Flow measurements head meters

Head-Area Meters. The Bernoulli principle, the basis of closed-pipe differential-pressure flow measurement, can also be appHed to open-channel Hquid flows. When an obstmction is placed in an open channel, the flowing Hquid backs up and, by means of the Bernoulli equation, the flow rate can be shown to be proportional to the head, the exact relationship being a function of the obstmction shape. 

Capacity. Pumps deHver a certain capacity, Q, sometimes referred to as flow, which can be measured directly by venturi, orifice plate (11), or magnetic meters (12) (see Flow measurement). The indirect way to determine capacity is often used. Whereas this method is less accurate than applying a flow meter, it often is the only method available in the field. The total head is measured and the capacity found from the pump head—capacity (H— curve (Fig. 2). More recently, sonic flow meters (13) have been used, which can be installed on the piping without the need for pipe disassembly. These meters are simple to use, but require relatively clean single-phase Hquid for reHable measurements. 

The principal classes of flow-measuring instruments used in the process industries are variable-head, variaBle-area, positive-displacement, and turbine instruments, mass flowmeters, vortex-shedding and iiltrasonic flowmeters, magnetic flowmeters, and more recently, Coriohs mass flowmeters. Head meters are covered in more detail in Sec. 5. 

General Principles The underlying principle of an ideal area meter is the same as that of a head meter of the orifice type (see subsection Orifice Meters ). The stream to be measured is throttled by a constriction, but instead of observing the variation with flow of the differential head ac-ross an orifice of fixed size, the constriction of an area meter is so arranged that its size is varied to accommodate the flow while the differential head is held constant. 

In those days, there were no oil refineries, nor bottlers of carbonated soda, nor sulfuric acid plants. There was only one liquid to consider, and move in large quantities. .. fresh water from the mountains. With only one liquid under consideration, fresh water, and no. sophisticated instrumentation, they measured the water s force, or pressure, in terms of elevation. It is for this reason that today all over the world, pump manufacturers u.se the term Head measured in meters or feet of elevation to express pre.ssure or force. The term flow expresses volume over time, such as gallons per minute, or cubic meters per second. 

The measurement of the linear velocity as a function of shaft RPM can be done at room temperature and pressure in air. It is best to do this on the catalyst already charged for the test. Since u is proportional to the square of the head generated, the relationship will hold for any fluid at any MW, T, and P if the u is expressed at the operating conditions. The measurement can be done with the flow measuring attachment and flow meter as shown in Figure 3.5.1. 

Differential Pressure Meters Differential pressure meters or head meters measure the change in pressure across a special flow element. The differential pressure increases with increasing flow rate. The pitot tubes described previously work on this principle. Other examples include orifices [see also Eqs. (6-111) and (8-102), and Fig. 10-14], nozzles (Fig. 10-19), targets, venturis (see also Sec. 8 and Fig. 10-17), and elbow meters. Averaging pitot tubes produce a pressure differential that is based on multiple measuring points across the flow path. 

In the presence of flow pulsations, the indications of head meters such as orifices, nozzles, and venturis will often be undependable for several reasons. First, the measured pressure differential will tend to be high, since the pressure differential is proportional to the square of flow rate for a head meter, and the square root of the mean differential pressure is always greater than the mean of the square roots of the differential pressures. Second, there is a phase shift as the wave passes through... 

Beitler, S. R., Lindahl, E. J., and McNichols, H. B., Developments in the Measuring of Pulsating Flows with Inferential-Head Meters, Trans. ASME 65 337, 1943. 

Head flow meters operate on the principle of placing a restriction in the line to cause a differential pressure head. The differential pressure, which is caused by the head, is measured and converted to a flow measurement. Industrial applications of head flow meters incorporate a pneumatic or electrical transmitting system for remote readout of flow rate. Generally, the indicating instrument extracts the square root of the differential pressure and displays the flow rate on a linear indicator. 

Head-type flowmeters include orifice plates, venturi tubes, weirs, flumes, and many others. They change the velocity or direction of the flow, creating a measurable differential pressure, or "pressure head," in the fluid. Head metering is one of the most ancient of flow detection techniques. There is evidence that the Egyptians used weirs for measurement of irrigation water flows in the days of the Pharaohs and that the Romans used orifices to meter water to households in Caesar s time. In the 18th century, Bernoulli established the basic relationship between the pressure head and velocity head, and Venturi published on the flow tube bearing his name. 

The detection of pressure drop across a restriction is undoubtedly the most widely used method of industrial flow measurement. If the density is constant, the pressure drop can be interpreted as a reading of the flow. In larger pipes or ducts, the yearly energy operating cost of differential-pressure (d/p)-type flowmeters can exceed the purchase price of the meter. The permanent pressure loss through a flowmeter is usually expressed in units of velocity heads, v2/2 g, where v is the flowing velocity, and g is the gravitational acceleration (9.819 m/s2, or 32.215 ft/s2, at 60° latitude). 

Full-bore meters include variable-head meters such as venturi and orifice meters and variable-area meters such as rotameters. These will be described in some detail. Briefer descriptions are given of other full-bore measuring devices V-element, magnetic, vortex shedding, turbine and positive-displacement meters, ultrasonic meters, and mass flow devices such as Coriolis and thermal flowmeters. 

There have been various applications to cryogenics of these head-type meters in the form of orifice plates, Venturi, and flow nozzles (see Fig. 8.11). This type of meter is probably the oldest method of measuring flowing fluids. The distinctive feature of head meters is that a restriction is employed to cause a change in the static pressure of the flowing fluid. This pressure change is measured as the difference between the static head and the total head at one section of the channel. 

The estimated uncertainty in cryogenic flow measurement using head-type meters ranges from 1 to 3%. This is composed of the uncertainty in bias shift caused by thermal contraction of the material, uncertainty in the effect of increased Reynolds number, and a large imprecision traceable to the methods of pressure measurement and pressure tap design. 

The three most extensively used types of flow-metering devices are the thin-plate square-edged oriflce, the flow nozzle, and the venturi tube. They are differential-head instruments and require secondaiy elements for measimement of the differential pressure produced by the primary element. The Supplement to ASME Power Test Codes Instruments and Apparatus, describes construction of the above primary flow-measuring elements and their installation as well as installation of the secondary elements. The method of flow measimement, the equations for flow computation, and the limitations and accimacy of measurements are discussed. Diagrams and tables showing the necessary flow coefficients as a function of Reynolds number and diameter ratio are included in the standards. Diagrams of the expansion factor for compressible fluids are given. 

Variable-Area Flow Meters. In variable-head flow meters, the pressure differential varies with flow rate across a constant restriction. In variable-area meters, the differential is maintained constant and the restriction area allowed to change in proportion to the flow rate. A variable-area meter is thus essentially a form of variable orifice. In its most common form, a variable-area meter consists of a tapered tube mounted vertically and containing a float that is free to move in the tube. When flow is introduced into the small diameter bottom end, the float rises to a point of dynamic equiHbrium at which the pressure differential across the float balances the weight of the float less its buoyancy. The shape and weight of the float, the relative diameters of tube and float, and the variation of the tube diameter with elevation all determine the performance characteristics of the meter for a specific set of fluid conditions. A ball float in a conical constant-taper glass tube is the most common design it is widely used in the measurement of low flow rates at essentially constant viscosity. The flow rate is normally deterrnined visually by float position relative to an etched scale on the side of the tube. Such a meter is simple and inexpensive but, with care in manufacture and caHbration, can provide rea dings accurate to within several percent of full-scale flow for either Hquid or gas. 

Dali Flow Tube - The advantage is this type of flowmeter is that it has a permanent head loss of only 5 % of the measured pressure differential. This is the lowest pressure drop of all orifice meter designs. Flow ratios as high as 1 10 (e.g., 1.0 to 10 kg/s) can be measured within + 2% of actual flow. Dali flow mbes are available in different materials and diameters up to 1500 mm. 

The rate of flow of water in a 150 mm diameter pipe is measured with a venturi meter with a 50 mm diameter throat. When the pressure drop over the converging section is 100 mm of water, the flowrate is 2.7 kg/s. What is the coefficient for the converging cone of the meter at feat flowrate and what is the head lost due to friction if the total loss of head over the meter is 15 mm water, what is the coefficient lor the diverging cone ... 

This equation defines the flow coefficient, Cv. Here, SG is the fluid specific gravity (relative to water), pw is the density of water, and hv is the head loss across the valve. The last form of Eq. (10-29) applies only for units of Q in gpm and hv in ft. Although Eq. (10-29) is similar to the flow equation for flow meters, the flow coefficient Cv is not dimensionless, as are the flow meter discharge coefficient and the loss coefficient (Af), but has dimensions of [L3][L/M]1/2. The value of Cv is thus different for each valve and also varies with the valve opening (or stem travel) for a given valve. Values for the valve Cv are determined by the manufacturer from measurements on each valve type. Because they are not dimensionless, the values will depend upon the specific units used for the quantities in Eq. (10-29). More specifically, the normal engineering (inconsistent) units of Cv are gpm/ (psi)1/2. [If the fluid density were included in Eq. (10-29) instead of SG, the dimensions of Cv would be L2, which follows from the inclusion of the effective valve flow area in the definition of Cv]. The reference fluid for the density is water for liquids and air for gases. 

The flow of fluids is most commonly measured using head flowmeters. The operation of these flowmeters is based on the Bernoulli equation. A constriction in the flow path is used to increase the flow velocity. This is accompanied by a decrease in pressure head and since the resultant pressure drop is a function of the flow rate of fluid, the latter can be evaluated. The flowmeters for closed conduits can be used for both gases and liquids. The flowmeters for open conduits can only be used for liquids. Head flowmeters include orifice and venturi meters, flow nozzles, Pitot tubes and weirs. They consist of a primary element which causes the pressure or head loss and a secondary element which measures it. The primary element does not contain any moving parts. The most common secondary elements for closed conduit flowmeters are U-tube manometers and differential pressure transducers. 

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