Variable Area

Radial transfer of heat through a hollow cylinder and a hollow sphere are two important applications of variable heat transfer area and are considered here. 

Equation (2.16) denotes the logarithmic-mean average of Ai and A2. For constant thermal conductivity, noting l—r2-rx = (A2 - A )/2 rL, we have from Rk = / A for a hollow cylinder 

For convenience, the average heat transfer area and the conductive resistance for the foregoing three configurations are summarized in Table 2.1. 

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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. 

There are do2ens of flow meters available for the measurement of fluid flow (30). The primary measurements used to determine flow include differential pressure, variable area, Hquid level, electromagnetic effects, thermal effects, and light scattering. Most of the devices discussed herein are those used commonly in the process industries a few for the measurement of turbulence are also described. 

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. 

Variable Area 3.2.1.1 Piping Systems-Metal-Straight 3.6.2.1 Vessels-Pressurized-Metallic... 

THonomf No. 2.1.3.2.1.2 Equipment Description TRANSMtl l ERS PNEUMATIC-FLOW-VARIABLE AREA ... 

Differential Pressure Variable Area Uagmeter Mass Row Vortex Shedding Turbine. 3.1.2 Level... 

A more difficult criterion to meet with flow markers is that the polymer samples not contain interferents that coelute with or very near the flow marker and either affect its retention time or the ability of the analyst to reproducibly identify the retention time of the peak. Water is a ubiquitous problem in nonaqueous GPC and, when using a refractive index detector, it can cause a variable magnitude, negative area peak that may coelute with certain choices of totally permeated flow markers. This variable area negative peak may alter the apparent position of the flow marker when the flow rate has actually been invariant, thereby causing the user to falsely adjust data to compensate for the flow error. Similar problems can occur with the elution of positive peaks that are not exactly identical in elution to the totally permeated flow marker. Species that often contribute to these problems are residual monomer, reactants, surfactants, by-products, or buffers from the synthesis of the polymer. 

A variable-area, fluid or gas flow-rate meter. Usually a cone inside a glass measuring cylinder that is suspended by the upward flow of gas or liquid. 

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. 

Vapour-solids equilibrium 753 Variable area flowmeters 257... 

Ardel polyarylate resins, 10 190 Ardeparin, 4 95t Arduengo carbenes, 26 847 Area, exponents of dimensions in absolute, gravitational, and engineering systems, Cross-sectional area Head- area meters Surface area Variable-area flowmeters Area detectors, 26 431 Area per surfactant molecule, 24 136 Arechloral hydrate, anesthetic properties of, 2 69... 

Changes in steam flow are achieved by increasing or decreasing the area used for condensing steam in the reboiler. This variable-area flooded reboiler is used in some processes because it permits the use of lower-pressure steam. However, as you will show in your calculations (I hope), the dynamic performance of this configuration is distinctly poorer than direct manipulation of steam flow. 

In the membrane reactor a wall of area separates the phases, and this area is generally fixed by the geometry of the reactor using planar or cylindrical membranes. However, most multiphase reactors do not have fixed boundaries separating phases, but rather allow the boundary between phases to be the interfacial area between insoluble phases. This is commonly a variable-area boundary whose area wiU depend on flow conditions of the phases, as shown in Figure 12-7. 

Before we deal with these situations, it is instructive to consider a fixed-area version of a membraneless reactor, the falling film reactor. We cannot think of many applications of this reactor type because one usually benefits considerably by using configurations where the surface area is as large as possible, but the falling film reactor leads naturally to the description of many variable-area multiphase reactors. 

Variable-Area Meters Variable-area meters, which are also called rotameters, offer popular and inexpensive flow measurement devices. These meters employ a float inside a tube that has an internal cross-sectional area that increases with distance upward in the flow path through the tube. As the flow rate increases, the float rises in the tube to provide a larger area for the flowing fluid to pass. 

Positive displacement Turbine Variable-area Differential pressure Vortex Target Thermal... 

Figure 7.9 shows a cylindrical duct whose radius varies as a function of position, R(z). As long as the radius varies smoothly and relatively smoothly, the channel flow may be treated as a boundary-layer problem. Discuss what, if any, changes must be made to the boundary-layer equations and the boundary-condition specifications to solve the variable-area boundary-layer problem. 

PLUG FLOW WITH VARIABLE AREA AND SURFACE CHEMISTRY 657... 

Assuming a variable-area channel and steady-state flow, the integrals can be evaluated for the differential control volume (Fig. 16.3) as... 

Gold, H., Straight, D. M., Gas Turbine-Engine Operation with Variable-Area Fuel... 

Simulation of Mouth Conditions for Flavor Analysis The RAS is not intended to simulate the size or structure of the mouth. The conditions in the mouth expected to affect volatility—i.e., temperature, breath flow, mastication, and salivation—are simulated. Temperature iscontrolled with a waterjacket (37°C). Gas (N2 or purified air) flow is controlled with a variable-area needle-valve flow meter (20 ml/sec). The shearing resulting from mastication is implemented with blender blades and a high-torque variable-... 

The primary components of the RAS are a 1-liter stainless-steel blender container, a stainless-steel jacket that water flows through, a variable-speed motor with controller, modified lid with inlet and outlet for gas flow, and a variable-area needle-valve flow meter. The large volume allows for the collection of sufficient volatiles to concentrate trace components for GC/MS analysis. Figure Gl.7.2 shows a diagram of the RAS. 

Other sensors which are described in Volume 1 (Sections 6.3.7-6.3.9) are the variable area meter, the notch or weir, the hot wire anemometer, the electromagnetic flowmeter and the positive displacement meter. Some of these flowmeters are relatively less suitable for producing signals which can be transmitted to the control room for display (e.g. weir, rotameter) and others are used in more specialist or limited applications (e.g. magnetic flowmeter, hot wire anemometer). The major characteristics of different types of flow sensor are summarised in Table 6.1. Brief descriptions follow of the principles underlying the more important types of flowmeter not described in Volume 1. In many instances such flow sensors are taking the place of those more traditional meters which rely upon pressure drop measurement. This is for reasons of versatility, energy conservation and convenience. 

Variable area Volume 1 Section 6.3.7 Volume Yes No No Yes Yes No Usually No No Glau < 400 Metal < 800... 

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. 

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