Introduction to Pipe Flow Measurement

Accurate measurement of flow rate of liquids and gases is an essential requirement for maintaining the quality of industrial processes. In fact, most of the industrial control loops control the flow rates of incoming liquids or gases in order to achieve the control objective. As a result, accurate measurement of flow rate is very important.

Needless to say that there could be diverse requirements of flow measurement, depending upon the situation. It could be volumetric or mass flow rate, the medium could be gas or liquid, the measurement could be intrusive or nonintrusive, and so on. While some techniques work better with some groups of fluids, and less well with others, some are not at all suitable for some applications. As a result there are different types of flow measuring techniques that are used in industries. The common types of flowmeters that find industrial applications can be listed as below:

1. Obstruction Flow Meter
   1. Differential Pressure Flow Meters
   2. Variable Area Meter
2. Positive Displacement Meter
3. Electronic Meter

Flow meter is a device that measures the rate of flow or quantity of a moving fluid in an open or closed conduit.

In this article, we will try to look at each category with brief details of particular devices that fall under that category.

Obstruction Flowmeter

Obstruction or head type flowmeters are of two types:

• Differential Pressure Type
• Variable Area Type

Basic Principle

Obstruction flow meters operate by introducing a restriction in the cross sectional area of a flowing fluid. Restricting the flow area causes a pressure drop across the obstruction, this pressure drop is cause by a change in the fluids velocity. The operating principal is based on the Bernoulli equation and the continuity equation of fluid flow. Combining these equations we can find the relationship between the flow rate and pressure drop.

We consider the fluid flow through a closed channel of variable cross section, as shown in Figure 1. The channel is of varying cross section and we consider two cross sections of the channel, 1 and 2. Let the pressure, velocity, cross sectional area and height above the datum be expressed as p1, v1, A1 and z1 for section 1 and the corresponding values for section 2 be p2, v2, A2 and z2 respectively. We also assume that the fluid flowing is in-compressible and flow is horizontal.

Figure 1. Flow through a varying cross section

Now from Bernloulli’s equation: (p1/γ) + (v1²/2g) + z1 = (p2/γ) + (v2²/2g) + z2

where γ is the specific weight of the fluid.

We assume that flow is horizontal: z1 = z2.

Thus, (p1/γ) + (v1²/2g) = (p2/γ) + (v2²/2g)                                                     ……(Applying z1 = z2)

v2² – v1² = (2g/γ) (p1 – p2)

We assume that fluid is in-compressible and velocity profile is uniform at section 1 and 2.

So from continuity equation : Q = v1A1 = v2A2

v2²(1-A2²/A1²) = (2g/γ) (p1 – p2)                                                                   ……(Applying v1A1 = v2A2)

v2 = ( (2g/γ) (p1 – p2) / (1-A2²/A1²) )½

Q =  A2 ( (2g/γ) (p1 – p2) / (1-A2²/A1²) )½                                                   …… equation 1

From the above expression, we can infer that if there is an obstruction in the flow path that causes the variation of the cross sectional area inside the closed flow channel, there would be difference in static pressures at two points and by measuring the pressure difference, one can obtain the flow rate using equation 1. However, this expression is valid for in-compressible fluids (i.e. liquids) only and the relationship between the volumetric flow rate and pressure difference is nonlinear. A special signal conditioning circuit, called square rooting circuit is to be used for
getting a linear relationship.

The most common types of obstruction or differential pressure flow meters are

• Orifice Meters / Orifice Plates (Differential Pressure)
• Flow Nozzles (Differential Pressure)
• Venturi Tubes (Differential Pressure)
• Rotameters (Variable Area)

Orifice Meter or Orifice Plate

In orifice meter an orifice plate is placed in the pipe line, as shown in Figure 2. If d1 and d2 are the diameters of the pipe line and the orifice opening, then the flow rate can be obtained using equation 1 by measuring the pressure difference (p1-p2).

Figure 2. Orifice Type Flow Meter

The flow expression obtained from equation 1 is not an accurate expression in the actual case, and some correction factor, named as discharge co-efficient (Cd) has to be incorporated in (3), as

Q =  Cd * A2 ( (2g/γ) (p1 – p2) / (1-A2²/A1²) )½ 

Cd is defined as the ratio of the actual flow and the ideal flow and is always less than one. There are in fact two main reasons due to which the actual flow rate is less than the ideal one.

1. Assumption of friction-less flow is not always valid. The amount of friction depends on the Reynold’s number (RD).
2. The minimum flow area is not the orifice area A2, but is somewhat less and it occurs at a distance from the orifice plate, known as the Vena Contracta, and we are taking a pressure tapping around  that point in order to obtain the maximum pressure drop.

As a result, the correction factor Cd <1, has to be incorporated.

The major advantages of orifice plate are that it is low cost device, simple in construction and easy to install in the pipeline.  The major disadvantage of using orifice plate is the permanent pressure drop that is normally experienced in the orifice plate as shown in Figure 3. The pressure drops significantly after the orifice and can be recovered only partially. The magnitude of the permanent pressure drop is around 40%, which is sometimes objectionable. It requires more pressure to pump the liquid.

Figure 3. Orifice plate and permanent pressure drop

Venturi Tubes

Venturi tubes, shown in Figure 4, are so designed that the change in the flow path is gradual. As a result, there is no permanent pressure drop in the flow path. The discharge coefficient Cd varies between 0.95 and 0.98. Venturi tubes are very
accurate over wide flow ranges and the gradual contraction and expansion reduces the drag and allows for a low pressure loss. The construction also provides high mechanical strength for the meter. However, the major disadvantage is the high cost of the meter.

Figure 4. Venturi Tubes

Flow Nozzle

Flow nozzle, as shown in Figure 5, is a compromise between orifice plate and venturi tube. The main difference is that flow nozzles have a gradual constriction rather than the abrupt constriction of an orifice plate. Flow nozzles are common for high velocity, low viscosity flows. Flow nozzles also have a greater flow capacity when compared to other differential pressure meters.

Figure 5. Flow Nozzle

Rotameters

The orifice meter, Venturi tube and flow nozzle work on the principle of constant area variable pressure drop. Here the area of obstruction is constant, and the pressure drop changes with flow rate. On the other hand Rotameter works as a constant pressure drop variable area meter.

Rotameter can be only be used in a vertical pipeline. Its accuracy is also less compared to other types of flow meters. But the major advantages of rotameter are, it is simple in construction, ready to install and the flow rate can be directly seen on a calibrated scale, without the help of any other device, e.g. differential pressure sensor etc. Moreover, it is useful for a wide range of variation of flow rates.

Rotameter, as shown in Figure 6, consists of a vertical pipe, tapered downward. The flow passes from the bottom to the top. There is cylindrical type metallic float inside the tube. The fluid flows upward through the gap between the tube and the float. As the float moves up or down there is a change in the gap, as a result changing the area of the orifice. In fact, the float settles down at a position, where the pressure drop across the orifice will create an upward thrust that will balance the downward force due to the gravity. The position of the float is calibrated with the flow rate.

Figure 6. Rotameter

Positive Displacement Flow Meters

Positive displacement flow meters are the only family of flow meters that directly measure the volume of fluid passing through a pipe. This is achieved by passing a specific amount of fluid with each rotation of the meter. A good analogy on how these work is to imagine filling a bucket and dumping it numerous times to measure the amount of water. Positive displacement flow meters are very accurate regardless of the fluids viscosity, density, velocity, or temperature. Because of the accuracy and ease of use, positive displacement flow meters are commonly used for domestic water measurement.

The most common types of positive displacement flow meters are:

• Piston Flow Meters
• Gear Flow Meters
• Helical Flow Meters

Piston Flow Meters

Piston flow meters or rotary piston displacement meters, as shown in Figure 7, are most commonly used for domestic water measurement. They operate by having a piston rotate in a chamber with a known volume. Every rotation the piston makes passes a volume of water equivalent to the chambers known volume down the pipe. Knowing the number of rotations and the volume of the chamber allows the flow rate to be calculated.

Figure 7. Piston Flow Meter

Gear Flow Meters

Gear flow meters, as shown in Figure 8, consist of two round gears that are mounted in overlapping compartments. When a fluid flows through the inlet it gets trapped in the teeth of the gear and is transported to the outlet. Knowing the volume of the voids between the teeth and the wall and the number of rotation, the flow rate can be calculated.

Figure 8. Gear Flow Meters

Helical Flow Meters

Helical or helical gear flow meters operate using the same principal of the previous displacement flow meters. As the fluid flows through the inlet it causes the helix shaped structure to rotate. As the meter rotates it traps a known amount of fluid in the rotors, this fluid is then released towards the outlet. Knowing the speed of rotation and the volume between the rotors, the flow rate is calculated.

Figure 9. Helical Flow Meters

Electromagnetic Flow Meter

Magnetic flow meters, as shown in Figure 10, use the principal of Faraday’s law of electromagnetic induction to calculate the fluid flow rate. Faraday’s law states that a voltage will be induced when a conductor moves through a magnetic field. For this case, the liquid fluid serves as the conductor and the magnetic field is applied to the metering pipe. This will create a potential difference that is monitored by electrodes that are aligned perpendicular to the flow. The potential difference, or voltage produced, is directly proportional to the velocity, which then allows us to find the flow rate.

Figure 10. Electromagnetic Flow Meter

Electromagnetic flow meters will only work if the fluid is conductive and the pipe, where the flow meter is attached, is non-conductive. Magnetic flow meters also have problems with the electrodes corroding while in contact with the fluid in the pipe. Magnetic flow meters are good for measuring difficult and corrosive liquids and slurries. They are also very convenient because they can measure flow rates in both directions very accurately.