centrifugal pump flow rate formula​

Centrifugal Pump Flow Rate (Q) Formula

The flow rate (Q) of a centrifugal pump can be calculated using several formulas, depending on available parameters. Here are the most common approaches:

1. Basic Hydraulic Power Formula

If you know the power input (P), head (H), and pump efficiency (η):

$$\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">P</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">3600</span>}}{\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">g</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">H</span>}}$$Q=ρ×g×HP×η×3600

Where:

• $\mathrm{<span\; style="font-size:\; 18px;">Q</span>}$Q = Flow rate (m³/h)

• $\mathrm{<span\; style="font-size:\; 18px;">P</span>}$P = Shaft power input (kW)

• $\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}$η = Pump efficiency (0.7–0.9, or 70–90%)

• $\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}$ρ = Fluid density (kg/m³, 1000 for water)

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

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

Example:

• $\mathrm{<span\; style="font-size:\; 18px;">P</span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">15</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}\text{<span style="font-size: 18px;">kW</span>}$P=15kW

• $\mathrm{<span\; style="font-size:\; 18px;">\eta </span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">0.85</span>}$η=0.85

• $\mathrm{<span\; style="font-size:\; 18px;">H</span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">30</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}\text{<span style="font-size: 18px;">m</span>}$H=30m

• $\mathrm{<span\; style="font-size:\; 18px;">\rho </span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">1000</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}{\text{<span style="font-size: 18px;">kg/m</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}$ρ=1000kg/m3

$$\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">=</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">15</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">0.85</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">3600</span>}}{\mathrm{<span\; style="font-size:\; 18px;">1000</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">9.81</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">30</span>}}<span\; style="font-size:\; 18px;">\approx </span><span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>\mathrm{<span\; style="font-size:\; 18px;">5.2</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}{\text{<span style="font-size: 18px;">m</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}\mathrm{<span\; style="font-size:\; 18px;">/</span>}\text{<span style="font-size: 18px;">h</span>}<span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>$$Q=1000×9.81×3015×0.85×3600≈∗∗5.2m3/h∗∗

2. Affinity Laws (For Speed or Impeller Change)

If pump speed (N) or impeller diameter (D) changes:

$$\frac{{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}<span\; style="font-size:\; 18px;">=</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}<span\; style="font-size:\; 18px;">=</span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">D</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}$$Q2Q1=N2N1=D2D1

Example:

• Original flow (${\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}$Q1) = 10 m³/h at 2900 RPM (${\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}$N1)

• New speed (${\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}$N2) = 1450 RPM

$${\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}<span\; style="font-size:\; 18px;">=</span>{\mathrm{<span\; style="font-size:\; 18px;">Q</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}<span\; style="font-size:\; 18px;">\times </span>\frac{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{{\mathrm{<span\; style="font-size:\; 18px;">N</span>}}_{\mathrm{<span\; style="font-size:\; 18px;">1</span>}}}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">10</span>}<span\; style="font-size:\; 18px;">\times </span>\frac{\mathrm{<span\; style="font-size:\; 18px;">1450</span>}}{\mathrm{<span\; style="font-size:\; 18px;">2900</span>}}<span\; style="font-size:\; 18px;">=</span><span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>\mathrm{<span\; style="font-size:\; 18px;">5</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}{\text{<span style="font-size: 18px;">m</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}\mathrm{<span\; style="font-size:\; 18px;">/</span>}\text{<span style="font-size: 18px;">h</span>}<span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>$$Q2=Q1×N1N2=10×29001450=∗∗5m3/h∗∗

3. Using Pump Performance Curve

Manufacturers provide H-Q curves showing flow vs. head.

• Locate your operating head (H) on the curve.

• Read the corresponding flow rate (Q).

https://www.pumpsandsystems.com/sites/default/files/styles/article_full/public/2021-04/pump-curve-example.png

4. Velocity-Based Flow Calculation

If discharge pipe diameter (d) and velocity (v) are known:

$$\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">=</span>\mathrm{<span\; style="font-size:\; 18px;">A</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">v</span>}<span\; style="font-size:\; 18px;">=</span><span\; style="font-size:\; 18px;">(</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">\pi </span>}<span\; style="font-size:\; 18px;">\times </span>{\mathrm{<span\; style="font-size:\; 18px;">d</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{\mathrm{<span\; style="font-size:\; 18px;">4</span>}}<span\; style="font-size:\; 18px;">)</span><span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">v</span>}$$Q=A×v=(4π×d2)×v

Where:

• $\mathrm{<span\; style="font-size:\; 18px;">A</span>}$A = Pipe cross-sectional area (m²)

• $\mathrm{<span\; style="font-size:\; 18px;">v</span>}$v = Flow velocity (m/s, typically 1–3 m/s for water)

Example:

• Pipe diameter ($\mathrm{<span\; style="font-size:\; 18px;">d</span>}$d) = 0.1 m (100 mm)

• Velocity ($\mathrm{<span\; style="font-size:\; 18px;">v</span>}$v) = 2 m/s

$$\mathrm{<span\; style="font-size:\; 18px;">Q</span>}<span\; style="font-size:\; 18px;">=</span><span\; style="font-size:\; 18px;">(</span>\frac{\mathrm{<span\; style="font-size:\; 18px;">\pi </span>}<span\; style="font-size:\; 18px;">\times </span>{\mathrm{<span\; style="font-size:\; 18px;">0.1</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">2</span>}}}{\mathrm{<span\; style="font-size:\; 18px;">4</span>}}<span\; style="font-size:\; 18px;">)</span><span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">2</span>}<span\; style="font-size:\; 18px;">\times </span>\mathrm{<span\; style="font-size:\; 18px;">3600</span>}<span\; style="font-size:\; 18px;">\approx </span><span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>\mathrm{<span\; style="font-size:\; 18px;">56.5</span>}\text{<span style="font-size: 18px;">\hspace{0.17em}</span>}{\text{<span style="font-size: 18px;">m</span>}}^{\mathrm{<span\; style="font-size:\; 18px;">3</span>}}\mathrm{<span\; style="font-size:\; 18px;">/</span>}\text{<span style="font-size: 18px;">h</span>}<span\; style="font-size:\; 18px;">\ast </span><span\; style="font-size:\; 18px;">\ast </span>$$Q=(4π×0.12)×2×3600≈∗∗56.5m3/h∗∗

Where:

• $\mathrm{<span\; style="font-size:\; 18px;">S</span>}\mathrm{<span\; style="font-size:\; 18px;">G</span>}$SG = Specific gravity (1 for water)

Key Notes:

• Efficiency (η) varies with pump type (e.g., 60–90% for centrifugal pumps).

• Density (ρ) must be adjusted for oils, chemicals, etc.

• Always check the pump curve for real-world performance.

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