Question

Power to be supplied by prime mover with 100 % drive efficiency:
A. Brake Horsepower = Shaft horsepower
B. Water horsepower = Shaft horsepower
C. Water horsepower/pump efficiency = Shaft horsepower
D. Input horsepower = Shaft horsepower
E. Horsepower = Shaft horsepower
Choose the correct answer from the options given below:

• A. B and C only
• B. A and C only
• C. A and D only
• D. C and E only

Hint:

Keep the power transmission sequence in mind:
$\text{Prime Mover (BHP)} \rightarrow [\text{Drive Transmission}] \rightarrow \text{Pump Shaft (SHP)} \rightarrow [\text{Pump Impeller}] \rightarrow \text{Water (WHP)}$.
Losses occur at each step, unless an efficiency of $100\%$ is specified.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Evaluating pump performance involves understanding the relationship between the different stages of power transmission:
1. Water Horsepower (WHP): The theoretical power delivered directly to the water.
2. Shaft Horsepower (SHP): The actual power delivered to the pump shaft.
3. Brake Horsepower (BHP): The power supplied by the engine or prime mover to the drive system.

Step 2: Detailed Explanation:
Let us analyze the power relationships under $100\%$ drive efficiency:
- Relation 1 (A):
Brake Horsepower ($\text{BHP}$) is the power output of the prime mover.
Shaft Horsepower ($\text{SHP}$) is the power that reaches the pump shaft.
The relationship between them is: \[ \text{SHP} = \text{BHP} \times \eta_d \] where $\eta_d$ is the drive transmission efficiency.
Since the drive efficiency is $100\%$ ($\eta_d = 1.0$), we have: \[ \text{BHP} = \text{SHP} \] Therefore, statement A is correct.
- Relation 2 (C):
The power delivered to the water ($\text{WHP}$) is less than the power delivered to the shaft ($\text{SHP}$) due to mechanical and hydraulic losses inside the pump.
The pump efficiency ($\eta_p$) is: \[ \eta_p = \frac{\text{WHP}}{\text{SHP}} \] Rearranging this equation to solve for Shaft Horsepower: \[ \text{SHP} = \frac{\text{WHP}}{\eta_p} \] Therefore, statement C is correct.
- Other Statements (B, D, E):
- Statement B ($\text{WHP} = \text{SHP}$) is only true if the pump is $100\%$ efficient, which is physically impossible.
- Statements D and E use non-standard terms that do not accurately represent these specific mechanical relationships.
Thus, only statements A and C are correct.

Step 3: Final Answer:
Under $100\%$ drive efficiency, Brake Horsepower equals Shaft Horsepower (A), and Shaft Horsepower equals Water Horsepower divided by pump efficiency (C).
Hence, the correct option is (B).