Question

Water from a reservoir passes over a dam through a turbine and discharges from a 70-cm ID pipe at a point 65 m below the reservoir surface. The turbine delivers 0.80 MW.

Calculate the required flow rate of water in m3 /min if friction is neglected.

Answer 1

ANSWER :

Apply the energy balance around the turbine

Inlet and outlet pressure is same
Then ΔP = 0

- Area A = (3.14/4) * (70/100)2 m2

= 0.38465 m2

- Velocity at the outlet
U 2 = (Q/A)2 = (Q/0.38465)2

   = 6.76*Q 2 m2/s2

- Then

gΔz = 9.8*(-65 )

= -637 m2/s2

- Ws/m = (0.8 * 106) / (Q/1000)

= 800/Q m2/s2

ΔP + u 2 + gΔz + Ws/m = 0

0 + 6.76Q2 - 637 + 800/Q = 0

Q = 1.27 m3/s

Q =1.27 *60   m3/mint

  Q = 76.2  m3/mint

For Friction ,energy loss will be considered and term hf would be minus the above energy equation .

* The Lower flow rate will be required *