A pump is required to raise 600 litres of fresh water a vertical distance of 120m. If the efficiency of the pump is
45%, how much work must be done on the pump to raise the water?
(600*9.81 * 120)/0.45 = ____
To find out how much work must be done on the pump to raise the water, we can use the equation:
Work = Force * Distance
First, we need to calculate the force required to lift the water. The force required can be found using the equation:
Force = Mass * Gravity
The mass of the water can be calculated using the density formula:
Density = Mass / Volume
Since we know the volume of water (600 liters) and the density of fresh water (1000 kg/m^3), we can calculate the mass of the water:
Mass = Density * Volume
Next, we can calculate the force:
Force = Mass * Gravity
The force required to lift the water will be equal to its weight, which is the mass of the water multiplied by the acceleration due to gravity (9.8 m/s^2).
Now, we need to calculate the work done by the pump. Since the efficiency of the pump is given as 45%, it means that only 45% of the input energy is converted into useful work. The remaining 55% is lost as heat or other forms of energy.
Efficiency = (Useful Work Output / Input Energy) * 100
Rearranging the equation, we get:
Useful Work Output = (Efficiency / 100) * Input Energy
The input energy is the work done on the pump. Therefore, the equation becomes:
Work Done = Useful Work Output / (Efficiency / 100)
We can substitute the value of the force into the equation for work to find the work done on the pump:
Work Done = Force * Distance
Finally, we can plug in the given values:
Density of fresh water = 1000 kg/m^3
Volume of water = 600 liters = 0.6 m^3
Distance = 120 m
Efficiency = 45%
1. Calculate the mass of the water:
Mass = Density * Volume
Mass = 1000 kg/m^3 * 0.6 m^3
2. Calculate the force required to lift the water:
Force = Mass * Gravity
Force = Mass * 9.8 m/s^2
3. Calculate the work done on the pump:
Work Done = Force * Distance
Finally, plug in the values and calculate the work done on the pump.
To calculate the work done by the pump, we need to use the formula:
Work = force x distance
In this case, force is the weight of the water being lifted, given by the formula:
Force = mass x gravity
First, let's calculate the mass of the water:
Mass = Volume x Density
Since the volume of water is given as 600 liters, and 1 liter of water has a mass of 1 kg, the mass of water is:
Mass = 600 kg
Next, we can calculate the force:
Force = Mass x gravity
= 600 kg x 9.8 m/s^2
= 5880 N
Now, we can calculate the work done by the pump:
Work = Force x distance
= 5880 N x 120 m
= 705600 J
However, the efficiency of the pump is given as 45%. This means that only 45% of the work is done effectively, while the remaining 55% is lost as waste heat.
To find the amount of work done by the pump, we can multiply the calculated work by the efficiency:
Effective Work = Work x Efficiency
= 705600 J x 0.45
= 317520 J
Therefore, the amount of work that must be done on the pump to raise the water is 317,520 Joules.