A centrifugal pump operates at sea level where atmospheric pressure head is $\frac{P_{\text{atm}}}{\gamma} = 10.33\text{ m}$. The suction water level is located at a vertical lift of $h_s = 3.50\text{ m}$ below the pump centerline. Total friction and minor head losses in the suction pipe are $h_{fs} = 0.85\text{ m}$. The saturation vapor pressure head of the water at operating temperature is $\frac{P_v}{\gamma} = 0.43\text{ m}$. The Net Positive Suction Head Available ($NPSH_a$) at the pump inlet in meters is ________ (round off to two decimal places).
Answer Key:
5.55
Step-by-Step Solution & Explanation
**Method 1: Head Balance from Water Sump to Impeller Eye**
1. By definition, $NPSH_a$ is the total absolute head above vapor pressure head at the pump suction nozzle:
$NPSH_a = \frac{P_{\text{atm}}}{\gamma} - h_s - h_{fs} - \frac{P_v}{\gamma}$
2. Substituting given values:
- Atmospheric head $\frac{P_{\text{atm}}}{\gamma} = 10.33\text{ m}$
- Suction static lift $h_s = 3.50\text{ m}$
- Suction friction loss $h_{fs} = 0.85\text{ m}$
- Vapor pressure head $\frac{P_v}{\gamma} = 0.43\text{ m}$
3. Evaluating $NPSH_a$:
$NPSH_a = 10.33 - 3.50 - 0.85 - 0.43 = 10.33 - 4.78 = 5.55\text{ m}$
**Method 2: Net Absolute Pressure at Suction**
$\text{Absolute suction head } H_{\text{suction}} = 10.33 - (3.50 + 0.85) = 10.33 - 4.35 = 5.98\text{ m}$
$NPSH_a = H_{\text{suction}} - \frac{P_v}{\gamma} = 5.98 - 0.43 = 5.55\text{ m}$