Variable area orifices

Variable Area Orifices. Variable area orifices consist of an orifice and a concentric obstruction. Fluid flows through the orifice around the concentric obstruction. As the flow rate increases, the area between the orifice and the obstruction changes, either by displacement of a spring loaded obstruction relative to a fixed orifice or by displacement of a spring loaded orifice relative to a fixed obstruction. The displacement is related to the flow rate. 

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. 

In the meters so far described the area of the constriction or orifice is constant and the drop in pressure is dependent on the rate of flow. In the variable area meter, the drop in pressure is constant and the flowrate is a function of the area of the constriction. 

Two or more of these conditions can occur at the same time, resulting in asymmetric axial, radial and tangential velocity vectors. Some flowmeters are more sensitive than others to particular types of flow distortion, e.g. orifice meters are affected by pure swirl more than venturi meters are magnetic flowmeters are unaffected by changes in the radial velocity component whereas ultrasonic time-of-flight meters are highly susceptible thereto swirl and asymmetry have the least effect on positive displacement meters and the greatest effect on variable area meters. 

The variable-area flowmeter is a head-type flow sensor, but it does not measure the pressure drop across a fixed orifice instead, the pressure drop is held relatively constant, and the orifice area is varied to match the flow (Figure 3.98). In gravity-type variable-area flowmeters, increase in flow lifts the float, piston, or vane, and it is the weight of these flow elements that has... 

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. 

The Aerotrak has an inherent capability to calibrate a variety of flow transducers, such as turbine, variable area, nozzles, vortex shedders, orifice plates, laminar, thermal mass flow controllers. 

The turbine-type flow meter probably has been used for flow measurement of liquefied gases more than any other type of meter. These meters have all of the disadvantages of the variable-area meters, are more expensive, have moving parts, and require electronic circuitry. There is a tendency to trust the reading of a turbine meter more than an orifice even though neither meter has been calibrated with the fluid being measured. 

Flow transmitters. Flow measurements are made in high-pressure lines by sensing the pressure drop across a calibrated orifice or venturi, or by the transmitting variable-area type of flowmeter. The latter meter resembles a Rotameter with float position transmitted electrically. It has the advantage of being an in-line element but is not readily applicable to large flows. 

Calculations of Orifice Flow Area using Pressure Relieving Balanced Bellows Valves, with Variable or Constant Back Pressure. Must be used when backpressure variation exceeds 10% of the set pressure of the valve. Flow may be critical or non-critical for balanced valves. All orifice areas. A, in sq in. [68]. The sizing procedure is the same as for conventional valves listed above (Equations 7-10 ff), but uses equations given below incorporating the correction factors K, and K,, . With variable backpressure, use maximum value for P9 [33a, 68]. 

A full opening valve or variable orifice should be able to restrict flows of liquid into the bottom of the reboUer so that the instability in the liquid in the column will not be direcdy introduced into the inlet of the reboUer. Generally, the liquid inlet nozzle size should be about 50% in the inlet tube flow cross-section area. A large line is sometimes used, but a restricting provision should be provided to to stabilize operations. 

Number of independent equations Number of degrees of freedom Number of independent variables Number of zeros of function Pressure upstream of nozzle in flapper/nozzle system Pressures applied to limbs of manometer tube or pressures downstream and upstream of orifice plate Distillation column pressure Pressure in feedback bellows of pneumatic controller Frictional drag per unit cross-sectional area of manometer tube... 

The difference between an orifice meter and a venturi meter or flow nozzle is that for both of the latter there is no contraction, so that A2 is also the area of the throat and is fixed, while for the orifice, A2 is the area of the jet and is a variable and is, in general, less than the area of the orifice A0. For the venturi tube or flow nozzle the discharge coefficient is practically a velocity coefficient, while for the orifice the value of C or K is much more affected by Cc than it is by Cv. 

Either Qi or Q2 or both may be variable and functions of z, or one of the two may be either constant or zero. For example, if liquid is discharged through an orifice or a pipe of area A under a differential head z, Q2 = Cd (2gz)m, where Cd is a numerical discharge coefficient and z is a variable. If the liquid flows out over a weir or a spillway of length B, Q2 = CBz3/2, where C is the appropriate coefficient. (For steady flow, z would be the constant H.) In either case z is the variable height of the liquid surface above the appropriate datum. In like manner, Qi may be some function of z. 

The prime variables affecting the orifice coefficient, Cv, are the fractional hole area and the ratio of tray thickness to hole diameter. More than 20 published correlations are available for evaluating Cv (12). Fair et al. (18) and Van Winkle (5) recommend the correlation by Liebson et al. (48 Fig. 6.21a). The Hughmark and O Connell correlation (66) is preferred by Ludwig (4) and Chase (30),... 

Because total air volume is the product of air-flow velocity (meters per second), orifice cross-sectional area (square meters), and time (seconds) any of these parameters could be changed in theory. In practice, a continuously variable orifice is difficult to build therefore, this value is fixed. The requirement for isokinetic flow will dictate the air-flow velocity. Therefore, only sample time can be independently controlled. 

AREA METERS ROTAMETERS. In the orifice, nozzle, or venturi, the variation of flow rate through a constant area generates a variable pressure drop, which is related to the flow rate. Another class of meters, called area meters, consists of devices in which the pressure drop is constant, or nearly so, and the area through which the fluid flows varies with flow rate. The area is related, through proper calibration, to the flow rate. 

A disadvantage of the nozzle method is that the nozzles are not variable in their cross-sectional area, that is, the concentrations and total flow rate are fixed and cannot be varied continuously. The built-in nozzles are chosen and fixed at the time of conception of the system. To enable the flow rate to vary, precise, reproducibly steerable pressure regulators for the inlet pressure would be necessary, which is not economically feasible. Orifices can be manufactured with various cross-sectional areas, but there is a technical lower limit, so that the minimum standard volumetric flow rate achievable lies at approximately 1 SCCM. 

Any mathematical model is subject to the limits imposed by its founding assumptions. For example, when we invoked the orifice equation we implicitly assumed that the fluid height in the tank preserved the physics of the draining process. When the tank is nearly empty the physics will be different - a whirlpool of air will form in the outlet, for example. Thus at long times the orifice equation, and subsequently Eq. (6.45), will not be valid. Similarly, a tank with a closed top, with variable cross-sectional area (such as a funnel), or density gradients in the fluid requires different mathematical models. 

The pneumatic or electrical signals depict only the analog measured variable. The direct measured variable is not always the desired result, however. Thus, for example, one obtains from flow measurements with diaphragms a differential pressure, not the mass flow, q , which for compressible flow in an orifice is given by Eq. (32), where Ap = pi — pi is the pressure drop between the taps upstream and downstream respectively, pj is the upstream density, Q is an empirical discharge coefficient, Ai is the area of the orifice, Y is a dimensionless expansion factor, and p = 2/ 1 is the ratio of the orifice to the upstream pipe diameter (see Section 12.2.5) [10]. 

The additional elements possibly present along a given pipeline can be widely variable bends (elbows) and other directional variations, connections like tees and others, cross-sectional area variations (restrictions, enlargements), joints (welds, flanges, others), orifices, nozzles, sensors for instrumentation, all different kinds of valves, and many others. All these elements introduce a pressure loss to the flowing fluid, which is not easy to predict because of both the extreme variability of those elements, and the difficulties in the mathematical representation of the flow characteristics through them. 

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