Question

At a ski resort, water at 40°F is pumped through a 3-in-diameter, 2000-ft-long steel pipe from a pond at an elevation of 4286 ft to a snow-making machine at an elevation of 4623 ft at a rate of 0.26 ft³/s. If it is necessary to maintain a pressure of 180 psi (gage pressure) at the snow-making machine, determine the horsepower added to the water by the pump. Neglect minor losses.

a) 20.5 HP
b) 23.7 HP
c) 25.9 HP
d) 28.1 HP

Answer 1

The horsepower added to the water by the pump can be calculated using the formula: Power = (Flow rate x Pressure)/(550). The horsepower added to the water by the pump is 63 HP.

Step-by-step explanation:

The horsepower added to the water by the pump can be calculated using the formula:

Power = (Flow rate x Pressure)/(550)

where the flow rate is given as 0.26 ft³/s and the pressure is given as 180 psi (gage pressure). Converting the units to consistent values, we have:

Flow rate = 0.26 ft³/s x 7.481 gal/ft³ x 231 in³/gal x 0.004329 m³/in³ = 0.021 m³/s

Pressure = 180 psi x 6895 N/m²/psi = 1241100 N/m²

Substituting these values into the formula, we get:

Power = (0.021 m³/s x 1241100 N/m²)/(550) = 47.1 kW

Converting this power value to horsepower, we get:

Horsepower = 47.1 kW x 1.341 hp/kW = 63.1 hp

Rounding this value to the nearest whole number, the horsepower added to the water by the pump is 63 HP.