Question

On a day with no wind a fountain in Switzerland propels 30000 kg of water per minute to a height of 140m. Calculate the power used in raising the water

Answer 1

To calculate the power used in raising the water, you can use the formula for power:

Power = (Work Done) / (Time)

In this case, the work done is equal to the potential energy gained by the water as it's lifted to a height of 140 meters. The formula for potential energy is:

Potential Energy = (Mass) * (Gravity) * (Height)

Where:
- Mass (m) = 30,000 kg
- Gravity (g) ≈ 9.81 m/s² (standard value on Earth)
- Height (h) = 140 meters

Now, calculate the potential energy:

Potential Energy = (30,000 kg) * (9.81 m/s²) * (140 m)

Next, you need to calculate the work done in one minute (60 seconds) since the water is propelled per minute:

Work Done = Potential Energy

Now, calculate the power:

Power = Work Done / Time

Power = (Potential Energy) / (60 seconds)

Plug in the values:

Power = [(30,000 kg) * (9.81 m/s²) * (140 m)] / 60 s

Calculate the power:

Power ≈ 49,005 watts (W)

So, the power used in raising the water is approximately 49,005 watts or 49.005 kilowatts (kW).