Question

Following are the statements pertaining to power in pumps :
(A) The efficiency of any given pump (\(\eta\)) is a ratio defined as the water horsepower out divided by the mechanical horsepower into the pump
(B) No pump can convert all of its mechanical power into water power
(C) Mechanical power is lost in the pumping process due to friction and other physical losses
(D) It is because of these losses that the horsepower going into the pump must be greater than the water horsepower leaving the pump
Choose the correct answer from the options given below:

• A. (A), (B) and (D) only.
• B. (A), (B) and (C) only.
• C. (A), (B), (C) and (D) only.
• D. (B), (C) and (D) only.

Hint:

Remember the power relationship in pumps:
\[ \text{Shaft Power (Input)} = \text{Water Power (Output)} + \text{Losses} \]
Since losses are always positive in any real system, Input Power is always greater than Output Power, and efficiency (\(\eta\)) is always less than 1.0 (100%).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Centrifugal and other water pumps require mechanical energy input to move water and increase its pressure (hydraulic head).
The efficiency of a pump represents its effectiveness in converting input mechanical power (shaft power) into output hydraulic power (water power).

Step 2: Detailed Explanation:
Let us evaluate each of the given statements:
- Statement (A): The efficiency of a pump (\(\eta\)) is mathematically defined as:
\[ \eta = \frac{\text{Power Output (Water Horsepower)}}{\text{Power Input (Shaft/Mechanical Horsepower)}} \]
Thus, Statement (A) is correct.
- Statement (B): According to the second law of thermodynamics, no real machine can be 100% efficient.
Therefore, no pump can convert 100% of its input mechanical power into water power.
Thus, Statement (B) is correct.
- Statement (C): During the pumping process, mechanical power is lost due to several physical factors:
1. Hydraulic losses (friction in the impeller and casing, turbulence, and eddy currents).
2. Mechanical losses (friction in bearings, gland packings, and seals).
3. Volumetric losses (leakage of fluid from high-pressure to low-pressure areas).
Thus, Statement (C) is correct.
- Statement (D): Because of these cumulative losses, the input power must always be greater than the output water power to overcome friction and deliver the required flow.
Thus, the input shaft power is always greater than the water power.
Thus, Statement (D) is correct.
Since all four statements are completely correct, Option (C) is the right choice.

Step 3: Final Answer:
The correct option is (C).