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.

4.326 MW

Explanation:

Given :

Discharge through system =

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 m

                         = 16.75 m/s

Head loss (H) =

The runner power obtained,

                                                     = 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