Question

Choose the correct formula/s: \[ \text{A. } Work = Force \times distance \] \[ \text{B. } Power\ received\ at\ the\ pump\ shaft\ is\ given\ by\ P=\rho gQH \] \[ \text{C. } Water\ Horsepower\ (WHP)=\frac{Q(lit/s)\times H(m)}{75} \] \[ \text{D. } Shaft\ Horsepower\ (SHP)=\frac{Water\ Horsepower}{Pump\ efficiency} \] \[ \text{E. } Brake\ Horsepower\ (BHP)=\frac{WHP}{Pump\ efficiency \times Drive\ efficiency} \] Choose the correct answer from the options given below:

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

Hint:

Remember: \[ P=\rho gQH \] gives water power or hydraulic power, not shaft power. Shaft power is greater because pump losses must be considered: \[ SHP=\frac{WHP}{Pump\ efficiency} \]

Answer 1

The Correct Option is C

Concept:
In pump and fluid power calculations, different types of power are used. The main terms are: \[ WHP = \text{Water Horsepower} \] \[ SHP = \text{Shaft Horsepower} \] \[ BHP = \text{Brake Horsepower} \] Water horsepower is the useful power given to water. Shaft horsepower is the power supplied at the pump shaft. Brake horsepower is the power supplied by the driving machine or motor to the shaft. Because of losses in the pump and drive system, the power required at the shaft or motor is generally greater than the useful water horsepower.

Step 1: Checking formula A.
Formula A is: \[ Work = Force \times distance \] This is the standard formula of work done when force acts in the direction of displacement. So, statement A is correct. \[ A \Rightarrow Correct \]

Step 2: Checking formula B.
Formula B is: \[ P = \rho gQH \] Here, \[ \rho = \text{density of water} \] \[ g = \text{acceleration due to gravity} \] \[ Q = \text{discharge} \] \[ H = \text{head} \] The formula: \[ P = \rho gQH \] gives the hydraulic power or water power. It represents the useful power delivered to water. But the statement says that this is the power received at the pump shaft. Power at the pump shaft should include pump efficiency. Actually, \[ Shaft\ Power = \frac{\rho gQH}{Pump\ efficiency} \] Therefore, statement B is not correct. \[ B \Rightarrow Incorrect \]

Step 3: Checking formula C.
Formula C is: \[ Water\ Horsepower\ (WHP)=\frac{Q(lit/s)\times H(m)}{75} \] When discharge is given in litre per second and head is given in metre, the water horsepower is calculated as: \[ WHP = \frac{Q \times H}{75} \] This is a standard formula in metric horsepower. So, statement C is correct. \[ C \Rightarrow Correct \]

Step 4: Checking formula D.
Formula D is: \[ Shaft\ Horsepower\ (SHP)=\frac{Water\ Horsepower}{Pump\ efficiency} \] Pump efficiency is given by: \[ Pump\ efficiency = \frac{Water\ Horsepower}{Shaft\ Horsepower} \] Rearranging the formula: \[ Shaft\ Horsepower = \frac{Water\ Horsepower}{Pump\ efficiency} \] Therefore, statement D is correct. \[ D \Rightarrow Correct \]

Step 5: Checking formula E.
Formula E is: \[ BHP=\frac{WHP}{Pump\ efficiency \times Drive\ efficiency} \] This formula is used when both pump efficiency and drive efficiency are considered. But in the given options, there is no option containing A, C, D and E only. Also, the option containing E includes B also, and statement B is incorrect because \(\rho gQH\) is hydraulic power, not shaft power. So, according to the given options, the correct combination is: \[ A,\ C,\ D \]

Step 6: Final conclusion.
The correct statements are: \[ A,\ C,\ D \] Hence, the correct answer is: \[ \boxed{\text{(C) A, C and D only}} \]