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A river flows into a hydroelectric power plant with a velocity v 1 = 1.15 m/s an

ID: 1261719 • Letter: A

Question

A river flows into a hydroelectric power plant with a velocity v1= 1.15 m/s and emerges from it with a final velocity v2=0.11 m/s. If water flows through the plant at a rate V? =3.22 m3/s and has a head of h=10.35 m.
- Calculate the water mass flow rate through the plant (in Kg/s).
- Calculate the rate of change in the gravitational potential energy through the plant (in kW).
- Calculate the rate of change of the kinetic energy through the plant (in kW).
- Calculate the theoretical rate of production of energy from this hydroelectric plant (in kW).

Explanation / Answer

according to continuty equation

Qinflow=AVI

A=3.22/1.15

=2.8m2

AVI=AVF

A=2.8*1.15/0.11

=29.27m2

in order determine mass

m=rho*V

=1000*10.35*2.8

=28980kg

but time is not given in question

rate of change in the gravitational potential energy through the plant (in kW).

=1000*9.8*10.35

=101.43KW

rate of change of the kinetic energy through the plant (in kW).

=0.5*1000(1.152-0.112)

=0.655KW

Due to energy loss the practically available power will be less than the theoretically power. Practically available power can be expressed as

P = 1000 ? q g h

where

P = power available (W)

? = efficiency (in general ranging 0.75 to 0.95)

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