Centrifugal Pump Sizing: A Worked Example (Head, NPSH and Power)

A centrifugal pump can meet its duty perfectly on paper and still fail on site. The flow is right, the head is right, the motor is big enough—and then it cavitates the moment someone warms up the feed, because nobody checked the suction side against the fluid’s vapour pressure. Pump sizing isn’t one calculation; it’s four that have to agree with each other. Here’s the whole chain worked through with real numbers: the duty point, total dynamic head, the NPSH margin that decides whether the pump survives, and the power that sizes the motor.

Start With the Duty Point, Not the Pump

Before you look at a single pump curve, you need four things nailed down: the flow rate the process actually demands, the total head the pump has to generate to move that flow, the fluid’s properties (density, viscosity, and — critically — vapour pressure at the operating temperature), and the suction conditions. Get any of these wrong and every downstream number inherits the error. The flow and head together define the duty point — the single spot on the pump curve you’re designing to hit.

A pump rarely lives alone. On a packaged unit it’s one item on a process skid, and its flow and temperature come straight off the same heat and mass balance that sets your reactor and heat exchanger duty. For this example, take a straightforward transfer: move a water-like liquid (density 1000 kg/m³) at 50 m³/h from a suction tank into an elevated delivery header, through a run of pipe with the usual valves, elbows and a control valve.

Step 1 — Fix the Flow and the Fluid

Flow is 50 m³/h, or 0.0139 m³/s. That number alone drives your pipe sizing, and pipe sizing quietly drives everything else. Run 50 m³/h through a DN100 line and the velocity works out to about 1.8 m/s — comfortably inside the 1–3 m/s band you want for a pump suction and discharge. Drop to DN80 and velocity jumps to roughly 2.8 m/s, which spikes your friction losses and eats into NPSH. The pipe you draw on the P&ID is a hydraulic decision, not just a layout one.

Step 2 — Total Dynamic Head (TDH)

Total dynamic head is what the pump has to produce, and it’s the sum of four components: static head (the vertical lift), friction head (losses in pipe and fittings), velocity head (usually small), and any pressure-head difference between the suction and discharge vessels.

For our transfer, say the delivery header sits 18 m above the pump centreline and the suction tank level is 2 m above it (a flooded suction). The static head is the difference:

Static head = 18 − 2 = 16 m

Friction losses come from summing the equivalent length of every pipe run, elbow, valve and the control valve’s drop — typically with Darcy–Weisbach, or Hazen–Williams for straight water service. For this system that totals about 6 m at 50 m³/h. Velocity head is negligible here. So:

TDH = static head + friction head = 16 + 6 = 22 m

One thing worth saying out loud: friction head is flow-dependent and rises with the square of flow, while static head is fixed. That’s why a pump sized for one flow behaves very differently when the operator throttles it — you’re sliding along a system curve, not sitting on a single point.

Step 3 — The NPSH Check (Where Pumps Actually Die)

This is the step that gets skipped, and it’s the one that causes cavitation, noise, impeller pitting and early seal failure. The rule is simple: the net positive suction head available from your system must comfortably exceed the net positive suction head required by the pump, with margin to spare.

NPSH available is set entirely by your system — not the pump:

NPSHa = (P_atm − P_vapour) / (ρ·g) + static suction head − suction friction

At 30 °C:
  (101,325 − 4,246) / (1000 × 9.81) = 9.90 m
  + 2 m static suction (flooded) − 0.8 m suction friction
NPSHa ≈ 11.1 m

If the pump’s curve gives an NPSH required of 3.5 m at this duty, you have 7.6 m of margin. Healthy. Job done — as long as nothing about the fluid or the suction ever changes.

But watch what happens when it does. Warm that same fluid to 80 °C and its vapour pressure climbs from about 4.2 kPa to roughly 47 kPa. Recompute:

At 80 °C:
  (101,325 − 47,400) / (1000 × 9.81) = 5.50 m
  + 2 m − 0.8 m  →  NPSHa ≈ 6.7 m   (still OK)

Now put the pump on a 3 m suction LIFT instead of a flooded suction:
  5.50 − 3.0 − 0.8 ≈ 1.7 m   →  BELOW the 3.5 m required

Same pump, same flow, same head — and it now cavitates, purely because of temperature and suction geometry. That’s the whole reason NPSH is a separate, non-negotiable check: the two conditions that destroy it, hot fluid and suction lift, are exactly the ones a duty-point-only calculation never sees.

Step 4 — Hydraulic Power, Shaft Power and Motor Selection

Hydraulic power is the useful work delivered to the fluid:

P_hydraulic = ρ · g · Q · H
            = 1000 × 9.81 × 0.0139 × 22
            ≈ 3.0 kW

That’s the ideal figure. The pump isn’t perfect, so shaft power is hydraulic power divided by pump efficiency. At a typical 65% for a pump of this size:

P_shaft = 3.0 / 0.65 ≈ 4.6 kW

Then add a motor margin so you’re not running at the ragged edge of the nameplate — around 15% here — and select the next standard motor frame up:

4.6 × 1.15 ≈ 5.3 kW  →  select a 5.5 kW motor

Note the margin is applied to shaft power, and it also protects you against runout: if the pump ever operates further out on its curve (higher flow, lower head), power demand can climb. Sizing the motor to the duty point alone is how you get nuisance trips six months after commissioning.

Step 5 — Land the Pump on Its Curve

With duty (50 m³/h at 22 m), NPSHr headroom and power in hand, you finally go to the pump curves. You’re looking for a model whose curve passes through — or just above — your duty point, ideally with that point sitting near the best efficiency point (BEP). A pump that hits your duty far to the left of BEP runs rough and wears fast; far to the right, it may run out of NPSH or overload the motor. The goal is a duty point that lives in the sweet 70–110% of BEP band, not merely a curve that happens to reach your numbers. And if the discharge can ever be blocked, a properly sized relief valve protects the pump and piping from deadhead pressure.

Where This Goes Wrong on Real Pump Jobs

Sizing to the duty point and ignoring NPSH. The most common and most expensive miss. The pump meets flow and head, then cavitates in service because the suction side was never checked against vapour pressure at the real operating temperature.

Forgetting that friction head moves with flow. Treating TDH as a fixed number instead of a system curve means the pump behaves unexpectedly the moment flow is throttled or increased.

Applying the power margin to hydraulic power, not shaft power. Skip the efficiency division and you’ll under-size the motor by a third and never know until it trips under load.

Selecting far from BEP. A pump chosen purely because its curve “reaches” the duty point, with no regard for where that point sits, buys you vibration, low efficiency and short bearing and seal life.

Designing suction piping as an afterthought. A long, undersized suction line with too many fittings quietly destroys NPSH available—the cure is short, generous suction piping, decided early, not patched later.

Doing This Without Starting From a Blank Sheet

This full chain—duty point, TDH, NPSH margin, power, and motor selection—is exactly what a good pump sizing worksheet automates, so you change inputs instead of rebuilding formulas and chasing vapor-pressure tables. Our centrifugal pump design templates handle the hydraulics, NPSH, and power checks in one place and sit inside the wider Engineering Design & Calculation Master Bundle alongside every other equipment type. It’s the same philosophy behind our engineering design Excel templates: buy the tested calculation once, and reuse it on every project.

Browse the full template library →

Prefer to prototype the numbers first, or have an engineer sanity-check a tricky suction arrangement? Try the free online engineering calculators, learn more about our engineering team, request a pump sizing review, or message us on WhatsApp.

Frequently Asked Questions

What is total dynamic head in pump sizing?

Total dynamic head (TDH) is the total head a pump must generate to move the required flow—the sum of static head (vertical lift), friction head (losses in pipe and fittings), velocity head, and any pressure difference between the suction and discharge vessels.

What is the difference between NPSH available and NPSH required?

NPSH available is set by your system—atmospheric pressure minus the fluid’s vapor pressure, adjusted for suction static head and friction. NPSH required is a property of the pump, read from its curve. NPSHa must exceed NPSHr, with margin, or the pump cavitates.

Why does a pump cavitate when the fluid gets hotter?

Higher temperature raises the fluid’s vapour pressure, which directly reduces NPSH available. A pump with healthy suction margin on a cold fluid can lose that margin entirely once the fluid is heated — which is why NPSH must be checked at the true operating temperature.

How do I size the motor for a centrifugal pump?

Calculate hydraulic power (ρ·g·Q·H), divide by pump efficiency to get shaft power, then add a margin (commonly around 15%) and select the next standard motor size up. Apply the margin to shaft power, not hydraulic power, and check power demand across the pump’s operating range.

Related Engineering Guides

Related Tools & Templates

Standards & Reference Frameworks

Hydraulic Institute (HI) standards for pump nomenclature, testing and NPSH; API 610 for centrifugal pumps in petroleum, petrochemical and gas service; ISO 5199 and ISO 2858 for chemical-process pumps; and ANSI/HI test procedures for verifying head, efficiency and NPSH required.