Calculating a Piping System Curve for Closed Loops

A piping system curve represents the differential head the pump must develop at each flow rate. The treatment of an expansion tank depends on whether the circulating stream passes through the tank and whether the flow path crosses a free surface. Tank pressure alone is not pump head.

Hydraulic definition of the loop

The term closed loop here means a circulating path with continuous liquid pressure from pump discharge back to pump suction. In a completely filled, pressurized loop, elevation head gained while fluid rises is recovered while it descends. Static inlet head and static discharge head therefore cancel around the circuit.

The pump must overcome the flow-dependent pressure losses of the piping, chiller, valves, fittings, strainers, and other components. A useful head-form system curve is:

H_system(Q) = H_static + H_pipe(Q) + H_equipment(Q) + H_minor(Q)

For a pressurized closed loop with no hydraulic break, H_static = 0 around the complete circuit. In the turbulent-flow region, many friction and minor-loss terms vary approximately with Q^2, although equipment data and pipe calculations should supply the actual relationship.

An expansion tank connected near the pump suction establishes the system pressure reference. Its gas charge and system fill condition affect suction pressure, available pressure throughout the installation, and pressure changes caused by thermal expansion. That pressure acts on the loop and does not become an additional differential-head requirement.

Check 1: Tank connection arrangement

Trace the actual circulating path rather than classifying the vessel by its name.

A one-connection diaphragm tank is a compliance volume, not an inline component. During temperature or pressure transients, water can move into or out of it; that temporary movement does not make the normal pump flow pass through the tank. Adding vessel volume, gas precharge, or static tank pressure to the steady-flow system curve is wrong practice.

Check 2: Pressure continuity and free surfaces

Inspect where the return pipe terminates relative to the operating liquid level. A system can recirculate the same water and still contain a hydraulic break. The deciding feature is pressure continuity, not whether the water is discharged from the facility.

If the return terminates below the liquid surface, pressure is transmitted through the liquid between the return and suction connections. The pump does not repeatedly lift the entire circuit elevation on every pass. Move to Check 4 and calculate the local connection losses.

If the return falls through an air gap, its pressure is reset at the free surface. The pump must raise the liquid from the source free surface to the return discharge elevation. Move to Check 3. Record both elevations under operating conditions; the tank size and shape can change the liquid-level elevation as volume changes.

For a diaphragm tank on a dead-end branch, verify that no normal-flow outlet exists. The branch pressure then follows the connection-point pressure, while the diaphragm separates the system water from the gas charge. Move directly to Check 5 after accounting for the tee in the main pipe.

Check 3: Static-head requirement

For a return discharging above a liquid surface, calculate static head from the vertical elevation difference:

H_static = z_return_discharge - z_source_surface

Use elevations referenced to the same datum. The source surface is the free surface from which the pump ultimately draws; the return point is where the liquid leaves the pressurized pipe and enters the air gap. Add this term to the system curve because it does not diminish as flow approaches zero while the stated elevations remain fixed.

Do not substitute expansion-tank gas pressure for this elevation term. Gas pressure establishes an absolute or gauge-pressure level in a sealed system; static head in a broken-pressure path represents energy that the pump must supply between two hydraulic boundaries.

If the return is submerged, omit this net lift around the circuit. Include the loss where flow leaves the return pipe and the loss where it enters the suction pipe. Move to Check 4.

Check 4: Local and through-tank losses

For each fitting or connection carrying the circulating flow, calculate pressure loss from its loss coefficient:

Δp_minor = K × ρ × v^2 / 2

h_minor = K × v^2 / (2g)

Use velocity in the pipe or nozzle to which the selected K value applies. Sum the relevant coefficients only once. A dead-end expansion-tank branch has essentially zero steady branch velocity, so entrance and exit coefficients for flow through the tank do not apply.

For a through-flow tank, an illustrative estimate uses one velocity pressure for entry and one-half velocity pressure for exit, giving K_total = 1.5. At v = 2.5 m/s and ρ = 1000 kg/m^3:

ρv^2/2 = 1000 × 2.5^2 / 2 = 3125 Pa

Δp = 1.5 × 3125 = 4687.5 Pa ≈ 4700 Pa

This is approximately 0.48 m or 19 in. of water head. Treat the coefficients as an estimate for the stated arrangement, not as universal tank values. Obtain project coefficients from the connection geometry, component data, or a tested pressure drop when accuracy affects pump selection.

Check 5: Symptom-to-cause test

Pressure readings must be compared at defined elevations and converted to head using the circulating fluid density. Separate pressure-level questions from differential-head questions: expansion-tank charge and fill pressure govern the former, while the system curve governs the latter.

System-curve construction procedure

1. Draw the complete path from pump discharge through the chiller and distribution piping back to pump suction.
2. Mark every free surface, air gap, diaphragm, tank inlet, tank outlet, and dead-end branch.
3. Classify the expansion tank as a one-connection compliance vessel, a submerged through-flow vessel, or an air-gap return vessel.
4. For a continuous pressurized loop, set net loop H_static to zero. For an air-gap return, calculate static head from the source free surface to the return discharge elevation.
5. Calculate pipe friction at each selected flow point using the installed pipe lengths, sizes, fluid properties, and fitting method.
6. Add chiller and other equipment pressure drops from their applicable performance data.
7. Add tee loss in the circulating main for a dead-end diaphragm branch. Do not assign full system flow to that branch.
8. For a through-flow tank, add inlet, outlet, and other applicable local losses using coefficients matched to the actual geometry.
9. Calculate total head over enough flow points to plot H_system(Q), then compare the curve with the pump curve on the same flow and head basis.

Numbered verification readings

1. Check 1: Tank-path reading. Confirm the pipe trace. Expect one connection and no sustained branch flow for a diaphragm expansion tank; expect identifiable inlet-to-outlet flow for a through-flow tank.
2. Check 2: Free-surface reading. Observe the return termination at the operating liquid level. Expect pressure continuity for a submerged termination and a visible hydraulic break for an air-gap discharge.
3. Check 3: Static-term reading. With a continuous pressurized loop, expect no net elevation term around the complete circuit. With an air gap, expect the curve intercept to include the measured vertical lift.
4. Check 4: Differential-pressure reading. At a stable measured flow, compare pump differential head with calculated pipe, fitting, chiller, and tank-connection losses. Expect agreement within the limits of the instruments and component data.
5. Check 5: Multi-point curve reading. Repeat at additional stable flows. After separating any static term, expect the resistance portion to increase with flow and the operating point to lie at the intersection of the measured system curve and pump curve.

Frequently asked questions