Question

A hydroelectric power station is required to generate a total of 4.2 MW from a number of single-jet Pelton wheel turbines each operating at the same rotational speed of 650 rpm, at the same power output and at a power specific speed of 1.0 rev. The nozzle efficiency η_N of each turbine can be assumed to be 0.98, the overall efficiency η_o is assumed to be 0.88, and the blades speed to jet speed ratio v is to be 0.47. If the effective head H_E at the entry to the nozzles is 250 m, determine:

1. The number of turbines required (round up the value obtained);
2. The wheel diameter;
3. The total flow rate.

Answer 1

Determine The number of turbines required (round up the value obtained).

Write expression for specific speed: Nsp=NPρ(gHE)54

Calculate power developed by each turbine.

Given: Nsp=1rpm,g=9.81 m/s2,HE=250 m,Ω=650rpm,ρ=1000 kg/m3

P=ρ(Nsp×(gHE)54N)2=1000×(1×(9.81×250)54650)2=705.01 kW

Calculate number of turbines required

Given: Pt=4200 kW,P=705.01 kW

n=PtP=4200705.01=5.957≃6

Hence, the number of turbines required is 6.

Determine The wheel diameter.

Calculate blade tip speed.

Given: ηN=0.98,v=0.47,g=9.81 m/s2,HE=250 m

U=ηNv2gHE=0.98×0.47×2×9.81×250=32.258 m/s

Calculate diameter of runner.

Given: U=32.258 m/s,N=650rpm

D=U×60πN=32.258×60π×650=0.948 m

Hence, the wheel diameter is D=0.948 m.

Determine The total flow rate.

Given: P=4.2×106 W,ηo=0.88,ρ=1000 kg/m3,g=9.81 m/s2,HE=250 m

Q=PrηoρgHE=4.2×1060.88×1000×9.81×250=1.946 kg/m3

Hence, the total flow rate is Q=1.946 kg/m3.

There is the true answer we calculate.