Question

The impeller Diameter (\(D\)) Speed (\(N\)), Capacity (\(Q\)), Head (\(H\)) and Brake Horse Power (\(P\)) of centrifugal pump have following characteristics A. \(Q\) varies directly with \(D\) B. \(P\) varies directly with square of \(N\) C. \(H\) varies directly with cube of \(D\) D. \(H\) varies directly with square of \(D\) E. \(P\) varies directly with cube of \(n\) Choose the correct answer from the options given below:

• A. A, B, C Only
• B. B, C, D Only
• C. C, D, E Only
• D. A, D, E Only

Hint:

Pump affinity laws: \[ \boxed{ Q \propto N } \] \[ \boxed{ H \propto N^2 } \] \[ \boxed{ P \propto N^3 } \] Also: \[ \boxed{ H \propto D^2 } \]

Answer 1

The Correct Option is D

Concept: Centrifugal pumps follow affinity laws, which relate:
• Discharge
• Head
• Power with:
• Speed
• Impeller diameter The important affinity laws are: \[ Q \propto ND^3 \] \[ H \propto N^2D^2 \] \[ P \propto N^3D^5 \] For constant diameter or constant speed, simplified proportionalities are obtained.

Step 1: Analyzing Statement A. Statement A says: \[ Q \text{ varies directly with } D \] For constant speed: \[ Q \propto D \] Hence: \[ \boxed{ \text{Statement A is correct} } \]

Step 2: Analyzing Statement B. Statement B says: \[ P \propto N^2 \] From affinity laws: \[ P \propto N^3 \] Therefore: \[ \boxed{ \text{Statement B is incorrect} } \]

Step 3: Analyzing Statement C. Statement C says: \[ H \propto D^3 \] But actually: \[ H \propto D^2 \] Therefore: \[ \boxed{ \text{Statement C is incorrect} } \]

Step 4: Analyzing Statement D. Statement D says: \[ H \propto D^2 \] This is directly obtained from pump affinity laws. Thus: \[ \boxed{ \text{Statement D is correct} } \]

Step 5: Analyzing Statement E. Statement E says: \[ P \propto N^3 \] This is correct according to affinity laws. Thus: \[ \boxed{ \text{Statement E is correct} } \]

Step 6: Selecting the correct combination. Correct statements are: \[ A,\; D,\; E \] Thus: \[ \boxed{ (D)\ A,\ D,\ E\ Only } \] Final Conclusion: Using centrifugal pump affinity laws, the correct relations are: \[ Q \propto D,\qquad H \propto D^2,\qquad P \propto N^3 \] Hence the correct answer is: \[ \boxed{ (D) } \]