1. An electric pump, used to obtain water from 20 metres below the ground, is marked 5000W.
a) If the pump operates as rated, how much energy is used to pump water every second?
b) Describe the energy conversions that take place when the pump is used.
c) What is the maximum mass of water that can be brought to the surface every second, and then discharged at 10 metres per second.
a. 5000 Watts = 5,000 J/s = 5000 Joules
every second.
a)p=Wnc÷time
5000=Wnc÷1s
Wnc=5000
a) To calculate the energy used to pump water every second, we need to determine the power consumption of the electric pump. Power is measured in watts (W). In this case, the pump is marked with a power rating of 5000W. This means that it is consuming 5000 joules of energy every second.
b) When the electric pump is used, several energy conversions take place. Firstly, the electrical energy from the power source is converted into mechanical energy in the pump itself. This mechanical energy is then used to move the water from the underground source to the surface. Therefore, the energy conversions involved are from electrical to mechanical energy.
c) To calculate the maximum mass of water that can be brought to the surface every second and then discharged at a given speed, we need to consider both the power of the pump and the velocity of the water.
First, let's calculate the water's potential energy at a depth of 20 meters. The potential energy can be determined using the formula:
Potential energy = mass * gravitational acceleration * height
Assuming gravitational acceleration is approximately 9.8 m/s², the potential energy per kilogram of water can be calculated as:
Potential energy per kilogram = 9.8 m/s² * 20 meters = 196 joules
Since the pump consumes 5000 joules of energy every second (as calculated in part a), we can find the maximum mass of water that can be brought to the surface by dividing the energy consumed by the potential energy per kilogram:
Maximum mass of water = 5000 joules / 196 joules per kilogram = 25.51 kilograms
Therefore, the maximum mass of water that can be brought to the surface every second is approximately 25.51 kilograms.
If this water is then discharged at a velocity of 10 meters per second, the amount of water that can be discharged per second is equal to the mass flow rate, which is calculated as:
Mass flow rate = mass of water / time
Assuming the entire mass of water is discharged in one second, the mass flow rate will be equal to the maximum mass of water calculated above:
Mass flow rate = 25.51 kilograms
Therefore, the maximum mass of water that can be discharged at a velocity of 10 meters per second is also approximately 25.51 kilograms.