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Pump Affinity Laws Calculator

Calculate new pump flow, head, and brake horsepower (BHP) when changing impeller RPM or diameter based on the mechanical affinity laws.
GPM
Feet
BHP
RPM / in
RPM / in
Calculated result for New Flow (Q₂):

New Flow (Q₂)

414.3 GPM
Directly proportional
Calculated result for New Head (H₂):

New Head (H₂)

82.4 Feet
Squared ratio
Calculated result for New Power (P₂):

New Power (P₂)

11.38 BHP
Cubed ratio
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What is The Physics of PumpAffinity?

The technical foundation and mathematics behind the PumpAffinityCalc tool.

Mathematical Foundation

Core Equation
Q1Q2=N1N2&H1H2=(N1N2)2&P1P2=(N1N2)3\frac{Q_1}{Q_2} = \frac{N_1}{N_2} \quad \& \quad \frac{H_1}{H_2} = \left(\frac{N_1}{N_2}\right)^2 \quad \& \quad \frac{P_1}{P_2} = \left(\frac{N_1}{N_2}\right)^3
QQ= Fluid volumetric flow rate delivery (GPM).
HH= Hydraulic head pressure generated against the piping system (ft of head).
PP= Brake horsepower drawn by the driving electrical pump motor (BHP).
NN= Impeller rotational speed (RPM) or physical diameter modification (inches).

Laws & Principles

  • The Pump Affinity Laws dictate that shaft horsepower demand mathematically scales by the cube of the impeller speed. Reducing pump RPM by exactly half physically requires only 1/8th (12.5%) of the original motor horsepower.
  • The laws strictly assume geometrically similar pump casings and absolute constant system efficiency, meaning extreme low-speed calculations may analytically underpredict actual VFD parasitic losses.

Step-by-Step Example Walkthrough

" A 10 HP chilled water booster pump delivering 400 GPM at 1,750 RPM is throttled down by a Variable Frequency Drive to 1,400 RPM to save facility energy. "

  1. 1. Calculate the speed reduction ratio (N2 / N1) = 1,400 / 1,750 = 0.80 (80%).
  2. 2. Flow capacity (Q) drops linearly: 400 GPM * 0.80 = 320 GPM.
  3. 3. Brake Horsepower drops by the cube (0.80³ = 0.512 multiplier): 10 HP * 0.512 = 5.12 BHP.
Final Result: 5.12 Brake Horsepower

Quick Answer: What does the Centrifugal Pump Affinity Laws Calculator do?

The Centrifugal Pump Affinity Laws Calculator calculates changes in volumetric flow rate (Q), discharge head (H), and power consumption (BHP) when varying pump rotational speed (RPM) or impeller diameter per Hydraulic Institute standards.

How to Use the Calculator

  1. 1.Enter your project parameters into the input fields above. All fields indicate expected measurement units.
  2. 2.Results calculate instantly as you adjust values — no submit button needed.
  3. 3.Use the Share button or export a PDF report to document your calculations.
  4. 4.Review the Knowledge Hub above for governing engineering standards, mathematical formulas, and worked examples.

Pro Tips

Best Practices

  • ✓Double-check input units: Confirm all dimensions match the expected unit (inches, feet, PSI, GPM, etc.) before finalizing designs.
  • ✓Factor in safety allowances: Always apply appropriate engineering service factors or code safety margins above theoretical minimums.

Common Mistakes

  • ✗Don't overlook local code amendments: Local municipal authority having jurisdiction (AHJ) codes may supersede national baseline standards.
  • ✗Don't ignore boundary conditions: Verify operating temperatures, pressures, and load limits do not exceed safe component thresholds.

Frequently Asked Questions

What are the three core centrifugal pump affinity laws?

Flow varies linearly with speed (Q2/Q1 = N2/N1); Head varies with the square of speed (H2/H1 = (N2/N1)²); and Power consumption varies with the cube of speed (P2/P1 = (N2/N1)³).

Why does reducing pump speed yield massive energy savings?

Because power scales with the cube of RPM, slowing a chilled water circulation pump down by just 20% (to 80% speed) reduces electrical brake horsepower consumption by nearly 50% (0.8³ = 0.512).

Are impeller diameter trimming calculations as accurate as speed changes?

Impeller trimming follows the affinity laws closely up to a 10% to 15% reduction. Trimming beyond 15% increases gap clearance to the volute casing, lowering hydraulic pump efficiency.

Does static system head affect the application of affinity laws?

Affinity laws assume pure friction systems. In systems with high static lift elevation, reducing pump speed too far will fail to overcome static head, resulting in pump deadhead with zero flow.

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