Questions: A flow of 300 gpm is pumped against a head of 75 feet. The pump is 80% efficient and the motor is 85% efficient. What is the Motor HP? 6.2 HP 9.5 HP 8.4 HP 7.3 HP

Solution Steps

First, we need to convert the flow rate from gallons per minute (gpm) to cubic feet per second (cfs).

1 gallon = 0.1337 cubic feet

\[ 300 \, \text{gpm} \times \frac{0.1337 \, \text{cubic feet}}{1 \, \text{gallon}} \times \frac{1 \, \text{minute}}{60 \, \text{seconds}} = 0.6685 \, \text{cfs} \]

Hydraulic horsepower (HP) is calculated using the formula:

\[ \text{Hydraulic HP} = \frac{\text{Flow (cfs)} \times \text{Head (ft)} \times \text{Weight of Water (lb/ft}^3\text{)}}{550} \]

The weight of water is approximately 62.4 lb/ft³.

\[ \text{Hydraulic HP} = \frac{0.6685 \, \text{cfs} \times 75 \, \text{ft} \times 62.4 \, \text{lb/ft}^3}{550} = 5.6782 \, \text{HP} \]

Brake horsepower (BHP) accounts for the efficiency of the pump. It is calculated as:

\[ \text{BHP} = \frac{\text{Hydraulic HP}}{\text{Pump Efficiency}} \]

Given the pump efficiency is 80% (or 0.80):

\[ \text{BHP} = \frac{5.6782 \, \text{HP}}{0.80} = 7.0978 \, \text{HP} \]

Motor horsepower (Motor HP) accounts for the efficiency of the motor. It is calculated as:

\[ \text{Motor HP} = \frac{\text{BHP}}{\text{Motor Efficiency}} \]

Given the motor efficiency is 85% (or 0.85):

\[ \text{Motor HP} = \frac{7.0978 \, \text{HP}}{0.85} = 8.3503 \, \text{HP} \]

Final Answer