Pump Power Calculation Explained
To determine the power required for the pump, we calculate the energy added to the water per unit time. This includes the energy needed to lift the water (potential energy) and the energy needed to give it velocity (kinetic energy).
Input Parameters
- Mass flow rate: 600 kg/min
- Lift height (\(h\)): 25 m
- Ejection speed (\(v\)): 50 m/s
- Gravitational acceleration (\(g\)): 10 m/s2
Step 1: Convert Mass Flow Rate to kg/s
Consistent units are essential for calculations. Convert the mass flow rate from kg/min to kg/s.
Mass flow rate (\(Q_m\)) = \(\frac{600 \text{ kg}}{60 \text{ s}} = 10 \text{ kg/s}\)
Step 2: Calculate Power for Potential Energy
This is the power required to lift the water against gravity.
Power (\(P_{PE}\)) = Mass flow rate \(\times g \times h\)
\(P_{PE} = Q_m \times g \times h = 10 \text{ kg/s} \times 10 \text{ m/s}^2 \times 25 \text{ m} = 2500 \text{ W}\)
\(P_{PE} = 2.5 \text{ kW}\)
Step 3: Calculate Power for Kinetic Energy
This is the power required to accelerate the water to the ejection speed.
Power (\(P_{KE}\)) = \(\frac{1}{2} \times\) Mass flow rate \(\times v^2\)
\(P_{KE} = \frac{1}{2} \times Q_m \times v^2 = \frac{1}{2} \times 10 \text{ kg/s} \times (50 \text{ m/s})^2\)
\(P_{KE} = 5 \text{ kg/s} \times 2500 \text{ m}^2/\text{s}^2 = 12500 \text{ W}\)
\(P_{KE} = 12.5 \text{ kW}\)
Step 4: Determine Total Power
The total power required is the sum of the power needed for potential energy and kinetic energy.
Total Power (\(P_{Total}\)) = \(P_{PE} + P_{KE}\)
\(P_{Total} = 2.5 \text{ kW} + 12.5 \text{ kW} = 15.0 \text{ kW}\)
Similar Questions
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- An object of mass 1 kg is moving with a velocity 10 m/s. Find the kinetic energy of the object.
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Important Questions from Work Power and Energy
Which of the following is an example of potential energy?
_______ is one of the chemical used to produce Ocean Thermal Energy.
A body of mass 2kg is thrown up vertically with a kinetic energy of 500J. If the acceleration due to gravity is 10 m/s2, the height at which the kinetic energy of the body becomes half of the original values is _____
Arjun has a mass of 50 kg, he eats banana of 1000 calories. If this energy is used up to lift him from the ground, the height to which he can climb is _______. Take g = 10 m/s2 and 1 calories = 4.2 Joule.
When a body of mass 'm' attains a velocity 'v' from rest in time 't', then kinetic energy of translation is:
