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Answer :
Final Answer:
The horsepower added to the water by the pump is approximately [tex]\(109.65 \, \text{hp}\)[/tex].
Explanation:
To calculate the horsepower added by the pump, we can use the following formula:
[tex]\[ P = \frac{\rho Q H}{550} \][/tex]
where P is the power in horsepower, rho is the density of water, Q is the volumetric flow rate, and H is the total head. The total head is given by the sum of the elevation head, pressure head, and velocity head. Given the data, we can calculate the total head using the formula:
[tex]\[ H = \frac{P}{\gamma} + \frac{V^2}{2g} + Z \][/tex]
where \(P\) is the pressure, \(\gamma\) is the specific weight of water, V is the velocity, g is the acceleration due to gravity, and Z is the elevation.
Substituting the known values, including the flow rate [tex]\(Q = 0.26 \, \text{ft}^3/\text{s}\)[/tex], and solving for the power P, we find that the horsepower added to the water by the pump is approximately [tex]\(109.65 \[/tex], [tex]\text{hp}\)[/tex]. This result represents the power required to pump water through the steel pipe to maintain the specified pressure at the snow making machine.
Understanding the power requirements in fluid systems is crucial in engineering applications, such as the design of water supply or snow-making systems. The calculation involves considerations of fluid properties, pipe characteristics, and elevation changes, providing insights into the energy demands of the pumping process.
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