centrifugal pump discharge formula

The discharge (Q) of a centrifugal pump refers to the volume of fluid delivered per unit time, typically measured in m³/s, L/s, or GPM (gallons per minute). The theoretical discharge can be calculated using the following formula:

1. Basic Discharge Formula (Volumetric Flow Rate)

$$Q=A\times v$$

where:

• $Q$ = Discharge/flow rate (m³/s)

• $A$ = Cross-sectional area of the pipe/discharge outlet (m²)

• For a circular pipe: $A=\frac{\pi d^2}{4}$ (where $d$ = diameter)

• $v$ = Flow velocity at the discharge (m/s)

2. Using Pump Parameters (Theoretical Flow Rate)

For a centrifugal pump, the discharge depends on the impeller dimensions and speed:

$$Q=\pi Db{C}_{m2}$$

where:

• $D$ = Impeller diameter at the outlet (m)

• $b$ = Width of the impeller at the outlet (m)

• $C_{m2}$ = Meridional (radial) component of the absolute velocity at the outlet (m/s)

3. Considering Pump Speed (RPM)

The flow rate can also be approximated using the pump's speed (N) and displacement:

$$Q={\eta }_v\times \frac{N\times V}{60}$$

where:

• ${\eta }_v$ = Volumetric efficiency (typically 0.90–0.98 for centrifugal pumps)

• $N$ = Pump speed (RPM)

• $V$ = Theoretical displacement volume per revolution (m³/rev)

4. Affinity Laws (For Variable Speed)

When pump speed changes, flow rate scales proportionally:

$$\frac{Q_1}{Q_2}=\frac{N_1}{N_2}$$

where:

• $Q_1,Q_2$ = Original and new flow rates

• $N_1,N_2$ = Original and new speeds (RPM)

Practical Considerations

• Actual flow rate may differ due to head losses, friction, and efficiency.

• Pump performance curves provide accurate flow rates at different heads.

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