2 A large proposed hydroelectric installation has a head of

2. A large proposed hydroelectric installation has a head of 1200ft, and desires an output of 30,000hp. Determine the required diameters and rotation rates for (i) a Pelton wheel with N\'sd-4.5, and (i) a Francis turbine with N\'sd-29, and a dimensionless power coefficient of Cp=0.0085.

Solution

Soution:-

Given

P = 30000 hp

C_p =0.0085

Head = 1200 feet

(i) Pelton turbine:-

N_s = N P/H^(5/4)

4.5 = N *(30000)/1200^(5/4)

Rotation rate (N) = 183.49 rpm Answer

C_p = P/(density of water *N³ * D⁵)

   0.0085 = 30000/(62.34*(183.49)³ *D⁵)

Diameter(D) = 0.39 feet Answer

(ii) Francis turbine:-

Ns = N P/H^(5/4)

29 = N *(30000)/(1200)^(5/4)

Rotation rate (N) = 1182.5 rpm   Answer

We know that

C_p = P/(density of water * N³*D⁵)

0.0085 = 30000/(62.34 * (1182.5)³ * D⁵)

Diameter(D) = 0.128 feet Answer