Correct Answer - Option 3 : 68%
Concept:
The overall efficiency ηo of turbine = volumetric efficiency (ηv) × hydraulic efficiency (ηh) × mechanical efficiency (ηm)
ηo = ηv × ηh × ηm
\({{\rm{η }}_{\rm{v}}} = \frac{{{\rm{volume\;of\;water\;actually\;striking\;the\;runner}}}}{{{\rm{volume\;of\;water\;actually\;supplied\;to\;the\;turbine}}}}\)
\({{\rm{η }}_{\rm{h}}} = \frac{{{\rm{Power\;deliverd\;to\;runner}}}}{{{\rm{Power\;supplied\;at\;inlet\;}}}} = \frac{{{\rm{R}}.{\rm{P}}}}{{{\rm{W}}.{\rm{P}}}}\)
\({{\rm{η }}_{\rm{m}}} = \frac{{{\rm{Power\;at\;the\;shaft\;of\;the\;turbine}}}}{{{\rm{Power\;delivered\;by\;water\;to\;the\;runner}}}} = \frac{{{\rm{S}}.{\rm{P}}}}{{{\rm{R}}.{\rm{P}}}}\)
Overall efficiency: \({η _o} = \frac{{S.P}}{{W.P}}\)
Water Power = ρ × Q × g × h
Calculation:
Given:
hydraulic efficiency = 85% and mechanical efficiency = 80%
ηo = ηv × ηh × ηm
ηo = 0.80 × 0.85 = 0.68 = 68%