Hong Life CalculatorsUnderstanding the differential pressure calculator — concept and principle
Differential pressure is the difference between pressures at two points, for example across a filter, valve, orifice plate or fan. This calculator finds Δp from two readings or a U-tube manometer, converts it into common units and, from a reference point, estimates the corresponding flow.
How it is calculated
- From two readings: Δp = p₁ − p₂ (both gauge or both absolute).
- From a manometer: Δp = (ρm − ρf) × g × h, with g = 9.80665 m/s².
- Flow at this Δp (turbulent devices): Q = Qref × √(Δp ÷ Δpref).
- Units: 1 mbar = 100 Pa; 1 psi = 6,894.757 Pa; 1 mm H₂O = 9.80665 Pa; 1 in H₂O = 249.089 Pa.
The principle
Fluid flows from high to low pressure, and resistances such as filters and orifices consume pressure. In turbulent flow, the pressure drop is proportional to the square of the velocity (from Bernoulli and loss coefficients), so flow is proportional to the square root of Δp. That is why orifice plates and venturis can measure flow from Δp, and why a filter's pressure drop rises as it clogs.
Worked example
Default inputs: p₁ = 350 kPa, p₂ = 325 kPa; reference 12 flow units at 30 kPa.
- Δp = 350 − 325 = 25 kPa = 25,000 Pa = 250 mbar; higher pressure at point 1.
- In psi = 25,000 ÷ 6,894.757 ≈ 3.626 psi.
- In water column = 25,000 ÷ 9.80665 ≈ 2,549.3 mm H₂O, or 100.37 in H₂O.
- Flow = 12 × √(25 ÷ 30) ≈ 10.95 (same units as the reference).
| Pressure at point 1, upstream (kPa) | Differential pressure Δp (kPa) |
|---|---|
| 87.5 | -237.5 |
| 175 | -150 |
| 262 | -62.5 |
| 350 | 25 |
| 438 | 112.5 |
| 525 | 200 |
| 700 | 375 |
How to read the result
Track Δp across filters over time: a rising value means loading, and manufacturers specify when to change them. For flow measurement, the square-root relationship means low Δp readings give poor flow resolution. Compare with equipment ratings to detect blockages or failures.
Common mistakes
- Mixing gauge and absolute pressures.
- Ignoring the density of the fluid above the manometer liquid.
- Using the square-root rule for laminar flow, where Δp is proportional to flow.
- Confusing mm H₂O and mm Hg.
Frequently asked questions
What is differential pressure?
The difference in pressure between two points in a system.
Why is flow proportional to the square root of Δp?
In turbulent flow, pressure loss grows with velocity squared.
How do I convert kPa to inches of water?
Divide pascals by 249.089; 25 kPa is about 100 in H₂O.
Sources: ISO 5167-1:2022, Measurement of fluid flow by means of pressure differential devices · NIST Special Publication 811 (pressure unit conversions)