Instrumentation · Flow Measurement
Square Root Flow Calculator
Convert a differential pressure transmitter's DP% reading to flow, with a configurable low-flow cutoff and hysteresis to suppress near-zero noise.
Orifice / DP Flow · ISO 5167
Worked example
A DP transmitter is ranged to a 500 m³/h flow span. It currently reads 64% of its differential-pressure scale, with a low-flow cutoff of 1%.
√(64/100) = 0.8000 → Flow = 500 × 0.8000 = 400.0000 m³/h (80.00% of span)
The form above is pre-filled with these exact numbers — press Calculate to reproduce this result, or change the inputs for your own transmitter.
∑Formula & variable legend
Flow = Qmax × √(DP% / 100)
Flow = 0, if DP% < cutoff
DP% — differential pressure signal, as a percentage of transmitter span
Qmax — flow at 100% DP (the transmitter's calibrated full-scale flow)
cutoff — low-flow DP% threshold below which flow is forced to zero
Frequently asked questions
What is a square root flow calculator for DP transmitters?
A differential-pressure transmitter reading across an orifice plate or venturi is proportional to the square of flow rate, not flow itself. This calculator applies the square root relationship to convert a DP% reading back into actual flow, and applies a low-flow cutoff so near-zero DP noise doesn't get reported as spurious flow.
Why does flow follow the square root of differential pressure?
For flow through a fixed restriction like an orifice plate, Bernoulli's equation shows that pressure drop is proportional to the square of velocity, and therefore to the square of volumetric flow. Flow is recovered from the pressure signal by taking the square root, which is why raw DP transmitter output must be square-root extracted before it represents flow linearly.
What is the low-flow cutoff and why is it needed?
Near zero flow, the DP signal is tiny and dominated by transmitter noise and turbulence, which the square root function amplifies into wildly fluctuating flow readings. A low-flow cutoff forces the output to a clean zero below a configured DP% threshold, avoiding a jumpy near-zero flow display when the process is essentially shut in.
Why does the cutoff use hysteresis instead of a single threshold?
A single on/off threshold can "chatter" — rapidly switching between zero and a calculated value — if the DP signal sits right at the cutoff point. Reactivating flow calculation slightly above the cutoff (rather than exactly at it) gives a small dead band that prevents this chatter, which is why this calculator reports both the cutoff and a distinct reactivation point.
Does this calculator convert between flow units?
No — the calculated flow is reported in whatever unit you select for the Max Flow Span, since that span defines the transmitter's calibrated 100% point. If you need to convert the result into a different flow unit afterward, use a separate flow unit converter.