You selected a pump for the required flow. The motor runs. The valves are open. Yet the process still receives less liquid than expected.
Before replacing the pump, check the relationship that determines its installed performance: the pump curve and the system curve.
A catalog duty point tells you what a pump can deliver under specified conditions. Your piping, equipment, vessel pressures, and liquid levels determine where it actually operates.
This guide explains how to build a pump system curve, calculate the operating point, and investigate a flow shortfall using a transparent worked example.
What Is a Pump System Curve?
A pump system curve shows the head a piping system requires at different flow rates. The operating point occurs where this curve intersects the pump’s head–flow curve.
At that intersection, the pump supplies the head the system requires at the same flow. KSB defines the centrifugal pump operating point using this intersection.
| Term | What it describes | Information source |
|---|---|---|
| Pump curve | Head the pump can develop at different flows | Manufacturer’s performance data |
| System curve | Head required to move liquid through the installation | System calculations and operating conditions |
| Operating point | Predicted flow and head where both curves meet | Comparison of the two curves |
The required process flow is a target. The curve intersection tells you whether the selected pump and system can achieve it.
The Pump System Curve Formula
For a simplified liquid-transfer system:
Hsystem = Hstatic + kQ²
- Hsystem = total system head, in metres of pumped liquid.
- Hstatic = flow-independent head component, in metres.
- Q = flow rate.
- k = resistance coefficient using units consistent with Q.
The static component includes elevation and pressure differences between the system boundaries. Between two large liquid surfaces with negligible surface velocities:
Hstatic = (z₂ − z₁) + (p₂ − p₁)/(ρg)
Here, z represents elevation, p pressure, ρ liquid density, and g gravitational acceleration. For two open tanks exposed to the same atmospheric pressure, the pressure terms cancel.
The flow-dependent component covers losses through pipes, fittings, valves, and equipment. Its approximately quadratic relationship with flow produces the familiar rising system curve. KSB’s system characteristic curve reference describes the static and dynamic components.
When Does the Q² Approximation Apply?
Use a constant k as an approximation for a fixed configuration with turbulent flow and relatively little change in friction factor.
Recalculate losses when viscosity, flow regime, valve position, or equipment resistance changes substantially. A single coefficient should not represent every operating condition.
Also, keep units consistent. A coefficient calculated with flow in m³/h cannot be reused unchanged with flow in L/s.
Worked Example: Calculate the Pump Operating Point
Consider a hypothetical water-transfer installation. These numbers illustrate the method; they are not results from a customer project.
- Static head: 10 m
- Combined friction and equipment losses at 60 m³/h: 18 m
- Fixed valve positions
- An illustrative pump curve at constant speed
Step 1: Calculate the System Resistance Coefficient
k = friction head ÷ flow² = 18 ÷ 60² = 0.005
With Q expressed in m³/h:
Hsystem = 10 + 0.005Q²
Step 2: Define the Illustrative Pump Curve
For this example only:
Hpump = 42 − 0.003Q²
For a real selection, use the manufacturer’s curve for the correct speed, impeller diameter, and liquid conditions. Do not assume every pump follows this equation.
Step 3: Compare Head at Several Flow Rates
| Flow, m³/h | System head, m | Pump head, m |
|---|---|---|
| 0 | 10.0 | 42.0 |
| 20 | 12.0 | 40.8 |
| 40 | 18.0 | 37.2 |
| 60 | 28.0 | 31.2 |
| 80 | 42.0 | 22.8 |
At 60 m³/h, the pump develops more head than the system requires. At 80 m³/h, it develops less. The intersection lies between those flows.
Step 4: Solve for the Intersection
Set pump head equal to system head:
42 − 0.003Q² = 10 + 0.005Q²
Rearrange: 32 = 0.008Q²
Therefore: Q = √4,000 ≈ 63.2 m³/h
Substitute the unrounded flow into either equation: H = 30.0 m
Calculated operating point: approximately 63.2 m³/h at 30.0 m head.
That is the predicted duty for these assumptions. A requirement of 70 m³/h would remain unmet, even if someone described this as a “70 m³/h pump.”
How Added Resistance Reduces Flow
Now suppose fouling increases the resistance coefficient from 0.005 to 0.008, while the static head and pump curve remain unchanged.
Hsystem,new = 10 + 0.008Q²
The new intersection satisfies: 42 − 0.003Q² = 10 + 0.008Q²
Therefore: Q = √(32 ÷ 0.011) ≈ 53.9 m³/h
The corresponding head is approximately 33.3 m.
| Result | Original condition | Higher-resistance condition |
|---|---|---|
| Operating flow | 63.2 m³/h | 53.9 m³/h |
| Operating head | 30.0 m | 33.3 m |
| Change in flow | — | Approximately 14.7% lower |
In this illustrative calculation, increased resistance reduces flow by approximately 14.7% without changing the pump itself.
This gives troubleshooting a useful starting point: compare the installation’s present resistance with the design assumptions. KSB identifies increased losses and changing tank levels as causes of operating-point shifts.
How to Build a Pump System Curve in Excel
A useful calculation should let another engineer follow the inputs, assumptions, and result.
1. Define the System Boundaries
Identify the suction and discharge boundaries. Record liquid levels and vessel pressures for the operating condition being studied. Create separate cases for conditions that can change materially, such as minimum suction level or maximum discharge pressure.
2. Gather the Resistance Inputs
- Pipe lengths and internal diameters.
- Pipe roughness and liquid properties.
- Fittings and valve positions.
- Equipment pressure-drop data.
- The flow basis for each supplied pressure drop.
Keep supplier data and assumptions distinguishable. “Assumed clean filter loss” and “measured filter loss” are different inputs.
3. Create a Flow Column
Enter a range of flows that brackets the expected duty and stays within the relevant manufacturer curve data.
For the worked example, if cell A2 contains flow in m³/h, the system-head formula is:
=10+0.005*A2^2The illustrative pump-head formula is:
=42-0.003*A2^24. Plot Both Curves
Use an XY scatter chart with flow on the horizontal axis and head on the vertical axis. For manufacturer data, use the supplied points and appropriate interpolation. Avoid extending a fitted curve beyond the supplied operating range.
5. Check the Difference
Create a column for: Head difference = pump head − system head
The intersection occurs where that difference reaches zero. A sign change between adjacent rows brackets the operating point.
GrowMechanical’s Pump System Curve Excel Sheet provides a dedicated workflow for system resistance, operating-point calculations, and comparison with the pump’s best efficiency point.
What to Check Before Accepting the Result
An intersection is the beginning of the selection review.
Compare the Duty With the Best Efficiency Point
The best efficiency point, or BEP, is the point of maximum pump efficiency for the specified configuration.
Locate your predicted duty on the manufacturer’s efficiency curve and check its permitted operating region. Do not apply an arbitrary universal percentage around BEP. KSB’s design-point guidance discusses the relationship between the design duty and best efficiency point.
Review Suction Conditions Separately
Add a suction review to the calculation package. Record the liquid temperature, suction pressure, tank level, and suction-line losses used.
Use GrowMechanical’s guide to pump suction line sizing, pressure loss, and NPSH to structure that review.
Include More Than One Operating Case
| Case | Input to change | Question to answer |
|---|---|---|
| Normal operation | Expected levels and clean equipment | Does the duty meet the process requirement? |
| Minimum suction level | Suction liquid elevation | Is the revised duty acceptable? |
| Fouled equipment | Equipment resistance | Is sufficient flow still available? |
| Different valve position | Valve resistance | How does the operating point move? |
| Reduced speed | Manufacturer’s speed-specific pump curve | Can the required duty still be reached? |
Record the accepted case and its limits so later modifications can be assessed against the same basis.
Will Reducing Pump Speed Save Energy?
The centrifugal pump affinity laws provide approximate relationships between corresponding points at different speeds:
- Flow is proportional to speed.
- Head is proportional to speed squared.
- Power is proportional to speed cubed, subject to the relevant similarity and efficiency assumptions.
These relationships help estimate a revised pump curve. The revised operating point must still be found against the system curve. KSB’s pump affinity laws reference explains the relationships and their limitations.
For example, a speed ratio of 0.8 gives a theoretical corresponding-point power ratio of: 0.8³ = 0.512
That does not establish a 48.8% electricity saving for an installed system. Static head, the new intersection, pump efficiency, motor efficiency, and drive losses affect the result.
Ask for the manufacturer’s performance data at the proposed speed before finalizing the change.
Frequently Asked Questions
What Is the Difference Between a Pump Curve and a System Curve?
The pump curve describes the head the pump can produce at different flows. The system curve describes the head the installation requires. Comparing them identifies the predicted operating duty.
Can I Build a System Curve From One Known Flow and Head?
You can construct an approximate curve if you know the static head separately and can justify the constant-resistance, Q² model. First subtract static head from total system head. Then divide the remaining loss head by flow squared to calculate k. State those assumptions alongside the result.
Is Rated Flow the Same as Operating Flow?
They may coincide, but the rated duty alone does not establish installed flow. Compare the actual system requirements with the correct manufacturer pump curve.
Can an Excel Calculation Replace Manufacturer Review?
Use the spreadsheet to organize inputs, compare cases, and identify questions. Complete the selection with the manufacturer’s performance data and the project’s operating requirements.
Check the Operating Point Before Changing the Pump
Start with three inputs: the correct pump curve, a defensible system-head calculation, and clearly defined operating conditions.
Then ask a concrete question: Where do the curves intersect, and does that duty satisfy the process?
Use the GrowMechanical Pump System Curve Excel Sheet to evaluate the intersection and compare operating scenarios. Bring your manufacturer’s curve and system inputs so your next pump decision rests on a calculation you can review.
