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 %
