Overlay multi-speed H-Q curves using affinity laws and find the operating point at the intersection with the system resistance curve. Evaluate NPSH cavitation margin in real time.
Parameters
Machine Type
Presets
Design Point (100% speed)
Design Flow Qd
m³/s
Design Head Hd
m
Design Efficiency ηd
%
Speed Setting
Speed ratio n/nd
%
Piping System
Static Head Hs
m
Resistance Coeff. R
NPSH
NPSHrequired
m
NPSHavailable
m
Performance Curves & Operating Point
Results
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Op. Flow Q (m³/s)
—
Op. Head H (m)
—
Efficiency η (%)
—
Shaft Power P (kW)
—
NPSH Margin (m)
—
Cavitation Status
Pump
Theory & Key Formulas
Speed ratio r = n/nd:
Q ∝ r | H ∝ r² | P ∝ r³
System curve:
Hsys = Hs + R·Q²
What is a Pump & Fan Performance Curve?
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What exactly is a "performance curve" for a pump or fan? I see the simulator has a graph with Flow (Q) on the bottom and Head (H) on the side.
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Basically, it's the machine's fingerprint. It shows you how much pressure (or "head") the pump can generate at different flow rates when running at a fixed speed. In practice, for a given pump, you can't have maximum flow and maximum pressure at the same time. Try moving the "Design Flow Q" and "Design Head H" sliders above—you'll see the peak of the curve shift, defining the machine's ideal design point.
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Wait, really? So the curve changes if I change the design? And what's that other line labeled "System Curve"?
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Exactly! The pump curve is what the machine can do. The system curve is what the piping network needs. It represents the total head required to push a certain flow through the pipes, accounting for static lift and friction. The point where these two curves cross is the actual operating point. In the simulator, you can change the "Static Head H" and "Resistance Coeff. R" to see how the system curve bends and shifts that operating point.
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That makes sense! But what about the "Speed ratio" control? I see multiple pump curves appearing when I move it.
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Great observation! That's the power of variable speed. When you change the "Speed ratio n/n", you're simulating a Variable Frequency Drive (VFD) changing the motor's RPM. According to the Affinity Laws, the whole pump curve shifts. A common case is reducing speed at night to match lower demand, which saves a huge amount of energy. Try sliding the speed ratio down and watch how the operating point moves left and down along the system curve.
Physical Model & Key Equations
The core scaling relationship for pumps and fans is governed by the Affinity Laws. They predict how performance changes with rotational speed (n) for a given machine.
Q is volumetric flow rate [m³/s], H is head [m], P is shaft power [W], and n is rotational speed [rpm]. The power's cubic relationship is key for energy savings.
The System Curve defines the hydraulic demand of the piping network. The total head required is the sum of the static head (lifting fluid) and the dynamic head (overcoming pipe friction).
$$ H_{sys} = H_s + R \cdot Q^2 $$
Hsys is the total system head [m], Hs is the static head (a constant), and R is the system resistance coefficient. The Q² term shows friction increases dramatically with flow.
Frequently Asked Questions
The system curve is determined by external conditions such as piping resistance and static head, so it does not change even if the rotational speed ratio is changed. However, since the pump performance curve changes according to the affinity laws, the intersection point (operating point) shifts, resulting in changes in flow rate and head.
On the simulator, the area where the NPSH (Net Positive Suction Head) value falls below the pump's required NPSH is visualized in red or another color. Check whether the operating point falls within this danger zone; if it does, measures such as reducing the rotational speed or decreasing piping resistance are necessary.
In the input fields on the screen, enter the numerical values for flow rate Qd, head Hd, and shaft power Pd at the design rotational speed. Based on these, the affinity laws are applied, and the performance curves for any rotational speed ratio are automatically calculated and displayed.
By displaying multiple curves with different rotational speed ratios simultaneously, you can visually compare energy-saving operation and responses to load fluctuations. For example, you can evaluate in real time which rotational speed is optimal for partial load conditions, as well as the flow rate and power consumption from the intersection with the system curve.
Real-World Applications
HVAC System Control: In large building air conditioning, fan speeds are varied based on daily occupancy and temperature. Using a VFD to lower fan speed by 20% reduces the power required by nearly 50%, as shown by the cubic law, leading to massive electricity savings compared to simply closing dampers.
Water Supply & Booster Pumps: Municipal water networks use pumps to maintain pressure. Demand fluctuates hourly. Instead of turning pumps on/off, operators use VFDs to smoothly adjust pump speed, matching the system curve's demand precisely and avoiding damaging pressure surges ("water hammer").
Industrial Process Cooling: In a chemical plant, cooling tower fans must reject heat based on the process load. The simulator's principle is used to select a fan that can operate efficiently across a range of speeds, ensuring the process stays at the correct temperature while minimizing operating costs.
Pump NPSH Analysis (Cavitation Prevention): The Net Positive Suction Head (NPSH) parameters in the simulator are critical for avoiding cavitation. Engineers use curves like these to ensure the pump's required NPSH is always below the available NPSH from the system, preventing damaging bubbles that erode impellers.
Common Misconceptions and Points to Note
When starting with this simulator, there are several pitfalls that engineers, especially those with less field experience, often fall into. A major misconception is thinking that "affinity laws are universal rules applicable to everything". Affinity laws hold true only when the internal flow conditions of the pump or fan are "dynamically similar", meaning the dimensionless numbers match. For example, with highly viscous liquids or when operating far from the design speed (e.g., speed ratio r below 0.5 or above 1.5), efficiency can drop significantly, and the simple cube law no longer applies. Remember, "the tool's results are merely an ideal guideline."
Next, a common error is incorrectly setting the static head (Hs) of the system curve. This is "the height the pump must lift the liquid", but it's often overlooked in closed systems (e.g., building HVAC circulation water systems). Even in closed systems, the pressure difference between the highest point in the system and the pump suction acts as an "apparent static head". Mistakenly setting this to zero will severely skew the operating point calculation. For instance, if a cooling coil is located 10m above the pump, you must set Hs=10m.
Finally, over-reliance on NPSH (Net Positive Suction Head) evaluation. Even if the tool indicates sufficient NPSH margin, cavitation can occur with poor piping design. For example, turbulence caused by an elbow placed too close to the pump suction can increase the required NPSH beyond the catalog value. Simulation results represent "necessary conditions"; meeting the sufficient conditions requires proper piping layout.
Enter design flow rate Qd (m³/s) and design head Hd (m) for your pump or fan baseline curve at 100% speed.
Input design efficiency ηD (%) and select the number of speed ratios to simulate (e.g., 80%, 90%, 100%, 110% for variable-frequency drive operation).
For each speed ratio, the simulator applies affinity laws (Q ∝ N, H ∝ N², P ∝ N³) and overlays H-Q curves. Adjust system resistance curve parameters and read the operating point intersection.
Monitor NPSH margin by entering inlet pressure, fluid vapor pressure, and elevation. The tool flags cavitation risk when margin drops below 0.5 m.
Worked Example
Centrifugal pump with Qd=150 m³/h (0.0417 m³/s), Hd=45 m, ηD=82%. At 90% speed ratio (VFD setpoint): affinity law yields Q=0.0375 m³/s, H=36.45 m, shaft power P = (ρgQH)/η = (1000×9.81×0.0375×36.45)/0.82 ≈ 16.2 kW. For inlet absolute pressure 101.3 kPa, fluid vapor pressure 2.34 kPa (20°C water), NPSH available = (101.3−2.34)/(1000×9.81)−0.5 m elevation = 9.8 m. Operating safely with 2.1 m margin above 3% efficiency loss threshold (7.7 m NPSH required).
Practical Notes
Always verify pump suction conditions: low inlet pressure (high altitude, hot fluid, flooded suction loss) reduces NPSH available rapidly. A 5 kPa drop costs ~0.5 m margin.
Affinity law accuracy degrades beyond ±20% speed variation for complex impeller geometries; use detailed pump curves when operating outside 80–120% range.
Operating point drift occurs when system resistance changes (pipe fouling, valve throttling); re-solve the intersection graphically to confirm efficiency doesn't fall below acceptable limits (typically >75% for process reliability).
Fan performance differs: pressure-rise curves are flatter, requiring explicit fan-laws correction Q̃=Q×(N/ND), Ĥ=H×(N/ND)² to prevent surge at low speeds.