Question

For a centrifugal pump with a specific impeller diameter, operating at a fixed speed and handling a fluid of constant density

• A. NPSH required decreases with increase in the capacity
• B. NPSH available increases with increase in the capacity
• C. NPSH required increases with increase in the capacity
• D. NPSH available decreases with decrease in the capacity

Hint:

As pump flow capacity (\(Q\)) increases: - \(\text{NPSH}_{\text{required}}\) (\(\text{NPSH}_R\)) increases (due to high internal velocities and friction). - \(\text{NPSH}_{\text{available}}\) (\(\text{NPSH}_A\)) decreases (due to increased suction line friction losses).

Answer 1

The Correct Option is C

Concept: Net Positive Suction Head (NPSH) is a critical metric used to ensure a centrifugal pump operates smoothly without encountering the damaging effects of cavitation. It is broadly categorized into two distinct forms:

• \(\text{NPSH}_{\text{available}}\) (\(\text{NPSH}_A\)): A property of the external suction piping system layout. It represents the actual fluid pressure head at the suction nozzle of the pump.

• \(\text{NPSH}_{\text{required}}\) (\(\text{NPSH}_R\)): A design property inherent to the internal geometry of the pump impeller. It represents the minimum pressure head needed at the pump inlet to prevent fluid vaporization.

Step 1: Analyzing \(\text{NPSH}_{\text{required}}\) as a function of pump capacity (flow rate).
The capacity or volumetric flow rate handled by the centrifugal pump is denoted as \( Q \). As the capacity \( Q \) through the pump increases, the velocity of the fluid entering the suction eye of the impeller increases proportionally (\( v \propto Q \)). According to Bernoulli's principle, an increase in fluid velocity causes a corresponding drop in static pressure head, as given by the kinetic energy term: \[ h_v = \frac{v^2}{2g} \propto Q^2 \]

Step 2: Evaluating internal pressure losses at high flow rates.
Additionally, internal fluid friction and turbulence losses within the suction passages of the pump increase quadratically with higher volumetric flow rates. To counteract these severe pressure drops and prevent the fluid's static pressure from falling below its vapor pressure inside the impeller eye, the pump demands a higher external suction pressure head. Therefore, the \(\text{NPSH}_{\text{required}}\) increases continuously with an increase in the operating capacity of the pump.

Step 3: Evaluating why other options are incorrect.
Let's look at how \(\text{NPSH}_{\text{available}}\) behaves in the suction system: \[ \text{NPSH}_A = H_{\text{atm}} \pm H_s - H_f - H_v \] As capacity \( Q \) increases, the suction piping friction loss (\( H_f \propto Q^2 \)) increases, which causes \(\text{NPSH}_A\) to decrease. Thus, Option (B) and Option (D) present incorrect behavioral trends, leaving Option (C) as the correct choice.