centrifugal pump pressure and flow rate​

In a centrifugal pump, pressure (often measured as head) and flow rate are interrelated and determined by the pump's design, operating conditions, and system characteristics. Here’s a breakdown of their relationship:

1. Pressure (Head) in a Centrifugal Pump

• Head (H) is the energy imparted by the pump per unit weight of the fluid, typically expressed in meters (m) or feet (ft).

• Pressure (P) is related to head by:

  $$\mathrm{<span\; style="font-size:\; 18px;">P</span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}<span\; style="font-size:\; 18px;">\cdot </span>\mathrm{<span\; style="font-size:\; 18px;">g</span>}<span\; style="font-size:\; 18px;">\cdot </span>\mathrm{<span\; style="font-size:\; 18px;">H</span>}$$P=ρ⋅g⋅H

  where:

• $\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}$ρ = fluid density (kg/m³)

• $\mathrm{<span\; style="font-size:\; 18px;">g</span>}$g = acceleration due to gravity (9.81 m/s²)

• $\mathrm{<span\; style="font-size:\; 18px;">H</span>}$H = pump head (m)

• Centrifugal pumps generate higher pressure (head) at lower flow rates and lower pressure at higher flow rates due to energy losses and fluid dynamics.

2. Flow Rate (Q)

• Volumetric flow rate (Q) is the volume of fluid delivered per unit time (m³/s, L/min, or GPM).

• Depends on:

• Pump speed (RPM)

• Impeller diameter

• System resistance (pipe friction, valves, elevation changes)

3. Pump Performance Curve

• A centrifugal pump's performance is represented by a H-Q curve (Head vs. Flow Rate).

• Head decreases as flow rate increases (due to friction and dynamic losses).

• Power consumption increases with flow rate.

• Efficiency peaks at the Best Efficiency Point (BEP).

Example Performance Curve:

4. System Resistance Curve

• The actual operating point is where the pump curve intersects the system curve (resistance due to pipes, valves, and fittings).

• Higher system resistance → Lower flow rate, higher pressure.

• Lower resistance → Higher flow rate, lower pressure.

5. Key Factors Affecting Pressure & Flow

• Impeller Diameter: Larger impellers increase head and flow.

• Pump Speed (RPM): Higher RPM increases both head and flow (affinity laws apply).

• Fluid Viscosity: Thicker fluids reduce flow rate and increase required pressure.

• Cavitation: Low suction pressure can reduce flow and damage the pump.

6. Affinity Laws (for Speed & Impeller Changes)

For changes in pump speed (N) or impeller diameter (D):

$$\frac{{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">=</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">=</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}$$Q1Q2=N1N2=D1D2$$\frac{{\mathrm{<span\; style="font-size:\; 18px;">H</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">H</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">=</span>{<span\; style="font-size:\; 18px;">(</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">)</span>}^{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}<span\; style="font-size:\; 18px;">=</span>{<span\; style="font-size:\; 18px;">(</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">)</span>}^{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}$$H1H2=(N1N2)2=(D1D2)2$$\frac{{\mathrm{<span\; style="font-size:\; 18px;">P</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">P</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">=</span>{<span\; style="font-size:\; 18px;">(</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">)</span>}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}<span\; style="font-size:\; 18px;">=</span>{<span\; style="font-size:\; 18px;">(</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">)</span>}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}$$P1P2=(N1N2)3=(D1D2)3

Conclusion

• High flow rate → Lower pressure (and vice versa).

• The pump operates at the intersection of its H-Q curve and the system curve.

• Proper selection ensures the pump runs near its BEP for efficiency.

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