Pelton Wheels question

[MIBRAHIM]

Single-jet Pelton wheel turbines are used to generate an electrical power of 27 MW for the available gross head of 280 meters in a hydro-electric power plant exploitation a natural water resource. Using the information provided below find the number of pelton wheels required for the task???

 

 

Relevant information:

Overall Efficiency speed of the wheels, 88%

Maximum Specific Speed of wheels, N_{s = 40}

Loss of head in pipes bringing water to nozzle, h_f = 20 m

Coefficient of discharge for nozzle, C_D = 0.94

Coefficient of velocity for nozzle, CV = 0.97

Bucket speed / Jet speed ratio = 0.46

Rotational speed of wheels, N = 640 rev/min

 

 

 

 

What I have done is find the Specific feed and then dividing that answer by the maximum specific speed of the wheels but I am getting 2.4 while my lecturer found 7 somehow as the final value. If someone can help it would be appreciated.

 

I used:

 

Specific Speed: N_{s =} NP^0.5 / H^5/4 = 640 x 27,000^0.5 / 280^{5/4 =} 91.82 / 40 = 2.3 ???/ i NEED TO GET 7. i PROBABLY AM USING THE WRONG METHOD so any help would be appreciated