Relationship between head and flow rate of centrifugal pumps

Relationship Between Head and Flow Rate in Centrifugal Pumps

The head (H) and flow rate (Q) of a centrifugal pump have an interdependent relationship, typically represented by the pump performance curve. Understanding this relationship is crucial for proper pump selection and operation.

1. Basic Head-Flow Relationship

• Head (H): The energy imparted to the fluid, expressed in meters (m) or feet (ft) of liquid column.

• Flow Rate (Q): The volume of liquid delivered per unit time (m³/h, L/s, GPM).

General Trend:

• As flow rate (Q) increases, head (H) decreases (for a fixed impeller speed).

• At zero flow (shutoff head), head is maximum.

• At maximum flow, head drops to its minimum.

This relationship is plotted as the H-Q curve (pump characteristic curve).

2. Why Does Head Decrease with Flow Rate?

• Higher flow rates increase friction losses (in pipes, impeller, volute).

• Recirculation & turbulence reduce energy transfer efficiency.

• Velocity head conversion becomes less effective at high flows.

3. Pump Performance Curve (H-Q Curve)

A typical centrifugal pump curve shows:

• Head (H) vs. Flow Rate (Q) – Declining curve.

• Efficiency (η) curve – Peaks at the Best Efficiency Point (BEP).

• Power (P) curve – Increases with flow.

https://www.pumpsandsystems.com/sites/default/files/styles/article_full/public/2020-03/pump-curve.png

Key Points on the Curve:

4. Factors Affecting the H-Q Relationship

A. Impeller Diameter

• Larger diameter → Higher head at all flows.

• Smaller diameter → Lower head.

B. Pump Speed (N)

• Affinity Laws predict changes:

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

• Higher speed (N) increases both Q and H.

C. Fluid Viscosity

• Higher viscosity reduces flow and head (shifts curve downward).

D. System Resistance (System Curve)

• The actual operating point is where the pump curve intersects the system curve.

• Higher system resistance (e.g., longer pipes, more fittings) reduces flow.

5. Practical Implications

• Operating far from BEP causes:

• Low efficiency → Higher energy costs.

• Cavitation (at high flow) or overheating (at low flow).

• Variable Speed Drives (VSDs) adjust pump speed to match demand, optimizing efficiency.

6. Example: How to Read a Pump Curve

1. Select desired flow (Q) (e.g., 100 m³/h).

2. Find corresponding head (H) (e.g., 50 m).

3. Check efficiency (η) (e.g., 75%).

4. Ensure NPSH available > NPSH required (to avoid cavitation).

Conclusion

• Head (H) decreases as flow (Q) increases in centrifugal pumps.

• The H-Q curve helps select the right pump for a system.

• Optimal operation is near the BEP for efficiency and longevity.

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