By Wu Peng, Senior Instrumentation Engineer · 20+ years in process instrumentation · Last reviewed July 6, 2026
Flow rate and pressure are related, but not by one single formula. Through a fixed restriction, flow rises with the square root of the pressure drop: double the differential pressure and flow increases by about 41 percent, not 100. Along a pipe run the relationship flips: pushing twice the flow through the same line costs roughly four times the friction pressure loss.
Much of the confusion starts because “pressure” means three different things in a piping system: static line pressure, differential pressure across a restriction, and pump discharge pressure. Each one has its own relationship with flow. This guide separates them, gives the five formulas that cover most plant calculations, works a full example in SI units, and includes a calculator you can run with your own numbers.
Contents
- Three relationships, not one
- The square-root law: flow and differential pressure
- The five formulas that cover plant work
- Worked example: flow rate from a 25 kPa pressure drop
- Square-root scaling and turndown
- Pressure vs flow rate chart
- Pressure drop in real piping
- Pump curves and system curves
- Measuring flow from pressure in practice
- Pressure to flow calculator
- FAQ
- Request a quote
Three relationships, not one
Two definitions first. Flow rate (Q) is the volume of fluid crossing a pipe section per unit time, in m³/h, L/min, or GPM. Pressure (P) is force per unit area, the energy per unit volume available to push the fluid, in Pa, bar, or psi. Flow is what you sell or dose; pressure is what you spend to move it.
Before reaching for a formula, decide which pressure you are actually looking at. A sealed pipe at 10 bar has zero flow; a wide-open drain at 0.2 bar can pass a lot of water. Line pressure by itself tells you nothing about flow. The table below sorts the five situations engineers usually mean when they ask how flow rate and pressure relate.
| You are looking at | How flow and pressure relate | Governing relation |
|---|---|---|
| DP across a restriction (orifice, venturi, nozzle) | Flow rises with the square root of the pressure drop | Q ∝ √ΔP |
| The same streamline, speeding up (Bernoulli) | Where velocity rises, static pressure falls | P + ½ρv² + ρgh = constant |
| Friction along a pipe run (turbulent) | Pressure loss rises with roughly the square of flow | ΔP ∝ Q² |
| A centrifugal pump discharge | More back-pressure means less flow, along the pump curve | pump curve |
| Laminar flow in small lines and viscous oils | Flow is directly proportional to the pressure drop | Hagen-Poiseuille, Q ∝ ΔP |
The square-root law: flow and differential pressure
Put a restriction in a pipe and the fluid must speed up to get through it. That velocity comes from pressure: Bernoulli says the static pressure falls where velocity rises. Kinetic energy scales with velocity squared, so the pressure drop across the restriction scales with flow squared. Read it the other way around and you get the working rule of every differential pressure flow meter:
Q = C · E · A · √(2ΔP / ρ) with E = 1 / √(1 − β⁴)
- Q: volumetric flow rate (m³/s)
- C: discharge coefficient, about 0.60 to 0.61 for a standard orifice plate per ISO 5167
- E: velocity-of-approach factor; β = d/D is the bore-to-pipe diameter ratio
- A: bore area (m²)
- ΔP: differential pressure across the element (Pa)
- ρ: fluid density (kg/m³)
Everything except ΔP is fixed by geometry and fluid, so Q is proportional to √ΔP. This one equation is the basis of orifice plates, venturi tubes, flow nozzles, and averaging pitot tubes. Many textbook examples quietly drop the E factor; at β = 0.6 that alone costs you about 7 percent of the answer.
The five formulas that cover plant work
These five relations handle roughly 90 percent of day-to-day flow and pressure calculations in a plant. The notes column tells you when each one applies.
| Use case | Formula | Notes |
|---|---|---|
| Bernoulli (ideal fluid) | P + ½ρv² + ρgh = constant | Energy conservation along a streamline, no friction |
| Orifice / venturi (liquid) | Q = C·E·A·√(2ΔP/ρ) | The basis of DP flow measurement, ISO 5167 |
| Pipe friction (turbulent) | ΔP = f·(L/D)·(ρv²/2) | Darcy-Weisbach; friction factor f from the Moody chart |
| Laminar flow (Re below 2300) | Q = π·ΔP·D⁴ / (128·μ·L) | Hagen-Poiseuille; small bores, viscous oils; linear in ΔP |
| Valve or fitting with a Cv rating | Q = Cv·√(ΔP/SG) | Unit-bound: Q in US GPM, ΔP in psi, SG = specific gravity |
Two practical warnings. First, the orifice formula uses the differential pressure across the element, never the line pressure; a gauge reading 5 bar upstream tells you nothing about flow on its own. Second, the Cv formula only works in US units (GPM and psi). Substituting bar and m³/h without converting is one of the most common calculation errors we see in supplier quotes.
Worked example: flow rate from a 25 kPa pressure drop
An orifice plate sits in a horizontal water line, pipe inside diameter 100 mm, bore 60 mm. The DP transmitter reads 25 kPa. Water at 20 °C, density 1000 kg/m³.
- Beta ratio: β = d/D = 60/100 = 0.6
- Velocity-of-approach factor: E = 1/√(1 − 0.6⁴) = 1/√0.8704 = 1.072
- Discharge coefficient for a standard orifice at this β and a turbulent Reynolds number: C ≈ 0.61 (ISO 5167 tables)
- Bore area: A = π(0.030)² = 2.827 × 10⁻³ m²
- Velocity term: √(2 × 25000 / 1000) = √50 = 7.07 m/s
- Q = 0.61 × 1.072 × 2.827×10⁻³ × 7.07 = 0.0131 m³/s
- Convert: 0.0131 × 3600 ≈ 47.1 m³/h, about 207 US GPM
The same 25 kPa across a different bore gives a different flow. That dependence on geometry is why a DP flow element carries a calculation sheet matched to the installed bore, pipe ID, and fluid, and why swapping an orifice plate without recalculating the range silently corrupts the reading.
Square-root scaling and turndown
Because ΔP scales with Q², the DP signal collapses much faster than the flow does. Using the example above (47.1 m³/h at 25 kPa full scale):
| Flow (% of full scale) | Flow (m³/h) | DP (% of full scale) | DP (kPa) |
|---|---|---|---|
| 100% | 47.1 | 100% | 25 |
| 50% | 23.5 | 25% | 6.25 |
| 25% | 11.8 | 6.25% | 1.56 |
| 10% | 4.7 | 1% | 0.25 |
At 10 percent flow the element produces only 1 percent of its full-scale DP, and transmitter error becomes a large share of the signal. This is why a conventional orifice installation is usually applied across about a 4:1 flow range, and why a high-turndown differential pressure transmitter paired with careful range selection is worth the money when your load swings widely.
Pressure vs flow rate chart
There is no universal pressure-to-flow chart: the numbers depend entirely on the geometry and the fluid, so a chart that does not state its pipe, bore, and fluid is a guess. For one defined case, here is the calculated chart for the element in the worked example (water at 20 °C, 100 mm pipe, 60 mm bore, C = 0.61):
| Differential pressure (kPa) | Flow (m³/h) | Flow (US GPM) |
|---|---|---|
| 5 | 21.0 | 93 |
| 10 | 29.8 | 131 |
| 25 | 47.1 | 207 |
| 50 | 66.5 | 293 |
| 100 | 94.1 | 414 |
Read the shape, not just the values: a 20x increase in pressure drop buys only a 4.5x increase in flow. To build the same chart for your own line, change the diameters, density, and coefficient in the calculator below and tabulate the results.
Pressure drop in real piping
The pressure a pump must supply is the sum of friction in straight pipe, losses at every fitting, and elevation. Working forms:
- Straight pipe: Darcy-Weisbach, ΔP = f·(L/D)·(ρv²/2). In turbulent flow, doubling the flow roughly quadruples the friction loss.
- Fittings: ΔP = K·(ρv²/2). Typical K values: 90-degree elbow about 0.75, gate valve fully open about 0.15, sudden contraction up to about 0.5.
- Elevation: ρgh. Each meter of water column adds 9.81 kPa to the static head the pump must overcome.
Most underperforming pump installations we get called about trace back to a friction estimate that ignored the elbows and valves, or to strainers and heat exchangers fouling up over time and quietly steepening the system curve.
Pump curves and system curves
A centrifugal pump delivers more flow at lower head and less flow at higher head. Plot the pump curve and the system friction curve on the same axes; the intersection is your operating point. If the operating point sits far left of the best efficiency point (BEP), you waste energy and risk recirculation damage. Far right of BEP, the motor can overload when system resistance drops, for example right after a filter change. Size the pump so the design point lands within about 10 percent of BEP.
Positive displacement pumps behave differently: their flow stays nearly constant as pressure rises, until the relief valve opens. If a supplier quotes you a flow at one test pressure, ask for the curve, not the point.
Measuring flow from pressure in practice
If your process already tolerates a restriction, the DP family is the cheapest path to a flow measurement, and it scales to any pipe size. The primary element sets the geometry; a DP transmitter converts the pressure drop to a 4-20 mA or digital flow signal.
- Orifice plate: the default choice for clean liquids, gases, and steam
- Venturi tube: recovers most of the pressure drop; large water and air lines
- Averaging pitot tube: lowest permanent loss, hot-tap insertion into large ducts and mains
- Browse all differential pressure flow meters
When you would rather not add any restriction, measure flow directly instead of inferring it from pressure: a magnetic flow meter for conductive liquids, or a Coriolis mass flow meter where you need mass flow and density in one instrument. For saturated or superheated steam, where density moves with pressure, see the options on our steam flow meter page.
Application example
Steam metering with pressure compensation. A process plant in South Asia needed to meter saturated steam on a DN100 line at 7 bar, spanning 0 to 8 t/h. Steam density changes with line pressure, so a plain volumetric reading turns every boiler pressure swing into a mass-flow error. We configured a vortex flow meter with integrated temperature and pressure compensation: the flow computer reads both variables and converts the volumetric signal to mass flow continuously, so the meter tracks true steam consumption through normal header pressure swings instead of drifting with them.
Pressure to flow calculator
Run your own numbers below. The first tab solves the orifice equation from this guide, the second rescales an existing DP flow reading with the square-root law, and the third handles valve Cv. For the full version with worked notes, see the flow rate from pressure calculator, or browse all engineering tools.
Pressure to flow calculator
Liquids only. Gases and steam are compressible: density changes with pressure and temperature, so these formulas need an expansibility correction and density at operating conditions. Results are engineering estimates, not a calibration.
If the pressure values in your calculation arrive in mixed units, our pressure units guide has the exact conversion factors.
The worked examples above run in m3/h. If your process figures are in GPM or L/min, the flow rate units guide covers the exact conversions before you size anything.
FAQ
Can you convert psi to flow rate?
Not directly. A pressure value alone does not define a flow; you also need the geometry the fluid passes through. If you know the differential pressure across a defined restriction (an orifice, a valve with a published Cv, a nozzle), you can calculate flow with the formulas above. Line pressure without a known restriction cannot be converted to flow.
How do you convert flow rate into pressure?
Through the system resistance. For turbulent flow, pressure loss scales with roughly the square of flow: ΔP = K·Q², where K comes from pipe length, diameter, roughness, and fittings. Calculate friction with Darcy-Weisbach, add fitting losses and elevation head, and you have the pressure required to drive that flow.
Does a higher flow rate mean more pressure?
It depends which pressure you mean. More flow through the same piping consumes more pressure as friction, so the drop along the line increases. But at a fixed centrifugal pump, more flow comes with less discharge pressure, because the operating point slides down the pump curve. And across a flow element, higher flow always means higher differential pressure.
Is pressure directly proportional to flow rate?
Only in laminar flow, where Hagen-Poiseuille gives a linear relationship between pressure drop and flow. That applies below a Reynolds number of about 2300, typically in small bores and viscous oils. In turbulent flow, which covers most plant piping, pressure drop rises with approximately the square of flow.
Wu Peng, Senior Instrumentation Engineer. 20+ years specifying flow elements, DP transmitters, and flow meters for refining, water, and OEM equipment. He has sized more orifice plates than he can count and still checks the beta ratio twice.
Request a quote
Send the line size, fluid, operating pressure and temperature, and the flow range you need to cover. We will size the primary element, select the transmitter range for your real turndown, and return a documented configuration. Tell us the application and we configure one unit, not a shelf part.