Contents
Every process plant is full of pumps, and most of them were sized from the same handful of numbers: how much flow, against how much head, with how much suction margin, using how much power. Get one wrong and the pump runs off its curve, cavitates or trips its motor. This three-part series sizes the main equipment in the feed section you met in How to Read a PFD and a P&ID: pump P-101 here, heater E-101 in Part 2 and feed tank T-101 in Part 3.
The aim is not to replace the engineer who specifies the pump. It is to show owners and managers where the numbers on a pump data sheet come from, so that they can check them and ask the right questions.
Step 1: set the flow
P-101 moves the feed from T-101 through E-101 to reactor R-101 at 6,250 kg/h. With a density of 850 kg/m³ that is 7.35 m³/h at normal flow. Pumps are specified at a rated flow above normal, to cover uncertainty and control. A 10% margin gives 8.09 m³/h. Margins belong in the design basis, stated once, not added again by each discipline.
Step 2: add up the head
The pump must lift the liquid, overcome every pressure drop on the way and deliver it at the pressure the reactor needs. Work out the pressure the pump must produce at its discharge, subtract what it already has at its suction, and convert the difference to metres of liquid.
| Discharge side, at rated flow | kPa | Basis |
|---|---|---|
| Reactor operating pressure | 100 | 1.0 barg |
| Static lift to the reactor nozzle | 67 | 8 m above the pump |
| Pipe friction, discharge | 41 | 1½" pipe, 60 m equivalent length |
| Heater E-101, tube side | 50 | Allowance; checked in Part 2 |
| Flow control valve | 120 | Enough drop to control well |
| Flow meter and strainer | 20 | Allowance |
| Required discharge pressure | 398 | 3.98 barg |
| Less: suction pressure at low tank level | 7 | 1.0 m of liquid, less suction friction |
| Differential pressure | 391 | Total head 46.9 m |
Pipe friction comes from the Darcy–Weisbach equation, ΔP = f × (L/D) × ρv²/2. In the discharge line the velocity is 1.71 m/s, the Reynolds number is about 99,085 (fully turbulent) and the friction factor is 0.0227. The control valve is often the term people want to cut. Don't: a valve with too little pressure drop cannot control the flow.
The head is converted from pressure with H = ΔP / (ρg). Head in metres is the natural unit for pumps because a centrifugal pump produces the same head whatever the liquid's density; the pressure it produces scales with density.
Step 3: check the system curve
Static lift and fixed pressures do not change with flow. Friction rises roughly with the square of flow. Plotting the total against flow gives the system curve. The pump's own curve falls as flow rises. The pump runs where the two cross.
Two things follow from the shape. First, because most of the head here does not depend on flow, a small error in the friction estimate barely moves the operating point. Second, a pump with a curve that is too flat in this region will hunt as the control valve moves. Pick a pump whose rated point sits near its best efficiency point.
Step 4: check the suction (NPSH)
If the pressure at the pump inlet falls below the liquid's vapour pressure, bubbles form and collapse inside the impeller. That is cavitation: noise, vibration, lost head and eroded impellers. The check compares the net positive suction head available from the system with the NPSH required by the pump, from the vendor's curve.
NPSHa = (Patm − Pvap) / (ρg) + liquid height above the pump − suction friction
With the tank open to atmosphere, a vapour pressure of 2.9 kPa at 20 °C, 1.0 m of liquid at low level and 0.19 m of suction friction, NPSHa is about 12.6 m. A small pump of this kind typically needs 2.5 m. The margin is ample. It shrinks quickly if the liquid is hot or volatile, which is why NPSH is checked at the worst case: lowest tank level, highest liquid temperature, highest flow.
Step 5: power and motor
Hydraulic power is P = ρ g Q H. At rated flow and head that is 0.88 kW. Small centrifugal pumps are not very efficient. At 45%, the shaft power is about 1.95 kW. The motor is sized for the end of the pump curve, not the rated point. Allowing about 25% for that and a margin, the next standard size, 3 kW, is a reasonable selection. The PFD in the earlier article shows P-101 delivering 4.0 barg; the build-up above arrives at 3.98 barg, which is how a number on a PFD is checked.
The data sheet
| Item | P-101 value |
|---|---|
| Service | Reactor feed, T-101 to R-101 via E-101 |
| Normal / rated flow | 7.35 / 8.09 m³/h |
| Liquid density / viscosity | 850 kg/m³ / 0.60 mPa·s at 20 °C |
| Suction / discharge pressure (rated) | 0.07 / 3.98 barg |
| Differential head | 46.9 m |
| NPSH available | 12.6 m |
| Estimated shaft power | 1.95 kW; motor 3 kW |
The data sheet goes to vendors, who return their curves. The engineer then checks each offer against the system curve, the NPSH margin and the motor size, and confirms that the shutoff head does not exceed the design pressure of the discharge piping and E-101. That last check links pump sizing to pressure relief.
Key points
- Size at a rated flow above normal, with the margin set once in the design basis.
- Head is the discharge pressure needed minus the suction pressure available, converted to metres of liquid.
- Most of the head in a typical plant is static lift and fixed pressure drops, not pipe friction.
- Check NPSH at the worst case: lowest level, hottest liquid, highest flow.
- Size the motor for the end of the pump curve, and check shutoff head against the design pressure downstream.
Next: Part 2 sizes the heater, E-101.
The plant, fluid properties and equipment in this series are an illustrative example. The calculations are preliminary sizing estimates. Final sizing needs vendor data, the applicable codes and a qualified engineer.
