A water tank measuring 4 m x 4 m x 2m is at an average weight of 10 m above the ground level. How much work has to be done in filling the tank from a reservoir at ground level? What must be the power of an engine working at 80% efficiency if it fills the tank in 100 minutes?
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Verified answer
Explanation:
♪To calculate the work done to fill the water tank and the power required for an engine working at 80% efficiency, we can use the following steps:
1. Calculate the volume of the water tank:
Volume = Length x Width x Height
Volume = 4m x 4m x 2m
Volume = 32 cubic meters
2. Calculate the mass of water to be lifted:
Mass = Volume x Density of Water
Mass = 32 m^3 x 1000 kg/m^3 (density of water)
Mass = 32,000 kg
3. Calculate the height the water needs to be lifted:
Height = 10 m
4. Calculate the work done (in joules) to lift the water to the tank:
Work = Mass x Gravity x Height
Work = 32,000 kg x 9.8 m/s^2 x 10 m
Work = 3,136,000 joules (Joules is equivalent to one newton-meter)
5. Convert the work done to kilojoules:
Work = 3,136,000 joules ÷ 1000
Work = 3136 kilojoules (kJ)
So, the work done to fill the tank is 3136 kilojoules.
6. To find the power required for the engine, we can use the formula for power:
Power = Work / Time
However, the given time is in minutes, so we need to convert it to seconds:
Time = 100 minutes x 60 seconds/minute
Time = 6000 seconds
7. Now, calculate the power:
Power = 3136 kJ ÷ 6000 seconds
Power = 0.52267 kilojoules per second (kW)
8. The engine works at 80% efficiency, so we need to account for that:
Actual Power = Power / Efficiency
Actual Power = 0.52267 kW ÷ 0.80
Actual Power = 0.65334 kW
♦So, the power of the engine working at 80% efficiency to fill the tank in 100 minutes is approximately 0.65334 kilowatts.
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