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40 votes
40 votes
4. A hydropower installation is to be located where the downstream water-surface elevation is 150 m below the water-surface elevation in the reservoir. The 1.5-m-diameter concrete-lined penstock is 300 m long and has an estimated roughness height of 17.5 mm (ks). When the flow rate through the system is 30 m3 /s, the combined head loss in the turbine and draft tube is 7.5 m, and the average velocity in the tailrace is 0.60 m/s. Estimate the power that can be extracted from the system.

User Sebastian Meine
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1 Answer

4 votes
4 votes

Answer:

4.326 MW

Step-by-step explanation:

Given :

Discharge through system =
image

Gross head, H = 150 m

Diameter of the pipe = 1.5 m

Length of penstock = 300 m

Head loss due to turbine and draft tube = 7.5 m

Average velocity installed tail race = 0.60 m/s

The power exerted on the system is
image m


image


image


image


image


image

= 16.75 m/s

Head loss (H) =
image


image


image

The runner power obtained,
image


image

= 5.090 MW

So the power exerted by the shaft is up to 85% of the runner power due to mechanical losses = 0.85 x 5.090

= 4.326 MW

User Ken
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2.9k points