1. Laminar or turbulent: the Reynolds number
How a fluid moves in a pipe depends on the balance between its momentum (which keeps it moving) and its viscosity (which smooths it out). That balance is the Reynolds number, a number without units:
Re = ρ · v · D / μ (density × velocity × pipe diameter ÷ viscosity)
Below about 2300 the flow is laminar: smooth layers, fastest in the centre, a pointed (parabolic) velocity profile. Above about 4000 it is turbulent: eddies mix the flow and the profile becomes flat. In between is a transition zone. Most meters are calibrated for turbulent flow, so very slow or very viscous flows can read wrongly. Try a thick oil to see laminar flow.
2. Orifice plate: flow from differential pressure
A plate with a smaller hole forces the fluid to speed up. Faster fluid has lower pressure (Bernoulli), so a differential pressure (DP) appears across the plate. DP grows with the square of flow: double the flow and DP rises four times.
Q = K · √ΔP ΔP ∝ Q²
That is why the DP transmitter's signal must be square-rooted (in the transmitter or the DCS, never both) to read flow. It also explains the limited turndown: at 10 % flow the DP is only 1 % of span, lost in the noise.
3. Turbine meter: counting revolutions
The flow turns a bladed rotor. Its speed is proportional to the fluid velocity, so each blade passing a pick-up coil is a known volume. The pulses per unit volume are the meter's K-factor; flow = pulse frequency ÷ K-factor. Turbines are accurate on clean, steady liquids, but bearings wear and viscosity changes shift the K-factor.
4. Magnetic meter: Faraday's law
Coils create a magnetic field across the pipe. A conductive liquid moving through it acts like a moving wire, and a voltage appears between two electrodes, proportional to the average velocity:
E = k · B · D · v (field strength × pipe diameter × velocity)
No moving parts and no pressure loss, and it handles slurries well. But the liquid must conduct electricity (typically above about 5 µS/cm), so it can't measure oil, gas or very pure water. The pipe must run full.
5. Vortex meter: counting eddies
A bluff body (a "shedder bar") across the pipe sheds vortices alternately from each side, like a flag flapping in the wind. The shedding frequency is proportional to velocity:
f = St · v / d (Strouhal number × velocity ÷ bar width)
The Strouhal number stays nearly constant over a wide range of Reynolds numbers, so the meter is linear without needing density or viscosity. Below a minimum velocity, vortices stop forming and the meter reads zero (a low-flow cut-off). It needs a straight run of pipe upstream.
Choosing a flow meter
| Need | Good choices | Watch out for |
|---|---|---|
| Low cost, any clean fluid, standards-based | Orifice / venturi (DP) | Pressure loss, square-root, ~4:1 turndown, straight runs |
| Conductive liquids, slurries, no pressure loss | Magnetic | Conductivity, pipe must be full, grounding |
| Steam, gas and clean liquids, wide range | Vortex | Low-flow cut-off, vibration, straight runs |
| Mass flow, custody transfer, density too | Coriolis | Cost and size on large lines, gas bubbles |
| Clean, steady liquids, high accuracy | Turbine | Bearing wear, viscosity changes, debris |
| Large pipes, no pipe cutting | Clamp-on ultrasonic | Pipe condition, bubbles and solids |
Also check: required accuracy and turndown, pressure loss allowed, hazardous-area rating, upstream/downstream straight runs, and how the meter will be calibrated. More detail in Flow measurement; check a DP range with the Square Root Extraction app.