A water pump produces 20m^3/h at a height of 80m.The pump is driven by a diesel engine that develops 7kW to produce the water.
1.calculate work done per hour
2. Calculate power required to produce the water at a height of 80m
3. Calculate the efficiency of the pump
To calculate the answers to these questions, we need to use relevant equations and formulas. Here's a step-by-step explanation of how to solve each:
1. Calculating the work done per hour:
In this scenario, the work done by the pump per hour is equal to the energy consumed by the diesel engine. The energy can be calculated using the equation:
Energy (in Joules) = Power (in watts) x Time (in seconds)
Given that the diesel engine develops 7 kW (or 7000 W), and we need to calculate the energy per hour, which is 3600 seconds, we can substitute the values into the formula:
Energy (in Joules) = 7000 W x 3600 s
To get the work done, we can convert the energy into work using the equation:
Work (in Joules) = Energy (in Joules)
Now we can calculate the work done per hour.
2. Calculating the power required to produce the water at a height of 80 m:
The power required to raise an object vertically against gravity can be calculated using the equation:
Power (in watts) = Work (in Joules) / Time (in seconds)
In this case, the work done is equal to the weight of water lifted, which is the product of mass and gravity:
Work (in Joules) = Mass (in kg) x Gravity (in m/s^2) x Height (in meters)
To calculate the mass of water, we can use the given flow rate of 20 m^3/h. However, we need to convert it to kg/s, since power is calculated per second:
Mass (in kg) = Flow rate (in m^3/s) x Density of water (in kg/m^3)
The density of water is approximately 1000 kg/m^3.
Now we can substitute the values into the power equation to calculate the power required.
3. Calculating the efficiency of the pump:
Efficiency is defined as the ratio of useful output energy or work to the input energy or work. In this case, the useful output energy is the work done by the pump, and the input energy is the energy consumed by the diesel engine.
Efficiency (%) = (Work done by the pump / Energy consumed by the engine) x 100
We have already calculated the work done by the pump and the energy consumed by the engine, so we can substitute those values into the efficiency equation to find the efficiency percentage.
By following these steps and performing the necessary calculations, you can find the answers to each question.
water weighs 997kg/m^3 * 9.81N/kg = 9780.57 N/m^3
work = force * distance = 9780.57N * 80m = 782445 N-m/hr
Now use power = 1W = 1N/s
and divide to find the efficiency