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Some electric-power companies use water to store energy. Water is pumped by reversible turbine pumps from a low to a high reservoir. To store the energy produced in 1 hour by a 120 MW electric-power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is 470 m above the lower and we can neglect the small change in depths within each. Water has a mass of 1000 kg for every 1.0{m}^3.

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onyebuchinnaji

The volume of water that will be pumped from the lower to the upper reservoir to generate the energy is 93,790.7 m³.

What is the volume of water needed to generate the power?

The volume of water needed to generate the given power is calculated by applying the law of conservation of energy as shown below.

gravitational potential energy of water or work done by the water = energy generated

Mathematically, the equation is given as;

W = PV

where;

  • W is work done by the water
  • V is the volume of the water
  • P is the pressure of the water

W = (ρgh)V

where;

  • ρ is the density of water
  • g is acceleration due to gravity
  • h is the height through which the water is pumped

(ρgh)V  = Pt

where;

  • P is the power generated
  • t is the time in which the power was generated

V = Pt / ρgh

The given parameters include;

  • P, power = 120 MW = 120 x 10⁶ W
  • t , time = 1 hour = 3600 s
  • ρ, density of water, = 1000 kg/m³
  • g, acceleration due to gravity = 9.8 m/s²
  • h, height of water, = 470 m

The volume of water needed to generate the energy is calculated as follows;

V = (120 x 10⁶ x 3600) / (1000 x 9.8 x 470)

V = 93,790.7 m³

Learn more about volume of water here: https://brainly.com/question/19491767

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