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attashe74 [19]
3 years ago
14

Hoover Dam on the Colorado River is the highest dam in the United States at 221m, with a power output of 680 MW. The dam generat

es electricity by flowing water down to a point 150 m below the stop, at an average flow rate of 650 m3/s.
Part (a) Calculate the power in this flow in watts.
Physics
2 answers:
Lapatulllka [165]3 years ago
8 0

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 = \frac{d(mgh)}{dt}

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\frac{d(m)}{dt}

now,

m = ρV

where,

ρ = density

V = volume

substituting this in the above equation we get,

power = gh\frac{d(ρV)}{dt}

again ρ is a constant. Thus,

power = ρgh\frac{d(V)}{dt}

Given that,

h = 221 m

\frac{d(V)}{dt} = 650 m^{3}/s

g = 9.8 m/s^{2}

ρ = 1000 kg/m^{3}

substituting these values in the above equation

power =  1000 x 9.8 x 221 x 650

power = 1407.77 MW

Phantasy [73]3 years ago
4 0

Answer:

<u> Power = 9.75 ×10^8\frac{kgm^2}{s^3}</u>

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

    = <u>mass of water × height× gravity</u>

    = 6.5 ×10^5 × 150 × 10 =  9.75 ×10^8\frac{kgm^2}{s^2}

As it is transformed in a second it is also equal to <u>Power.</u>

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