An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?
Power is the rate at which work is done or energy is transferred over time. It is calculated using the formula Power = Work done / Time taken. The SI unit of power is the watt where one watt equals one joule per second. Power is essential in various physical and engineering applications.
Class 11 Physics Chapter 5 Work, Energy and Power explores essential concepts such as work done energy forms and power definitions. It highlights the relationship between kinetic and potential energy emphasizes conservation of energy and provides mathematical expressions and practical examples to enhance comprehension in preparation for CBSE EXAM 2024-25.
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To calculate the power of the engine, we can use the formula for power related to the flow of water through the hose:
Power (P) = (mass flow rate) × (velocity)² / 2
Step 1: Calculate the mass flow rate
Mass per unit length of water = 100 kg/m
Velocity of water = 2 m/s
The mass flow rate (ṁ) can be calculated as:
ṁ = (mass per unit length) × (velocity)
ṁ = 100 kg/m × 2 m/s
ṁ = 200 kg/s
Step 2: Calculate the power
Now using the power formula:
P = (ṁ × v²) / 2
P = (200 kg/s × (2 m/s)²) / 2
P = (200 kg/s × 4 m²/s²) / 2
P = (800 kg·m²/s³) / 2
P = 400 W
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