Positive displacement meters measure the volume flow rate (QV) directly by repeatedly trapping a sample of the fluid. The total volume of liquid passing through the meter in a given period of time is the product of the volume of the sample and the number of samples. Positive displacement meters frequently totalize flow directly on an integral counter, but they can also generate a pulse output which may be read on a local display counter or by transmission to a control room. Because each pulse represents a discrete volume of fluid, they are ideally suited for automatic batching and accounting. Positive displacement meters can be less accurate than other meters because of leakage past the internal sealing surfaces. Three common types of displacement meters are the piston, oval gear, and nutating disc.

Head Meters

Head meters are the most common types of meter used to measure fluid flow rates. They measure fluid flow indirectly by creating and measuring a differential pressure by means of an obstruction to the fluid flow. Using well-established conversion coefficients which depend on the type of head meter used and the diameter of the pipe, a measurement of the differential pressure may be translated into a volume rate. From the Equation of Continuity, assuming constant density (incompressible fluid) it can be seen that:

This equation is one of the most important relationships in fluid mechanics. It demonstrates that for steady, uniform flow, a decrease in pipe diameter results in an increase in fluid velocity. In addition, from Bernoulli’s equation on the conversation of energy, it is further seen that total head pressure (H) must remain constant everywhere along the flow or:

The first term of the equation is called “potential head” or “potential energy”. The second term is known as the “velocity head” or “kinetic energy”. Because potential and kinetic energy together are constant, it is clear that an increase in velocity as described by the Equation of Continuity must also be accompanied by a decrease in potential energy or line pressure. It is this relationship between velocity and pressure that provides the basis for the operation of all head-type meters. Head meters are generally simple, reliable, and offer more flexibility than other flow measurement methods. The head-type flowmeter almost always consists of two components: the primary device and the secondary device. The primary device is placed in the pipe to restrict the flow and develop a differential pressure. The secondary device measures the differential pressure and provides a readout or signal for transmission to a control system. With head meters, calibration of a primary measuring device is not required in the field.

The primary device can be selected for compatibility with the specific fluid or application and the secondary device can be selected for the type or readout of signal transmission desired.

Orifice Plates

A concentric orifice plate is the simplest and least expensive of the head meters (Figure 2). Acting as a primary device, the orifice plate constricts the flow of a fluid to produce a differential pressure across the plate. The result is a high pressure upstream and a low pressure downstream that is proportional to the square of the flow velocity. An orifice plate usually produces a greater overall pressure loss than other primary devices. A practical advantage of this device is that cost does not increase significantly with pipe size.

Venturi Tubes

Venturi tubes exhibit a very low pressure loss compared to other differential pressure head meters, but they are also the largest and most costly. They operate by gradually narrowing the diameter of the pipe (Figure 3), and measuring the resultant drop in pressure. An expanding section of the meter then returns the flow to very near its original pressure. As with the orifice plate, the differential pressure measurement is converted into a corresponding flow rate. Venturi tube applications are generally restricted to those requiring a low pressure drop and a high accuracy reading. They are widely used in large diameter pipes such as those found in waste treatment plants because their gradually sloping shape will allow solids to flow through.

Flow Nozzle

Flow nozzles may be thought of as a variation on the venturi tube. The nozzle opening is an elliptical restriction in the flow but with no outlet area for pressure recovery (Figure 4). Pressure taps are located approximately 1/2 pipe diameter downstream and 1 pipe diameter upstream. The flow nozzle is a high velocity flowmeter used where turbulence is high (Reynolds numbers above 50,000) such as in steam flow at high temperatures. The pressure drop of a flow nozzle falls between that of the venturi tube and the orifice plate (30 to 95 percent).

Pitot Tubes

In general, a pitot tube for indicating flow consists of two hollow tubes that sense the pressure at different places within the pipe. These tubes can be mounted separately in the pipe or installed together in one casing as a single device. One tube measures the stagnation or impact pressure (velocity head plus potential head) at a point in the flow. The other tube measures only the static pressure (potential head), usually at the wall of the pipe. The differential pressure sensed through the pitot tube is proportional to the square of the velocity. To install a pitot tube, you must determine the location of maximum velocity with pipe traverses. Although a pitot tube may be calibrated to measure fluid flow to ±1/2 percent, changing velocity profiles may cause significant errors. Pitot tubes are primarily used to measure gases because the change in the flow velocity from average to center is not as substantial as in other fluids. Pitot tubes have found limited applications in industrial markets because they can easily become plugged with foreign material in the fluid. Their accuracy is dependent on the velocity profile which is difficult to measure.

Target Meters

A target meter consists of a disc or a “target” which is centered in a pipe (Figure 5). The target surface is positioned at a right angle to the fluid flow. A direct measurement of the fluid flow rate results from the force of the fluid acting against the target. Useful for dirty or corrosive fluids, target meters require no external connections, seals, or purge systems. Much data is necessary, however, to determine the optimum size of the target and calibration is essential for its proper operation.

Elbow Tap Meters

An elbow tap operates by using a 45 degree pipe elbow in the fluid flow. A high pressure tap is taken from the outside of the elbow and a low pressure tap is taken from the inside of the elbow. This provides a differential pressure which is proportional to the flow rate. Measuring the differential pressure depends on the centrifugal force of the fluid flowing through the elbow. Hence, gas with its low density is not a good application for elbow taps. This also explains why a short curvature in the elbow develops a much greater differential pressure than a long curvature. The pressure drop of an elbow tap is no greater than that of the elbow. Though repeatable, accuracy of an elbow tap meter is only within ±5 percent.

Rotameters

Rotameters (also known as variable-area flowmeters) are typically made from a tapered glass tube that is positioned vertically in the fluid flow (Figure 6). A float that is the same size as the base of the glass tube rides upward in relation to the amount of flow. Because the tube is larger in diameter at the top of the glass than at the bottom, the float resides at the point where the differential pressure between the upper and lower surfaces balance the weight of the float. In most rotameter applications, the flow rate is read directly from a scale inscribed on the glass; in some cases, an automatic sensing device is used to sense the level of the float and transmit a flow signal. These “transmitting rotameters” are often made from stainless steel or other materials for various fluid applications and higher pressures. Rotameters may range in size from 1/4 inch to greater then 6 inches. They measure a wider band of flow (10 to 1) than an orifice plate with an accuracy of ±2 percent, and a maximum operating pressure of 300 psig when constructed of glass. Rotameters are commonly used for purge flows and levels.

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