1] Gross head - It is the difference between the 'Head race level' and 'Tail race level' when no water is flowing is known as 'Gross head'. It is denoted by 'Hg'.

2] Net Head - When water is flowing from head race to the turbine, a loss of head due to friction between the water and pen stocks occurs, through there are other losses such as loss due to bend, pipe fittings, loss at the entrance of pen stocks, etc. yet they are having small magnitude as compared to head loss due to friction. if head loss (Hf) is the head loss due to friction between pen stocks and water then net head turbine is given by

$H = H_g - H_f$

where $H_g =$ Gross Head

$H_f = \frac{4.f.L.v^2}{2gd}$

Efficiencies of Turbine -

1] Hydraulic Efficiency $( n_h )$

2] Mechanical Efficiency $( n_m )$

3] Volumetric Efficiency $( n_v )$

4] Overall Efficiency $(n_o )$

Hydraulic Efficiency $n_h$ - It is defined as the ratio of power given by water to the runner of a turbine to the power supplied by the water at the inlet of the turbine.

$n_h = \frac{\text{power delivered to runner}}{\text{power supplied at inlet}}$

$= \frac{R.P}{W.P}$ -------- (1)

R.P = Power delivered to the runner.

$= \frac{w [v_{w1} +- v_{w2}] \times u}{g 100} kw$ - For Pelton Turbine.

$= \frac{w}{g} \frac{[v_{w1} {u_1} + - v_{w_2} u_2]}{1000} kw$ - For a Radical flow turbine.

$= \frac{W \times H}{1000} kw$ ---- (2)

where, w = weight of water striking the vanes of the turbine per second, $= pg \times Q$

$v_{w1}$ = velocity of whirl at inlet.

$v_{w2}$ = velocity of whirl at outlet.

$u$ = Tangential velocity of vane. $u_1$ = Tangential velocity of vane at inlet. $u_2$ = Tangential velocity of vane at outlet. Power supplied at the inlet of turbine in S.I. unit is known as water power $w.p = \frac{p \times g \times q \times h}{1000} kw$ ------ (3) for water $p = 1000 kg/m^3$ $\therefore$ $w.p = \frac{1000 \times g \times q \times h}{1000}$

$= g \times Q \times H kw$ -------- (4)

Mechanical Efficiency $n_m$ - The power delivered by water to the runner of turbine is transmitted to the shaft of the turbine. due to mechanical loss, the power available at the shaft is less as that of power at runner of a turbine. Thus, the ratio of power available at the shaft of the turbine, to the power delivered to the runner is defined as mechanical efficiency.

$n_m = \frac{\text{power at the shaft of turbine}}{\text{power delivered by water to the runner}}$

$n_m = \frac{S.P}{R.P}$

Volumetric Efficiency $n_v$ -

The ratio of volume of water actually striking the runner to the volume of water supplied to the turbine is defined as volumetric efficiency.

$n_v = \frac{\text{volume of water actually striking the runner}}{\text{volume of water supplied to the turbine}}$

Overall Efficiency $n_o$ - 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.

$n_o = \frac{\text{shaft power}}{\text{water power}}$

$= \frac{S.P}{W.P}$

$= \frac{S.P}{W.P} \times \frac{R.P}{R.P}$

$= \frac{S.P}{R.P} \times \frac{R.P}{W.P}$

$[ n_0 = n_m \times n_h]$