Flow Measurement

Flow meters are the cash registers of process plants. Learn volumetric vs mass flow, Reynolds number and profiles, differential-pressure meters (orifice, venturi, nozzle, pitot) and the square-root law, and the modern families — magnetic, vortex, turbine, positive-displacement, ultrasonic, Coriolis and thermal — with straight-run requirements, rangeability and selection. Includes an orifice-meter calculation in Python.

Flow measurement is used for control (keep a reactor feed constant), accounting (billing gas and oil — custody transfer), and safety (detect leaks). Errors of 1% on a large pipeline can mean millions per year.

Each principle has strengths and blind spots: a magmeter can't see oil, a Coriolis meter is expensive in large sizes, an orifice plate needs long straight pipe runs. Understanding the physics lets you pick correctly.

An analogy

Measuring flow is like counting people through a doorway: you can count bodies passing (positive displacement), time how fast they walk (velocity meters), watch how crowded the corridor gets before a narrow door (DP), or weigh them as they pass (Coriolis mass flow).

What is being measured

Volumetric flow (m³/h) depends on temperature and pressure for gases, so gas is often reported as standard volume (Sm³/h) or mass flow (kg/h). Mass flow is what chemistry and energy balances need. Totalised flow is the integral — the quantity sold.

Differential-pressure meters

A restriction (orifice plate, venturi, flow nozzle, V-cone, wedge) accelerates the fluid and lowers its pressure (Bernoulli). The DP is measured by a DP transmitter. They are cheap, well standardised (ISO 5167) and work on almost any fluid, but have permanent pressure loss, limited turndown and need straight upstream pipe (10–40 D) for a developed profile. Pitot tubes and averaging pitots (Annubar) measure velocity pressure in large ducts.

Velocity and mass meters

Modern alternatives:

Installation, compensation and custody transfer

Flow conditioners shorten straight-run requirements. Gas DP flows are pressure/temperature compensated (Q_std ∝ √(ΔP·P/T)). Custody-transfer systems (API MPMS, OIML, AGA) use meter runs with provers or master meters, redundant transmitters and flow computers, and are audited. Diagnostics in smart meters detect coating (magmeters), two-phase flow (Coriolis) and profile distortion (multi-path ultrasonic).

Formulas

Worked example: Square-root extraction

Given: Orifice 0–25 kPa = 0–31.5 m³/h; transmitter reads 25% of DP span

Find: Flow.

Answer: 15.8 m³/h (50% flow)

Worked example: Magmeter voltage

Given: B = 0.01 T, D = 0.1 m, v = 2 m/s

Find: Electrode voltage.

Answer: 2 mV

Worked example: Vortex frequency

Given: Bluff body d = 20 mm, St = 0.2, v = 3 m/s

Find: Shedding frequency.

Answer: 30 Hz

Orifice-plate flow and the square-root law

import math
# Orifice plate: Q = Cd * A2 * sqrt(2 dP / (rho (1 - beta^4)))
D, beta, Cd, rho = 0.10, 0.5, 0.61, 998.0      # pipe m, d/D, discharge coeff, water kg/m3
d = beta * D
A2 = math.pi * d * d / 4
def Q(dp):
    return Cd * A2 * math.sqrt(2 * dp / (rho * (1 - beta**4)))
for dp in (25e3, 6.25e3, 1e3):
    print(f"dP {dp/1e3:5.2f} kPa -> Q {Q(dp)*3600:6.2f} m3/h")
print("rangeability: 4x lower dP gives only 2x lower flow (square-root law)")
# dP 25.00 kPa -> Q  31.52 m3/h
# dP  6.25 kPa -> Q  15.76 m3/h
# dP  1.00 kPa -> Q   6.30 m3/h
# rangeability: 4x lower dP gives only 2x lower flow (square-root law)

At 20% of full flow the DP is only 4% of full scale, where transmitter errors dominate — so orifice meters have limited turndown (≈ 3–4:1). The transmitter (or DCS) must take the square root of DP to get flow. ISO 5167 gives exact C_d equations (Reader-Harris/Gallagher).

Common mistakes

Applications

Key takeaways

Going further