Respuesta :
Answer:
Power = 9.75 ×10^8[tex]\frac{kgm^2}{s^3}[/tex]
Explanation:
- Power is rate of change of energy.
- Here gravitational energy is transferred to kinetic energy of water at a definite rate.
For one second 650m^3 of water flows out down to 150m oh depth.
So, the energy at a height of 150m is transformed to kinetic energy.
for a second,
650m^3 of water flows down ⇒ (1000kg/m^3 × 650m^3) = 6.5×10^5kg of warer flos down.
The total gravitational potential energy stored in water is
= mass of water × height× gravity
= 6.5 ×10^5 × 150 × 10 = 9.75 ×10^8[tex]\frac{kgm^2}{s^2}[/tex]
As it is transformed in a second it is also equal to Power.
Answer:
power = 1407.77 MW
Explanation:
The basic principle of a hydro electric station is the conversion of potential energy to electrical energy. Here, water is allowed to fall from a height which will increase its the kinetic energy. This high speed flowing water is used to rotate the shaft of a turbine which will in turn produce electrical energy.
So here,
power = rate of change of potential energy with respect to time
power = [tex]\frac{d(mgh)}{dt}[/tex]
where,
m = mass of water
g = acceleration due to gravity
h = height through which the water falls
here h and g are constants ( h is the total height through which the water falls and it doesn't change with time). Therefore we can take them out of differentiation.
thus,
power = gh[tex]\frac{d(m)}{dt}[/tex]
now,
m = ρV
where,
ρ = density
V = volume
substituting this in the above equation we get,
power = gh[tex]\frac{d(ρV)}{dt}[/tex]
again ρ is a constant. Thus,
power = ρgh[tex]\frac{d(V)}{dt}[/tex]
Given that,
h = 221 m
[tex]\frac{d(V)}{dt}[/tex] = 650 [tex]m^{3}[/tex]/s
g = 9.8 m/[tex]s^{2}[/tex]
ρ = 1000 kg/[tex]m^{3}[/tex]
substituting these values in the above equation
power = 1000 x 9.8 x 221 x 650
power = 1407.77 MW
