Adjust impeller diameter, rotational speed, and pipe resistance to plot H-Q, efficiency, and system curves simultaneously. The operating point and BEP are detected automatically — affinity law scaling included.
Pump Parameters
Impeller Diameter D [mm]
mm
Speed N [rpm]
rpm
Flow Coefficient φ
System Parameters
Static Head Hs [m]
m
Pipe Resistance K
Operating Point
Results
—
Qop [m³/h]
—
Hop [m]
—
ηop [%]
—
Specific Speed Ns
—
QBEP [m³/h]
—
ηmax [%]
Pump
■ H-Q curve
■ System curve
■ Efficiency (right axis)
⬤ Operating point
What exactly is an H-Q curve? I see it's a downward slope in the simulator, but what does that mean in practice?
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Basically, it's the pump's performance signature. The Head (H) is the pressure energy it can add to the fluid, measured in meters. The curve shows that as the Flow rate (Q) increases, the pump can provide less pressure. Try moving the 'Impeller Diameter' slider up—you'll see the whole curve shift higher, meaning a bigger impeller can generate more pressure at any given flow.
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Wait, really? So the curve itself can change? What about that other line labeled 'System Curve' that crosses it?
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Exactly! The pump curve is what the pump can do. The system curve is what the piping system requires to move the fluid—it needs more pressure to overcome friction and static lift as flow increases. Their intersection is the operating point. In the simulator, increase the 'Pipe Resistance K' parameter. See how the system curve gets steeper and the operating point moves to a lower flow? That's the real balancing act of pump selection.
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Okay, and the BEP (Best Efficiency Point) is the peak of the efficiency curve. But why is it bad to run a pump far from the BEP?
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Great observation. Running far from the BEP wastes energy, causes excessive vibration, and can damage the pump. In the simulator, drag the operating point away from the BEP by adjusting the 'Static Head H' way up. Notice how the efficiency dot plummets? A common case is an oversized pump—it's forced to run at a low flow, far left on its curve, which is inefficient and stressful. Engineers use tools like this to select a pump whose BEP matches the system's typical demand.
Physical Model & Key Equations
The core performance of a centrifugal pump is modeled by a parabolic Head-Flow (H-Q) characteristic curve. The head produced decreases with the square of the flow rate.
$$H = H_0 - K_p Q^2$$
H is the total dynamic head [m]. H₀ is the shut-off head (head at zero flow). K_p is the pump's characteristic resistance coefficient [s²/m⁵]. Q is the volumetric flow rate [m³/s].
The system curve defines the head required by the piping network to move the fluid at a given flow rate. It combines static lift (constant) and dynamic friction losses (proportional to flow squared).
$$H_{system}= H_{static}+ K_{system} Q^2$$
H_system is the total head required by the system [m]. H_static is the static head (e.g., height difference, tank pressure) [m]. K_system is the overall system resistance coefficient [s²/m⁵], determined by pipe friction, fittings, and valves.
Frequently Asked Questions
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From the current impeller diameter and rotational speed, you can predict the new H-Q curve, efficiency curve, and operating point when the diameter or rotational speed is changed. After entering the changed values with the slider, a real-time comparison is displayed.
The BEP is automatically calculated from the pump performance curve and efficiency curve. It refers to the flow rate point where efficiency is maximized, and the head, flow rate, and efficiency at that point are displayed with markers on the graph. Since efficiency decreases when the operating point deviates from the BEP, use it as a design guideline.
The value of K depends on the pipe length, diameter, and friction coefficient. As a general guideline, it is about 0.1 to 1 for short straight pipes, and about 5 to 20 for long pipes or systems with many valves. If you have calculated or measured pressure loss values from the actual equipment, inputting those is the most accurate.
Real-World Applications
Building HVAC Systems: Centrifugal pumps circulate chilled or hot water through air handling units. Engineers use pump curves to select a pump that meets the building's peak cooling load (operating point) while running near its BEP for most of the year to minimize electricity costs.
Water Treatment Plants: Pumps move raw water through filtration and chemical treatment processes. The system curve changes as filters get clogged. Understanding the pump curve allows operators to predict how flow will drop over time and schedule maintenance.
Industrial Process Cooling: In a chemical plant, a centrifugal pump might circulate a coolant to control reactor temperature. A variable speed drive (simulated by changing the 'Speed N' parameter) is often used to adjust the pump curve on-the-fly to match changing process demands efficiently.
Irrigation Systems: Agricultural pumps draw water from a well or canal and distribute it through miles of piping and sprinklers. The pump must be selected to provide enough head to overcome the significant friction losses (high 'Pipe Resistance K') and elevation changes across the field to ensure even water delivery.
Common Misunderstandings and Points to Note
When you start using this simulator, there are a few key points to keep in mind. First, remember the fundamental principle: "The system curve is not determined by the pump." It is determined by the conditions on the piping system side, such as pipe diameter, length, valve opening, and the complexity of the piping layout. So, it's a common story in the field: people might be complaining about insufficient pump capacity when the real cause is piping that's too narrow, creating excessive resistance. For example, if you double the piping resistance coefficient K for the same pump, the flow rate drops to about 70%. Before suspecting the pump, re-examine the system curve.
Next, don't forget that the affinity laws assume "complete similarity." When you change the impeller diameter in this tool, the curve changes similarly because it assumes the pump shapes are geometrically similar and that efficiency and internal flow conditions are identical. In actual product lineups, complete similarity is rare, and significant size differences can cause deviations due to factors like changes in efficiency. The golden rule is to always verify the "theoretical value" from the tool against the actual measured curve in the catalog.
Finally, note that the simulation is based on "water." The formulas used in this tool cannot be directly applied to liquids with viscosities significantly different from water (e.g., oil or syrup). Higher viscosity not only increases piping resistance but also increases internal pump losses, causing the characteristic curve itself to shift downward. For handling high-viscosity fluids, you'll need dedicated correction factors or catalog data.
What is Centrifugal Pump Curves Simulator?
Centrifugal Pump Curves Simulator is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.
By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.
Set impeller diameter (vD) in mm, typically 80–300 mm for standard centrifugal pumps
Choose rotational speed (vN) in rpm; common values are 1450, 2900, or 3600 rpm for electric motors
Adjust system resistance curve (vPhi, dimensionless) to simulate friction losses and static head in your piping network
Observe the operating point where pump curve intersects system curve on the H-Q plot
Monitor efficiency at operating point (η op) and compare against best efficiency point (BEP)
Worked Example
A 150 mm impeller pump running at 2900 rpm with system resistance exponent Phi=2.0 (typical for centrifugal systems) produces: Q op = 85 m³/h, H op = 28 m, η op = 78%. The BEP occurs at Q BEP = 92 m³/h with η max = 82%, yielding specific speed Ns = 45 rpm·(m³/h)^0.5/m^0.75. Operating 7% away from BEP toward lower flow indicates acceptable efficiency margin for variable demand.
Practical Notes
Larger impellers at fixed speed shift the pump curve right (higher Q) and up (higher H); reducing speed by 20% cuts flow by 20% and head by 36% (cube law dependence)
System curves with Phi > 2 represent heavily friction-dominated networks (long pipelines, small diameter); Phi = 1 indicates pure static lift
Operating far left of BEP increases radial thrust on bearings; far right risks cavitation and vibration—stay within ±15% Q BEP for reliability
Specific speed Ns < 50 favors high-head, low-flow designs (gear pumps); Ns > 150 indicates mixed-flow or axial geometries