18.1 Pump Curves, System Curves, and Operating Point
Key Takeaways
- The pump operating point is the intersection of the pump curve and the system curve, not a flow selected from either curve alone.
- A system curve combines static head with velocity-dependent losses; static head moves the curve vertically while friction steepens it.
- For pumps in series, heads add at the same flow; for pumps in parallel, flows add at the same head.
- Pump power depends on flow, total dynamic head, specific gravity, and efficiency; forgetting efficiency understates required brake horsepower.
- Cavitation checks require available net positive suction head to exceed required net positive suction head with a practical margin.
Pump Curves as Energy Statements
The April 2024 PE Civil WRE specification includes pump application and analysis within closed-conduit hydraulics, with wet wells, lift stations, and cavitation as named applications. A pump curve is not just a vendor graph. It is the relationship between flow and head the pump can add at a given speed and impeller. A system curve is the head the piping system demands at each flow. The operating point occurs where those two curves meet.
What Each Curve Means
| Curve or value | What it represents | Exam use |
|---|---|---|
| Pump head curve | Head added by one pump as flow changes | Usually slopes downward as Q increases |
| Efficiency curve | Wire-to-water or pump efficiency versus Q | Used for horsepower and best efficiency point checks |
| System curve | Static head plus friction and minor losses | Usually rises with Q because losses rise with velocity |
| NPSHR curve | Net positive suction head required by the pump | Compared with calculated NPSHA |
| BEP | Best efficiency point | Preferred operating region, not automatically the design point |
Write the system head as Hsys = Hstatic + hL. For Darcy-Weisbach and most minor-loss setups, hL varies approximately with Q^2. For Hazen-Williams, hL varies approximately with Q^1.85. Static head is the elevation or pressure difference that remains even at zero flow. If the suction and discharge reservoirs have fixed water surfaces, static head is the discharge water surface elevation minus the suction water surface elevation.
Operating-Point Workflow
- Identify the datum and compute static head.
- Express all pipe, valve, entrance, exit, meter, and fitting losses as a function of flow.
- Add static head and losses to form the system curve.
- Intersect the system curve with the pump curve by graph, table interpolation, or equation.
- At that flow, check velocity, horsepower, efficiency, NPSHA, and whether the pump arrangement matches the station requirement.
For horsepower in U.S. customary units, brake horsepower is approximately Q(gpm) x H(ft) x specific gravity / [3960 x efficiency]. Efficiency must be decimal. A 70 percent pump uses eta = 0.70, not 70. For SI work, hydraulic power is rho g Q H, then divide by efficiency to get input power.
Series, Parallel, and Speed Changes
Pumps in series carry the same flow and add head. They are used when one pump cannot overcome the required head. Pumps in parallel operate at the same head and add flow. They are used when demand varies or firm capacity is needed. Parallel pumps do not double station flow unless the system curve is flat; added flow increases headloss and shifts each pump to a lower individual flow.
Affinity laws describe the same pump near similar operating conditions. For speed N, Q varies with N, head varies with N^2, and power varies with N^3. These laws are useful for variable-frequency drive questions, but the revised pump curve still must meet the system curve.
Cavitation and Suction Checks
Cavitation occurs when local absolute pressure falls near vapor pressure and vapor bubbles collapse inside the pump. For a vented wet well feeding a pump, NPSHA is approximately atmospheric pressure head plus liquid surface elevation above the pump centerline minus vapor pressure head minus suction losses. Low wet-well level, clogged suction screens, hot water, long suction piping, or high suction velocity can reduce NPSHA. On the exam, treat NPSHA greater than NPSHR as necessary but not a license to ignore margin, cycling, or operations.
Common traps are using discharge pressure instead of total dynamic head, adding pump heads for parallel pumps, reading a pump curve at the design flow without checking the system curve, and forgetting that a throttled valve raises system head and lowers flow. Always sketch the direction of change before trusting the arithmetic.
A pump has the approximate curve H = 120 - 0.000030Q^2, where H is in ft and Q is in gpm. The connected system has Hsys = 48 + 0.000020Q^2. What is the operating flow?
A pump draws from a vented wet well. The water surface is 8 ft above the pump centerline, atmospheric pressure head is 33.9 ft, vapor pressure head is 1.0 ft, and suction losses are 4 ft at the operating flow. If the pump curve shows NPSHR = 22 ft, what is the approximate NPSH margin?