As shown in the sketch, water flows at 2550 kg/s from a very large reservoir thr

ID: 1857875 • Letter: A

Question

As shown in the sketch, water flows at 2550 kg/s from a very

large reservoir through a penstock (pipe) to a hydro turbine. The

water exits the turbine through a 0.5 m diameter pipe. The

reservoir surface is 30m above the location where the water exits.

(Hint: Assume steady flow and reservoir area is very large compared to the water exit area). Density of water = 997 kg/m3.

A) Assuming no head loss, find the power produced by the hydro turbine. (12)

B) What will be the power output, if total head loss is 3m? (3)

Key assumptions: reservoir is large compared to exit so Velocity(in) = 0 m/s

Use mechanical energy equation :

P1/density + .5*Velocity_in^2 + g*height_in = P2/density + .5*velocity_out^2 + g*height_out + power/mass_flowrate + headloss*g

P1 = P2 = Patm , so those terms cancel each other out

Velocity_in = 0

g= 9.8 m/s^2

height_in = 30m

velocity_out = mass_flow rate/ (density*cross sectional area of pipe)

height_out = 0

mass_flowrate = 2550 kg/s

headloss = 0 (for part A)

plug all these terms into equation and solve for power. Units should be watts or kg*m2 /s^3

Part B:

use everything above except headloss now equals 3m.

Be sure to double check units!

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