Coriolis Flow Meter

How a Coriolis flow meter works

Picture a U-shaped tube fixed at both ends, like a tuning fork bent into a hairpin. An electromagnetic driver in the bend gives the loop a gentle shove a few hundred times a second, so the whole U swings up and down at its natural frequency — typically 80 to 1000 Hz depending on size. With no flow, the two straight legs of the U swing in perfect unison: a sensor on the inlet leg and a sensor on the outlet leg cross through their midpoint at exactly the same instant.

Now start the fluid flowing. As the tube swings, every particle of fluid inside it is being carried sideways along with the tube. The particles entering on the inlet leg have to be accelerated up to the tube's sideways velocity; the particles leaving on the outlet leg have to give that sideways velocity back. By Newton's third law, the fluid pushes back on the tube — and crucially, it pushes in opposite directions on the two legs. The inlet leg gets dragged back, the outlet leg gets dragged forward. The U-tube no longer flaps as a rigid loop; it twists.

That twist is the Coriolis effect, the same fictitious force that deflects winds and ocean currents on the spinning Earth. Here the "rotation" is the tube's oscillating angular velocity, and the deflection acts on the flowing fluid. The amount of twist is set by how much mass is moving through per second — the mass flow rate. The faster the mass throughput, the bigger the twist.

You don't read the twist as an angle. You read it as time. Because the inlet leg now lags and the outlet leg leads, the two pickoff sensors no longer cross their midpoint together — there's a delay Δt between them. That delay, measured in microseconds, is directly proportional to mass flow. Zero flow, zero delay. The meter's whole job is to time-resolve a few microseconds of phase shift cleanly enough to call it 0.1%.

The physics: Coriolis force to phase delay

The Coriolis acceleration on a mass moving with velocity v in a frame rotating at angular velocity ω is the familiar a = 2 ω × v. For a tube swinging at angular velocity ω with fluid moving along it, the resulting transverse force on a length of tube carrying mass flow rate q_m over an effective arm of length L produces a twisting torque, and that torque deflects the tube into the characteristic twist. Working it through, the measured time delay reduces to a clean linear law:

Coriolis force per unit length on the tube:

  F_c = 2 · q_m · ω        (q_m = mass flow rate, kg/s per unit length term)

Resulting time delay between the two pickoffs:

  Δt = (2 · K_s · L²) / (K_stiff) · q_m   →   q_m = K · Δt

  where K is a single fixed calibration constant set by tube
  geometry and stiffness — NOT by the fluid.

Mass flow rate:        q_m = K · Δt
Density (separate):    ρ = C1 / f²  −  C2     (f = resonant frequency)
Volumetric flow:       Q = q_m / ρ

The headline is the middle line: mass flow is a single constant times a measured time delay. That constant K depends only on the meter's mechanical geometry — tube length, wall stiffness, sensor spacing — and is burned in at the factory on a gravimetric flow rig (weigh the water that comes out, time it, solve for K). Because the fluid's properties never appear in q_m = K·Δt, the meter does not care whether you run water, crude oil, liquid CO₂, or honey. This is what "direct mass measurement, no density assumption" means in equations.

Density comes from a completely different feature of the same vibration. A fluid-filled tube is a spring-mass oscillator: stiffer tube raises the frequency, more mass lowers it. The vibrating mass is the fixed tube mass plus the fluid mass inside, so the square of the resonant frequency falls as density rises. Track the drive frequency and you get density to roughly ±0.5 to 2 kg/m³ — for free, on the same instrument.

Worked example: metering a crude-oil transfer

Suppose a 4-inch Coriolis meter is loading crude oil onto a tanker. The transmitter reports a phase delay and a tube frequency; here is how those become a custody-transfer ticket:

Meter calibration constant:  K   = 3.2 × 10⁵ kg/s per second of Δt
Measured time delay:         Δt  = 12 µs  = 12 × 10⁻⁶ s

  Mass flow  q_m = K · Δt = 3.2e5 × 12e-6 = 3.84 kg/s
                          ≈ 13,800 kg/h ≈ 13.8 tonne/h

Tube resonant frequency gives density:
  ρ = 850 kg/m³  (typical light crude)

  Volumetric flow Q = q_m / ρ = 3.84 / 850
                    = 4.52 × 10⁻³ m³/s ≈ 16.3 m³/h ≈ 102 barrels/h

Loading 5,000 tonnes:  time = 5000 / 13.8 ≈ 362 h of metered flow,
  totalised to ±0.1% → uncertainty ≈ ±5 tonnes on the ticket.

The point of custody transfer is that money changes hands on the totalised mass. At ±0.1% on a 5,000-tonne cargo, the disputed quantity is about ±5 tonnes — and because the meter reads mass directly, neither party has to agree on a temperature, pressure, or density correction the way they would with a volumetric turbine meter. That removed argument is worth a lot in oil-and-gas contracts, which is why API MPMS Chapter 5.6 and OIML R 117 write Coriolis meters into the rules.

Coriolis vs other flow meters

	Coriolis	Orifice / DP	Turbine	Magnetic (mag)	Vortex	Ultrasonic
Measures directly	Mass flow + density	Volumetric (√ΔP)	Volumetric	Volumetric	Volumetric	Volumetric
Typical accuracy	±0.1% (liquid)	±0.5 to 2%	±0.25 to 0.5%	±0.2 to 0.5%	±0.65 to 1%	±0.15 to 1%
Turndown	100:1+	~3:1 to 5:1	~10:1 to 20:1	~20:1 to 40:1	~10:1 to 30:1	~50:1+
Upstream straight run	None needed	10 to 40 D	10 to 20 D	5 D	15 to 30 D	5 to 20 D
Needs conductive fluid?	No	No	No	Yes (mag only)	No	No
Permanent pressure drop	Moderate (bent tube)	High	Moderate	None (full bore)	Moderate	None (full bore)
Moving / wetted parts	Vibrating tube (no bearings)	None	Spinning rotor + bearings	None	Shedder bar	None
Relative cost (small bore)	High	Low	Medium	Medium	Medium	Medium to high
Worst case	Two-phase / entrained gas	Low flow, varying density	Bearing wear, low viscosity	Non-conductive fluids	Low Reynolds number	Bubbles, scale on liner

Tube geometries: bent vs straight, single vs dual

• Bent dual-tube (U, V, B, omega, triangle). The classic Micro Motion-style design splits the flow into two parallel curved tubes vibrating in opposition, like the tines of a tuning fork. Driving them out of phase makes the assembly self-balancing — the two tubes cancel each other's reaction forces so the meter doesn't pump vibration into the pipework, and external pipe vibration is rejected as common mode. Bent tubes give a long effective arm L, so the Coriolis twist (and Δt) is large, which makes them the most sensitive and the most accurate. The cost: higher pressure drop and harder to drain/clean.
• Straight single or dual tube. A straight tube has lower pressure drop, drains completely, and is easier to clean — important in food, pharma, and high-viscosity service. But a straight tube is stiffer and has a shorter effective arm, so the twist is smaller and the electronics work harder for the same accuracy. Straight-tube meters also transmit more stress to the flanges and are more sensitive to mounting strain and temperature gradients.
• Single-tube vs dual-tube balance. Dual-tube designs are inherently balanced and dominate the market. Single straight-tube designs need an active or passive counter-balance mass and careful mounting because there's no second tube to cancel against.
• Drive and pickoffs. The driver is usually a coil-and-magnet voice-coil actuator at the apex; the two pickoffs are matched coil-and-magnet velocity sensors on the inlet and outlet legs. A platinum RTD on the tube corrects the elastic modulus of the tube wall for temperature, since a hotter tube is softer and would read a false flow and density shift if uncorrected.

Real-world specs and products

Class / example	Line size	Mass-flow accuracy	Typical service
Micro-bore dosing (e.g. Bronkhorst mini CORI-FLOW)	<1 mm to 6 mm	±0.2%	Lab dosing, catalyst injection, additive metering
General process (e.g. Endress+Hauser Promass F)	DN8 to DN250	±0.1%	Chemical, oil-and-gas, batching
Custody transfer (e.g. Emerson Micro Motion CMFS / ELITE)	DN25 to DN100	±0.05 to 0.1%	Crude, refined products, LPG fiscal metering
Large bore high-capacity	up to DN350 / 14 in	±0.1 to 0.35%	Pipeline allocation, tanker loading
Gas / steam variant	DN15 to DN100	±0.35 to 1%	Natural-gas energy metering, hydrogen, CO₂

Concrete numbers worth carrying around: drive frequency 80 to 1000 Hz; vibration amplitude at the tube apex on the order of tens of micrometres; full-scale Δt a handful of microseconds, with the transmitter resolving down to nanoseconds; tube material usually 316L stainless or, for chlorides and hydrofluoric acid, super-duplex, nickel alloy C-22, or titanium. Pressure ratings reach hundreds of bar; a large-bore meter can weigh 100 kg or more and cost five to ten times a comparable orifice plate — the accuracy and direct-mass reading have to earn that premium.

When to use a Coriolis flow meter

• You need true mass flow, not volume. Chemical reactions, fuel mass for combustion, fiscal mass-based contracts, and recipe batching all care about kilograms, not litres. Coriolis gives mass without a density correction.
• The fluid's density varies or is unknown. Crude oil whose density drifts with temperature and composition, multi-product pipelines, or blended streams — a volumetric meter would need a separate densitometer; Coriolis bundles it in.
• High accuracy and wide turndown matter. Custody transfer and high-value dosing justify the cost when ±0.1% over a 100:1 range is the requirement.
• Piping is tight or messy. No straight-run requirement means it fits in skids and after elbows where an orifice plate can't meet spec.
• The fluid is non-conductive or has no clean velocity profile. Where a magnetic meter (needs conductivity) or a DP meter (needs developed flow) fails, Coriolis still works.

Reach for a different meter when the fluid carries entrained gas or is genuinely two-phase (use a different technology or separate the phases first), when the line is very large and the capital cost of a big Coriolis body is prohibitive (use ultrasonic or DP), or when you only need a rough volumetric reading on a clean conductive liquid (a magnetic meter is cheaper and full-bore).

Common misconceptions and pitfalls

• "It uses the Earth's rotation." No. The Coriolis force here comes from the tube's own oscillating rotation, hundreds of times a second. Earth's rotation (~7.3×10⁻⁵ rad/s) is utterly negligible compared to the tube's swing rate and plays no role.
• "It measures velocity or volume." It measures momentum, which is mass flow. Volume is a derived number (mass divided by the separately-measured density), not the primary reading. This is the opposite of nearly every other flow meter.
• "More accuracy is always better, so always buy Coriolis." The two-phase weakness is real and unforgiving. Pumping a liquid with entrained air bubbles can make the tube stall, throw a fault, or read wildly wrong. If you can't guarantee single-phase flow, the high-accuracy spec is a trap.
• "Mounting doesn't matter, there's no straight run." True for flow profile, false for mechanics. Pipe stress and strain transmitted into the meter body shift the zero, and external vibration near the drive frequency can beat against the measurement. Good installs use proper supports and avoid resonance with nearby pumps.
• "Zeroing is a one-time factory thing." Field zeroing at no-flow (valve closed, tube full, fluid at rest) is part of commissioning, because residual mounting stress and fluid differences shift the zero point. A bad zero is the most common cause of a Coriolis meter reading a small flow when the line is actually shut in.
• "It needs the tube to be full to read density, but flow is fine either way." Both readings degrade if the tube isn't completely full of single-phase fluid. A partially empty tube changes the vibrating mass and ruins the density reading, and gas pockets break the momentum coupling that flow measurement depends on.