Consider a river flowing toward a lake at an average velocity of 3 m/sec at a rate of 50 m³/sec at a location 90 m above the lake surface. Determine the total mechanical energy of the water per unit mass and the power generation potential of the entire river at that location.

Here, L = 2000m 

$Z_1=100m$
$Z_2=20m$
$V_1=0$
$V_2 = 1m /sec$
$P_1=0$
Diameter of pipe, d = 20cm = 0.2m 
p = 0.015 
$\alpha = 1$
 

Solution: Head loss, 

$H_L=\frac{f^{\text{'}}LV{2}^2}{2gd}=\frac{0.015\times 2000\times 1^2}{2\times 9.81\times 0.2}=7.645 m$

Now, Bernoulli Equations, 

$Z_1+\alpha \frac{V_1^2}{2g}+\frac{P_1}{\gamma }=Z_2+\alpha \frac{V_2^2}{2g}+\frac{P_2}{\gamma }{H}_L$

$100+0+0=20+1.0\times \frac{1^2}{2\times 9.81}+\frac{P_2}{9.81}+7.645 m$

$P_2=709.3 kPa \left(Ans\right)$

Here, 

$A=25k{m}^2=25\times {10}^6{m}^2$
$V=1.5\times {10}^6{m}^3$
i = 10cm = 0.1m

Solution: 

Effective rainfall  $=\frac{V}{A}=\frac{1.5\times {10}^6}{25\times {10}^6}=0.06m=6cm$

Runoff coefficient $= \frac{6}{10} = 0.6\left(Ans\right)$