At what rate can a half-horsepower well pump deliver water to a tank 50 m above the water level

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At what rate can a half-horsepower well pump deliver water...

Key Concepts

Power Conversion

This concept involves converting a given measure of power from one unit to another—in this case, half a horsepower to watts—so that it can be used in standard physical formulas. Accurate power conversion is essential when applying energy balance equations to determine how much work can be performed, such as lifting water to a determined height.

Gravitational Potential Energy

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. When lifting water to an elevated tank, the minimum required energy per unit mass is given by the product of gravitational acceleration and the height. This concept explains how much work must be done to raise each kilogram of water to a specific height.

Mass Flow Rate Calculation

Mass flow rate quantifies the amount of mass moving through a system per unit time. By equating the power available from the pump to the gravitational potential energy given to the water per unit time (using the mgh relationship), one can derive the rate at which water (in kilograms per second) is delivered. This method directly ties the energy supplied to the energy required for lifting the water.

Unit Conversions

Unit conversions are critical in ensuring consistency across different systems of measurement. In this problem, once the mass flow rate in kilograms per second is calculated, it must be converted to volumetric flow rate in gallons per minute using the density of water and volume conversions. This step ensures that the final result is expressed in both common engineering units and practical everyday units.

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