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A 65% efficient turbine receives 2 m^3/s of water from a reservoir. The reservoir water surface is 45 m above the centerline of the turbine. The water leaves the turbine through a 1-m diameter pipe into a river. How many kilowatts of power is generated by the turbine? Assume losses in the flow system to be 5 m.

User Stevejay
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1 Answer

5 votes

Answer:


P_(out) = 508.071 kW

Given:

efficiency of the turbine,
\eta = 65% = 0.65

available gross head,
H_(G) = 45 m

head loss,
H_(loss) = 5 m

Discharge, Q =
2 m^(3)

Solution:

The nozzle is 100% (say)

Available power at the inlet of the turbine,
P_(inlet) is given by:


P_(inlet) = \rho Qg(H_(G) - H_(loss)) (1)

where


\rho = density of water = 997
kg/m^(3)

acceleration due to gravity, g =
9.8 m^(2)

Using eqn (1):


P_(inlet) = 997* 2* 9.8(45 - 5) = 781.65 kW

Also, efficency,
\eta is given by:


\eta = (P_(out))/(P_(inlet))


0.65 = (P_(out))/(781.648* 1000)


P_(out) = 0.65* 781.648* 1000 = 508071 W = 508.071 kW


P_(out) = 508.071 kW

User GeniusHawlah
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6.2k points