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Flow Measurement Formulas Cheat Sheet

The key flow measurement formulas and rules of thumb on one page: pipe velocity, Reynolds number, the orifice equation, gas standard flow, meter selection rules and conversions.

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Basic relations

Volume flow	Q = A × v
Pipe area	A = π × D² ÷ 4
Mass flow	q_m = ρ × Q
Velocity	v (m/s) = Q (m³/h) ÷ (2827 × D² (m))

Reynolds number

Definition	Re = ρ × v × D ÷ μ = v × D ÷ ν
Laminar	Re < 2300
Transitional	2300 to 4000
Turbulent	Re > 4000 (most meters need this)

Orifice plate (ISO 5167-2)

Mass flow	q_m = C ÷ √(1 − β⁴) × ε × (π ÷ 4) × d² × √(2 × ΔP × ρ)
Beta ratio	β = d ÷ D, usually 0.2 to 0.75
Square law	Q ∝ √ΔP, so 50 % flow = 25 % DP
Typical C	about 0.6 for a sharp edged orifice
Permanent pressure loss	about (1 − β^1.9) × ΔP, roughly 40 to 95 % of the DP

Gas: actual to standard flow

Ideal gas	Q_std = Q_act × (P ÷ P_std) × (T_std ÷ T) × (Z_std ÷ Z)
Rule	Use absolute pressure (bar a) and absolute temperature (K)
Normal conditions	Nm³: 0 °C, 1.01325 bar a
Standard (often)	Sm³: 15 °C, 1.01325 bar a (check your contract)

Meter selection rules

Meter	Key rule
Magnetic	Conductive liquid, typically ≥ 5 µS/cm; full pipe
Coriolis	Mass flow and density direct; check pressure drop
Vortex	Needs Re above about 10,000 to 20,000; no low flow
Ultrasonic	Clean liquids or gas; long straight runs
Turbine	Clean, low viscosity fluids; K factor in pulses per litre
DP (orifice)	Turndown about 3:1 to 4:1 per DP range

Straight pipe runs (guide)

Typical: 10 D upstream and 5 D downstream
Orifice after two bends out of plane: up to 30 to 40 D upstream (ISO 5167-2 tables)
A flow conditioner shortens the requirement
Always use the meter data sheet for the final value

Velocity guidelines

Service	Typical velocity
Water, pump discharge	1.5 to 3 m/s
Water, pump suction	0.6 to 1.5 m/s
Steam (saturated)	20 to 35 m/s
Compressed air	6 to 10 m/s
Magmeter best accuracy	1 to 3 m/s

Conversions

From	To
1 m³/h	16.667 L/min
1 m³/h	4.4029 US gpm
1 US gallon	3.7854 L
1 kg/s	3.6 t/h
1 ft³/min (CFM)	1.699 m³/h

K factor and totals

Flow from pulses	Q = f ÷ K
Total	V = pulse count ÷ K
K factor	pulses per unit volume (for example per litre)

Related Calculators and Tools

Orifice Flow CalculatorFree on instrumentationblog.in Reynolds Number CalculatorFree on instrumentationblog.in Gas Flow Conversion CalculatorFree on instrumentationblog.in Pipe Flow Velocity CalculatorFree on instrumentationblog.in

Frequently Asked Questions

Why is DP flow a square root relationship?

Bernoulli's equation gives ΔP proportional to velocity squared, so flow is proportional to the square root of the DP.

What Reynolds number is turbulent?

Above about 4000. Most flowmeters are specified for turbulent flow.

What is the difference between Nm³ and Sm³?

Both are gas volumes at reference conditions. Nm³ is usually 0 °C and 1.01325 bar a; Sm³ is often 15 °C, but the definition varies, so always check.

Learn more on the blog

Types of flow meters: a complete guide with selection chart

A practical guide on instrumentationblog.in that explains the theory behind this cheat sheet.

Read Full Article

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