Shaft Power $P_{3}$=11772 kw

Head H=380m

N=750 rpm

overall efficiency, h0=0.86

i) Wheel diameter,D;

Velocity of jet $V_{1}=C\times\sqrt{2gH}$

=0.985$\sqrt{2\times 9.81\times 380}$

=85.05m\s

ku=$\frac{u}{V1}$=0.45

Wheel velocity u=$0.5\times 85.05$

=38.273 m/s

4=$\frac{\pi DN}{60}$

38.273=$\frac{\pi\times D\times 150}{60}$

D=0.975 m

ii) Diameter of jet d

Discharge jet q=$\frac{Q}{h}=\frac{4}{4}=1m^{3}/s$

q=$Area \ of \ jet\times V_{1}$

1=$\frac{\pi}{4}\times {d}^{2}\times 65.14$

d=0.1398 m

iii) Diameter of pipe cline D

let Vm be the Velocity of pipleline

Then Q=$A_{p}\times V_{p}$

$V_{p}=\frac{16}{\pi}\times \frac{1}{D^{2}}$

hf=$\frac{4fLv^{2}_{p}}{D.2g}$

22.5=$0.0045\times 3000\times (\frac{16}{\pi}\times \frac{1}{D^{2}})^{2}\times \frac{1}{D}\times \frac{1}{2\times 9.81}$

$D^{2}$=0.7932

D=0.955 m

Efficiency of transmission through pipe line an nozzles,

n transmission $\frac{Hg-hf}{Hg}$

0.91=$\frac{250-hf}{250}$

h1=22.5m

Net head are turbine

H=Hg-hf

=250-225=22.75m

Velocity of jet $V_{1}=Cv\sqrt{2gH}$

=0.975$\sqrt{2\times 9.81\times 227.5}$=65.14m/s

water power of inputr power to runner

$p_{1}$=k.E of jets

=$\frac{1}{2}mv^{2}_{t}$

=$\frac{1}{2}(PQ)V^{2}_{1}$

$p_{1}=\frac{1}{2}\times 4\times (65.14)^{2}$

=8486.44 $\times 10^{3}w$

$p_{1}$=8486.4 kw

Assuming hydraullic efficiency to be 90 % i.e $h_{4}$=0.9

$p_{3}=n_{n}\times p_{1}$

$0.9\times 8486.4$

=7637.8 kW