The mechanical efficiency of a particular...

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Question 1 of 205eccef9dbacbc34ba4d45de2

The mechanical efficiency of a particular centrifugal bilge pump is 92.5%. What is the smallest horsepower motor that can effectively operate this pump at a capacity of 100 gpm with a discharge head of 15 feet?

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🔍 Key Concepts

• Hydraulic horsepower for pumps using flow (gpm) and head (feet) • Relationship between mechanical efficiency and required motor horsepower • Unit conversion between gpm, feet of head, and horsepower

💭 Think About

• How do you compute the hydraulic horsepower of a pump from its capacity in gpm and the discharge head in feet? Write that formula first. • Once you know the hydraulic horsepower, how does a mechanical efficiency of 92.5% change the motor horsepower you must supply? Should the motor HP be greater or less than the hydraulic HP? • After calculating the required motor horsepower, which listed option is the smallest standard size that is still large enough to meet or exceed that requirement?

✅ Before You Answer

• Use the standard pump formula: ( \text{HP}\text{hydraulic} = \frac{Q(\text{gpm}) \times H(\text{ft})}{3960} ). Double-check your substitution of 100 gpm and 15 ft. • Apply efficiency correctly: ( \text{HP}\text{motor} = \frac{\text{HP}_\text{hydraulic}}{\text{efficiency}} ), with 92.5% written as 0.925, not 92.5. • Compare your numerical result to the answer choices and pick the smallest HP value that is not less than your required motor HP.

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