Pump Affinity Law Calculator

Select Input Mode (Speed or Diameter change). Enter baseline point. Calculates new Q₂, H₂, P₂. Export to Excel with live formulas.

Input Mode

Speed Change Diameter Change

Baseline Speed n₁

rpm

Baseline Impeller Dia D₁

mm cm m inch

Baseline Flow Q₁

m³/s m³/h L/s gpm

Baseline Head H₁

m ft

Baseline Power P₁

kW HP

New Speed n₂ (Speed Change)

rpm

New Diameter D₂ (Diameter Change)

mm cm m inch

Calculate Export Excel Reset Copy

Mode

Speed Change

Ratio used (r)

–

New Flow Q₂

– m³/h

New Head H₂

– m

New Power P₂

– kW

Formulas, units & assumptions

• Speed Change (D constant): Q₂ = Q₁·(n₂/n₁), H₂ = H₁·(n₂/n₁)², P₂ = P₁·(n₂/n₁)³
• Diameter Change (n constant): Q₂ = Q₁·(D₂/D₁), H₂ = H₁·(D₂/D₁)², P₂ = P₁·(D₂/D₁)³
• Results shown in the same units as inputs (Flow: m³/s, m³/h, L/s, gpm; Head: m, ft; Power: kW, HP; Diameter: mm, cm, m, inch).
• Assumes constant efficiency. For large changes, verify with pump curves.

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Pump Efficiency Calculator

Compute hydraulic power and efficiency from flow, head, and input power.

Flow rate

m³/hr L/s GPM (US) m³/s

Total head

m ft

Input power (to pump shaft)

kW HP

Specific Gravity (SG) Water ≈ 1.00. Heavier liquids have SG > 1.

Calculate Reset Copy Excel

Hydraulic power

– kW   (– HP)

Efficiency

– %

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Pump Affinity Laws

Q1 / Q2                =             N1 / N2

Flow Changes directly to the change in Speed

H1 / H2                =             (N1 / N2)²

Head Changes directly proportional to the Square of the change in Speed

BHP1 / BHP2    =             (N1/ N2)³

Brake Horse Power Changes directly proportional to the Cube of the change in Speed

For a fixed speed and varying impeller diameter pump affinity laws are as follows:

Q1 / Q2                   =            D1 / D2

H1 / H2                  =           (D1 / D2)²

BHP1 / BHP2       =           (D1 / D2)³    

Nomenclature:

Q1, Q2 – Volumetric Flow rate in m³/hr

H1, H2 – Head  in m

D1, D2 – Diameter of the impeller in mm

N1, N2 – Speed in rpm

BHP – Brake Horse Power in kW

The above two cost reduction techniques in Centrifugal pump may be analyzed using the Pump Affinity Laws before implementation of the project.

Pump Affinity Laws Calculator in Excel

To help the process engineers in Chemical Processing Industry, Pump Affinity laws are incorporated in Excel file and uploaded. You may download this template and use it for Pump Affinity law Calculations.

Excel Calculation File Available Here

Application of Pump Affinity Laws

The practical application of Centrifugal Pump Affinity laws is helpful in implementing energy savings in oversized pumps. In an industry process related pumps may be over sized because of various reasons or it may be underutilized based on the required operating conditions. This results in waste of energy. Pump affinity laws are helpful in implementing “VFD” and “Impeller Trim”.

Variable Frequency Drives are installed for the motor to vary the pump speed according to the requirement and it reduced power requirement.

“Impeller Trim” operation is carried out to reduce the impeller diameter of the pump to reduce the power consumption.

Centrifugal Pump Affinity Law Online Calculator

Simplify Pump Performance Calculations with Our Free Centrifugal Pump Affinity Law Calculator!

Are you a process or chemical engineer looking to quickly estimate pump performance changes with speed or impeller diameter variations?

Check out our easy-to-use online Pump Affinity Law Calculator! It helps you calculate new flow rate, head, and power based on the affinity laws — saving time and improving accuracy for pump scaling and selection.

Key Features:

Input mode for speed or diameter change

Instant calculation of new Q (flow), H (head), and P (power)

Export live formulas to Excel for further analysis

Supports a variety of units: m³/h, m, kW, and more

Perfect for energy savings, pump optimization, and troubleshooting

Try it now and streamline your pump performance calculations:

https://chemicalengineeringsite.in/centrifugal-pump-affinity-law-calculator/

Visit Chemical Engineering Online Calculators

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Formula for Calculation of Pump Specific Speed

Specific speed of the pump is calculated with the help of the formula:

N_s = (N * √Q )/ H^(3/4)

Where

N_s is Specific speed of the pump Dimensionless

N is Speed of the pump in rpm

Q is the Volume Flow rate of the pump at its best efficiency point – BEP in gpm

H is Discharge head of the pump at BEP in ft

In SI units the formula can be used as

N_s = (N * √Q)/ (1.16 * H ^(3/4) )

Where

Ns is Specific speed of the pump Dimensionless

N is Speed of the pump in rpm

Q is the Volume Flow rate of the pump at its best efficiency point – BEP in m³/hr

H is Discharge head of the pump at BEP in m

Note:

While calculating specific speed use flow rate and discharge head at its best efficiency point.

For Double suction pumps use half of the volume flow rate at BEP while calculating specific speed.

Per stage pump head to be used in calculations.

Application of Pump Specific Speed

Based on suction specific speed impellers are selected from the following three types

Radial Flow Impellers

In radial flow type impellers fluid leaves perpendicular to the pump shaft center line giving high head and low flow rate. Radial flow impellers develop head with centrifugal action. Radial flow type of impeller is selected when the pump specific speed is between 500 to 4200.

Axial Flow Impellers

In axial flow type impellers fluid enters and leaves along the same direction parallel to the rotating shaft centerline giving high flow rate and low head. Axial Flow type of impeller is selected when the specific speed is greater than 9000

Mixed Flow Impellers

In Mixed flow type impellers fluid leaves at an angle below 45 degree from the shaft center line.  In mixed flow design, part of head is developed by centrifugal action and part of head is developed by impeller design. Mixed flow type of impeller is selected when the pump specific speed falls between 4200 to 9000.

Find it Interesting? Learn more about Centrifugal Pump in our website and Dont miss our Pump Quiz

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PUMP HANDBOOK 4ED 0004 Edition from Flipkart.com

Centrifugal Pump Design from Flipkart.com

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Components of Centrifugal Pump Curve

1. Head Vs Flow Curve : H-Q Curve
2. Efficiency Vs Flow Curve: Efficiency Curve
3. Brake Horse Power Vs Flow Curve: Energy Curve
4. NPSH_R Vs Flow Curve

Details about Centrifugal Pump Characteristic Curve

H-Q Curve

Pump manufacturers use the terminology called “Head” and Pump users use “Pressure” to measure the performance. On x-y plot, Head is plotted in y axis and the Flow is plotted in x axis. Shut off head is the Head developed by the pump at zero flow. For a Pump user Shut off pressure of the centrifugal pump is an important tool to identify the priming loss/Cavitation of the pump. Head curve will fall for increased flow rates.

Efficiency Curve

In a Centrifugal Pump Characteristic curve, Efficiency curve starts from zero at zero flow and goes like a trajectory having a Best Efficiency point and then the efficiency starts falling for increased flow rates. Best Efficiency Point – BEP is the point on a pump performance curve corresponding to the flow rate with the highest possible efficiency.

Energy Curve

Brake Horse power is plotted against the Flow to obtain energy curve in a centrifugal pump curve. It is a simple straight line. There will be minimum power consumed by the pump even at zero flow which is used to develop shut off head of the pump. Brake horse power rises with the flow.

NPSH_R Curve

Net Positive Suction Head Required is plotted against the Flow rate.  NPSH_R curve is a flat curve till the BEP of the pump and then it rises sharply beyond the Best efficiency point. Net Positive Suction Head Available must be greater than the Net Positive Suction Head Required to avoid Cavitation of the pump. NPSH Available is calculated based on the friction losses in the system while NPSH Required is specified by a pump vendor. Hope these information helps you to understand about the Centrifugal Pump Curve better. If so share it with friends!

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Buy Centrifugal Pump Design from Flipkart.com

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Hydraulic Power (Power Output from Pump):

Centrifugal Pump consumes energy to develop the discharge pressure and to deliver flow. Therefore Hydraulic Horsepower of the Pump depends on these two parameters.

Power Output from Pump = (P2 – P1) * Q

P2: Pump Discharge pressure in N/m²

P1: Pump suction pressure in N/m²

Q: Flow delivered by pump in m³/s

Brake Horse Power (Power Input to Pump):

This is the power given to the pump through Electric Motor. Power output from the electric driver is calculated by the formula

Power Input to Pump = 1.732 * V * I * PF * Motor Efficiency * Coupling Efficiency

V: Measured Voltage of Motor in Volt

I: Measured Current of Motor in Ampere

PF: Power Factor

Motor Efficiency May be considered as design efficiency or may be obtained from Motor efficiency calculation data through tests

Coupling Efficiency is obtained from Supplier Manual

Centrifugal pump efficiency equation

Centrifugal pump efficiency = Power Output from Pump/ Power Input to Pump * 100

Centrifugal Pump Efficiency and Discharge Temperature

Actual Power required in pump can also be derived from Heat balance across the pump.  Difference in Heat flow Outlet and Heat flow inlet is the actual power required for the pump. This indicates the fall in centrifugal pump efficiency increases the temperature of liquid at the pump discharge.

Factors Influencing Centrifugal Pump Efficiency

1. In Recirculation lines Minimum Thermal flow is maintained to avoid Cavitation during low flow operation of the pump. This will also result in lowering the efficiency.
2. Internal Surface Roughness. Smooth surface finish in pump internals gives high efficiency
3. Increase in Wear Ring Clearances decreases the efficiency of Centrifugal pump. Wear rings are used reduce clearance between Pump impeller and Pump casing
4. Increase in viscosity decreases the pump efficiency
5. Mechanical losses in Couplings, Bearings, Packings etc will decrease the efficiency
6. Impeller Trimming will also decrease efficiency

The post Centrifugal Pump Efficiency Calculation appeared first on Chemical Engineering Site.

Minimum Thermal Flow in Centrifugal Pump is defined as, “The lowest flow at which the pump can operate without its operation being impaired by the temperature rise o f the pumped liquid”

The temperature of the liquid in the pump casing is to be kept below the saturation temperature of the liquid.  The overheating of the liquid inside the centrifugal pump casing may occur because of two ways. First is  Recirculation of liquid inside the casing and the second way is Energy from Driver Equipment is converted to heat and it raises the temperature of liquid inside the pump.

If the temperature of the liquid inside the pump casing increases beyond the saturation temperature, liquid starts to vaporize and results in cavitation of the pump.

Effects of Minimum Safe Flow:

If the Minimum flow through centrifugal pump is not ensured it may result in any one of the following.

Mechanical Damage due to Overheating

Cavitation and Vibration due to recirculation of liquid inside the casing

Mechanical Seal and Bearing Failure

Catastrophic failure due to hazardous liquid explosion/fire

How to Maintain Minimum Thermal Flow in Centrifugal Pumps?

The minimum flow operation in centrifugal pumps may arise during the situations of low load operations and during the start up and shutdown of the process plants. The methods of maintaining minimum thermal flow in centrifugal pumps are as follows.

1. Spill back Flow through Restriction Orifice

2. Control Valves

a)      Trip Valve in Spill Back line

b)      Split Range Control Valves in Discharge and Spill back lines

c)       Pressure Control Valve in Spill back line

3. Automatic Recirculation Valves in Discharge

Spill back Flow through Restriction Orifice

Recycle flow using restriction orifice in spill back line maintains the continuous minimum thermal flow.  Simple and highly reliable system. Lower investment Cost. Continuous recycle flow result in waste of energy when the centrifugal pumps operate above the minimum flow and process requirement may not be adequate for higher loads of the plant.

Control Valves for Minimum Thermal Flow

a)      Trip Valve in Spill Back line – To be actuated sensing the low flow in the pump discharge to recycle the flow through spill back. Resets and Control valve gets closed when the Process demand exceeds the minimum thermal flow of the Centrifugal pumps

b)      Split Range Control Valves in Discharge and Spill back lines – Discharge and Spill back lines are equipped with Split range Control valves. The control valve in the discharge line will cater the process requirement and if it becomes less than the minimum safe flow the control valve in the spill back line recycles the flow and protects the pump

c)       Pressure Control Valve in Spill back line – When the discharge pressure increases due to low process demand, the pressure control valve gets opened and reduces the pressure to the required value.

The above system requires Controllers and Control valves to be installed. Operating cost is required for both power and Instrument air. The control valves are not most commonly used for ensuring the minimum safe flow requirements of the centrifugal pump because of high capital cost.

Automatic Recirculation Valves (ARC)

Automatic Recirculation valves (ARC) or Minimum Flow Check Valves (MFCV) are spring loaded recirculation valves. It re circulates the only the minimum flow required to operate the pump and if  pump flow for process demand is more than the minimum thermal flow the recirculation port closes automatically and recirculation flow becomes zero. It eliminates the higher capital cost required for installation of control valves. The pump and driver need not be oversized to take care of minimum pump flow since recirculation flow can be made zero during high process demands.

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PERRY’S CHEMICAL ENGINEERS’ HANDBOOK,8/ED from Flipkart.com

PUMP HANDBOOK 4ED 0004 Edition from Flipkart.com

Centrifugal Pump Design from Flipkart.com

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