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『Coriolis Flow Meter Formula: Mass Velocity and Phase Lag Mathematics』Related information(v cone flow meter|rotary gas meter|gallon meter|gear meter|metal tube rotameter|glass tube rotameter|nutating disk meter|transit time ultrasonic flow meter|wedge flow meter|pd meters|hydraulic flow meter|ultrasonic water flow meter|water flow meter|air flow meter|magnetic water flow meter|oxygen flow meter|gas flow meter|argon flow meter|air velocity meter|gasoline flow meter|fuel flow meter|ultrasonic water meter|digital water meter|nitrogen flow meter|solid flow meter|Oxygen tank flow meter|digital water flow meter|diesel fuel flow meter|steam flow meter|02 flow meter|compressed air flow meter|oil flow meter|liquid flow meter)
Coriolis Flow Meter Formula: Mass Velocity and Phase Lag Mathematics
Quick Answer: The Coriolis flow meter formula converts a measured time delay between two sensor pickups into direct mass flow. Phase lag is the physical signal and mass velocity is the process result. Silver Automation Instruments is a Coriolis mass flow meter manufacturer and supplier for DN15 to DN300 process lines with 4-20 mA HART and pulse output.
Most engineers first meet the Coriolis principle through a catalog drawing. The drawing shows a tube vibrating at its natural frequency. With zero flow, both ends move together. With flow, a phase shift appears. That shift is not a calibration trick. It is the direct result of mass moving through an oscillating frame.
Where the Phase Lag Comes From
When a fluid mass moves through a vibrating tube, Coriolis force acts perpendicular to the flow direction and the vibration direction. This force deforms the tube slightly. On a bent tube meter, the inlet leg and outlet leg twist in opposite directions. On a straight tube meter, the deformation appears as a small rotation. Pickup sensors at two points detect the deformation as a time delay. The time delay is often called delta t. Phase lag is delta t divided by the oscillation period, normally expressed in microseconds or degrees.
In practice, a DN50 Coriolis meter measuring water at ambient temperature may show a phase lag of only a few microseconds. That is why sensor spacing and digital signal processing matter. A cheap pickup or a loose mounting bracket can bury the signal in noise.
The Formula Used in Field Commissioning
The simplified formula most service engineers use is:
Qm = K x delta t
Qm is mass flow in kg/h. K is the meter factor from factory calibration. Delta t is the time difference between the two pickup signals. The meter factor includes tube geometry, tube wall stiffness, sensor location, and the spring constant of the meter structure. For a dual bent tube meter, K is not a universal constant. It changes with temperature because tube stiffness changes with temperature. That is why a good Coriolis transmitter measures tube temperature with a PT100 and applies a stiffness correction.
That is the phase lag mathematics in a field friendly form. The full derivation includes integrals over the tube length and mode shape, but the transmitter hides that work.
Some engineers want the full mathematics. The phase lag depends on mass velocity, tube angular velocity, and the compliance of the tube. Mass velocity is the mass flow rate divided by the cross sectional area of the tube. In a Coriolis meter, mass velocity is not inferred from volumetric flow and density. It is measured directly from the magnitude of the Coriolis force. That is the main reason a Coriolis meter handles custody transfer and dense phase fluids better than a turbine or vortex meter.
Why Mass Velocity Matters More Than Volumetric Flow
Gas flows change volume with pressure. Liquid flows change density with temperature. A volumetric meter has to compensate for both. A Coriolis meter does not need density compensation for mass flow. The meter measures mass velocity directly. Density output is a secondary calculation from the resonant frequency of the tube. Here is the thing. The mass flow formula does not need density as an input. It uses time delay, tube stiffness, and tube geometry.
We saw this on a fuel oil skid in Malaysia. The customer first used a turbine meter with temperature compensation. The repeatability was poor because the oil density changed from batch to batch. After a trial with a DN40 Coriolis meter, the mass totalizer matched the weighbridge withi
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What the Mathematics Means for Installation
Because phase lag is small, mechanical noise from pumps and piping can affect the zero. Most engineers skip this part during the first evaluation. They focus on pressure drop and wetted materials. Then they ask why the zero drifts after installation. The answer is usually pipe stress or a partially filled tube.
Silver Automation Instruments recommends the following data before a quote: flow range in kg/h, process pressure in bar, process temperature in °C, line size DN, fluid viscosity in cP or conductivity in µS/cm for water based fluids. This data lets our engineers check if a Coriolis meter is suitable or if an electromagnetic flow meter would be better for high water content lines.
Model Selection Based on Flow Range
We supply Coriolis mass flow meters from DN15 to DN300. Small lines from DN15 to DN40 suit chemical dosing, pilot plants, and food additives. Medium lines from DN50 to DN100 cover most oil and gas loading skids, brewery batches, and water based emulsion lines. Large lines from DN150 to DN300 cover bulk custody transfer and marine fuel supply. For hazardous areas, specify ATEX Zone 1 or Zone 2. Our standard transmitter supports 4-20 mA HART, pulse, and Modbus RTU. Wetted parts range from 316L stainless steel to Hastelloy C for aggressive fluids.
One example from a paint manufacturer in Southeast Asia is useful. They needed a DN25 Coriolis meter for solvent batching. The recipe required 4 different solvents with densities from 0.79 to 1.16 g/cm3. A volumetric oval gear meter caused ratio errors because each solvent had a different factor. The Coriolis meter read mass flow directly. The batch controller used the pulse output. After the change, the batch cycle dropped by 18 percent because the operator did not stop to correct density tables.
A seawater desalination plant in Saudi Arabia uses a DN200 Coriolis meter on brine concentrate. The meter reads mass flow even when the brine conductivity changes. This avoids the compensation errors that can appear with a magnetic flow meter on high salinity streams.
FAQ: Five Questions Engineers Ask Before Buying
What is the most useful formula for a Coriolis flow meter?
Qm = K x delta t. K is the factory meter factor. Delta t is the time lag between the two pickups. The transmitter corrects K for temperature using a PT100 input.
Does phase lag change with fluid pressure?
Yes, high pressure can change tube stiffness slightly. For most process pressures up to PN40, the effect is small. For pressures above PN100, tell us the maximum pressure so we can apply a pressure correction factor.
Can a Coriolis meter measure gas and liquid with the same formula?
Yes. The meter measures mass velocity directly. Gas flow needs a higher tube drive gain because gas density is low. We size gas meters carefully to keep the phase lag signal above the noise floor.
What is the minimum flow range Silver Instruments can handle?
A DN15 Coriolis meter can read very low mass flow, often below 1 kg/h for liquid depending on viscosity. For micro flow below that, we review the application case by case.
What information do you need for a Coriolis flow meter price?
Send us your pressure (bar), temperature (°C), pipe size (DN), and flow range in kg/h. Tell us the fluid and if the area requires ATEX Zone 1 or Zone 2. We will reply with a model and quote.
Contact Silver Automation Instruments at Tel +86-135-1213-1526, WhatsApp 86-135-12131526 or WeChat +86 13512131526 for application support.