Correct Answer - Option 4 : Power available at the shaft of the turbine to the power supplied by the water at the inlet of the turbine
Explanation
Efficiencies of a Turbine:
The following are the important efficiencies of a turbine-
1. Hydraulic Efficiency (η h)
2. Mechanical Efficiency (η m)
3. Volumetric Efficiency (η v)
4. Overall Efficiency (η o)
1. Hydraulic Efficiency:
It is defined as the ratio of power given by water to the runner of turbine to the power supplied by the water at the inlet of turbine.
The power at the inlet of the turbine is more and this power goes on decreasing as the water flows over the vanes of the turbine due to hydraulic loses as the vanes are not smooth.Hence, power delivered to the runner will be less than the power available at the inlet of the turbine.
\({η _h} = \frac{{power\;delivered\;to\;runner}}{{Power\;supplied\;at\;inlet}}\)
Power delivered to runner for Francis turbine also called runner power, R.P. \(= \frac{w}{g}{V_{{w_1}}}\frac{u}{{1000}}\;kW\)
Power supplied at inlet of turbine also called water power, W.P. \(= \frac{{w \times H}}{{1000}}\;kW\)
where,
w = weight of water striking the vanes per second = ρ×g×Q
Vw1 = velocity of whirl at inlet.
u = tangential velocity of vane
H = net head on the turbine
\(\therefore {η _h} \propto \frac{{{V_{w1}}}}{H}\)
2. Mechanical Efficiency:
It is the ratio of the power delivered by water to the runner of a turbine and the power transmitted to the shaft of turbine. Due to mechanical losses, the power available at the shaft of the turbine is less than the power delivered.
3. Volumetric Efficiency:
It is the ratio of volume of water striking the runner of a turbine to the volume of water supplied to the turbine.
4. Overall Efficiency:
It is defined as the ratio of power available at the shaft of the turbine to the power supplied by the water at the inlet of the turbine.
\({η _o} = {η _h} \times {η _m}\)
