How do I calculate the answer to this question about power and efficiency?

Question

A hydroelectric dam generates 50 MW of power at an efficiency of 80%. If the water level is 400m above the height of the generator, calculate the flow of water (in kg s-1) from the dam. How do I calculate this answer?

Answers

a) 40 kg s-1

b) 8.6*10^3 kg s-1

c) 1.6*10^4 kg s-1

d) 1.3*10^4 kg s-1

e) 1.0*10^4 kg s-1

Answer 1

Power= 50MW  

80% Efficiencyency

input= (50/0.8) = 62.5 MW.

if the water is flowing freely without any external force, the energy here is potential energy (PE)



PE= mgh

m= mass

g=gravitational force

h=height

I dont know what is the value of m here?????

If i take m=1,

PE =1*9.8*400 = 3920 kgm2/s2        

62.5*1000000/3920 = 1.3*10^4 Kg/sec

Answer 2

with 50MW and 80% effiiency, that means the input is 50/.8 = 62.5 MW.

One kg of water falling 400 m has this much energy:

PE = hmg = 1*9.8*400 = 3920 J

62.5 MW is 62.5 MJ per second.

62.5 MJ/3920 = 15944 per second, or in this casse, 15944 kg/sec (c)

.

Answer 3

This is the same as the tea urn question which is a favourite mathematical modelling problem, to get students to see that the flow is reduced as the level in the urn gets lower, the flow rate is - dv/dt, the equ V = Vo exp -kt is used substitute -at/pi r  squared for -kt and solve,

besides the height you should have been given an area of water.

I'm puzzled by the 5 answers unless this is a multi-choice question, as it could relate to reduced output from the generator as the water level drops.

Footnote

from a foundation course in technology there are 3.6MJ in one Kilowatt