The Coriolis Mass Flow Meter
Sometimes a measurement of the volumetric flowrate is not fully sufficient to satisfy the customers requirements. A measurement of the mass quantity of material transferred over time may be required. Units of kg/sec may be preferred instead of m3/sec, particularly if a product or component is sold or purchased by weight instead of volume.
Mass is equivalent to density times the volume. Therefore, it may be sufficient to multiply the measured volumetric flowrate by the density to give the mass flowrate. This only applies, however, if the fluid is of constant density which is often the case. If the density is not constant because the temperature fluctuations of the fluid are large or because of inconsistent composition then some other type of measurement is necessary.
It is possible to measure the density continuously aswell as the volumetric flowrate and combine the two measurements to give a mass flowrate. This is an inferential method of determining mass flow.
One method of directly measuring the mass flowrate is based on the Coriolis effect.
The Coriolis effect. First discussed by and named after the French scientist Gaspard Coriolis (1792 - 1843), this phenomenon is described as follows - any object moving above the earth with constant speed is deflected relative to the surface of the rotating earth. For example, if a bullet is fired from the North Pole and travels a constant velocity around the earth it will not follow a straight line relative to the earth. The earth has rotated by the time it lands with the result that from our frame of reference on earth it has followed a curved path. If the bullet was fired in the direction of Dublin it will actually land in Enfield (only an estimate! it will land to the west of Dublin).
If we are observing the bullet from the North Pole we notice that it bends to the right. If we do the same experiment at the other end of the planet we notice that a bullet fired from the South Pole bends to the left. The Coriolis effect explains why river banks in the northern hemisphere erode their right hand banks more so than their left. River banks in the southern hemisphere erode their left hand banks more so than their right. Similarly, railroad tracks can wear out quicker on one side than the other. Motion of air over the earth is also affected. In the northern hemisphere, air tends to rotate counter clockwise as it enters a low pressure area while in the southern hemisphere it rotates clockwise around a low pressure area. The Coriolis effect is very important when calculating the trajectory of a missile - a term to compensate for the Coriolis effect must be included.
Consider a particle of mass M travelling away from the centre of a rotating disc. It will not follow a direct path across the disc but will follow a curved path relative to the disc exactly like the bullet above.
If the particle of mass M was confined inside a tube and the experiment repeated it would try to follow the same path but would be prevented from doing so by the tube wall. The Coriolis force would be exerted on the tube wall. The magnitude of this force is given as follows:
Where V is the particle velocity
W is the angular velocity of the disc.
If fluid is flowing through the pipe instead of a particle the same effect is observed. The mass flowmeter consists of a tube that is bent into a U shape. The fluid flows away from the centre point on one limb, then travels around the U and returns to the centre point through the return limb. The device is not rotated but vibrated around the centre point. The fluid motion alters the shape of the tube as it is vibrated due to the Coriolis effect. The amount of distortion of the shape of the tube increases as the mass flowrate increases.
The operating principle of another mass flow meter is based on the Coriolis effect. The flow is directed through one or two parallel U shaped tubes which are vibrated at high frequency (150Hz) by an electromagnetic driver. The fluid affects the tube vibration by twisting the tube slightly. The inertia of the fluid flowing into the tube resists the upward motion of the tube. This causes the entrance tube to bend down more than up. The fluid then travels around the bend to leave the device. It now has an upward motion which is added to the upward motion of the tube and resists the downward motion. This causes the exit tube to bend up more than down. Thus, the tube is twisted down on the entry side and up on the exit. This affects the timing of the vibrations which are measured to give a density and mass reading. These can be converted to a volumetric flowrate. Temperature compensation is important with this device because a change in temperature can significantly affect the measurements.