η _h} × {η _m}$

${{\rm{η }}_{\rm{v}}} = \frac{{{\rm{volume\;of\;water\;actually\;striking\;the\;runner}}}}{{{\rm{volume\;of\;water\;actually\;supplied\;to\;the\;turbine}}}}$

${{\rm{η }}_{\rm{h}}} = \frac{{{\rm{Power\;deliverd\;to\;runner}}}}{{{\rm{Power\;supplied\;at\;inlet\;}}}} = \frac{{{\rm{R}}.{\rm{P}}}}{{{\rm{W}}.{\rm{P}}}}$

${{\rm{η }}_{\rm{m}}} = \frac{{{\rm{Power\;at\;the\;shaft\;of\;the\;turbine}}}}{{{\rm{Power\;delivered\;by\;water\;to\;the\;runner}}}} = \frac{{{\rm{S}}.{\rm{P}}}}{{{\rm{R}}.{\rm{P}}}}$

Overall efficiency: ${η _o} = \frac{{S.P}}{{W.P}}$

Water Power = ρ × Q × g × h

Calculation:

Given:

overall efficiency = 65 % and mechanical efficiency = 80%

$\begin{array}{l} {η _{o}} = {η _{vol}}\times{η _{mech}}\times{η _{hyd}}\\ 65 = 80\times{η _{hyd}}\; \end{array}$

ηhyd = 81.25 %