Viscous loss

The last term is the rate of viscous energy dissipation to internal energy, dV, also called the rate of viscous losses. These... 

Example 3 Venturi Flowmeter An incompressible fluid flows through the venturi flowmeter in Fig. 6-7. An equation is needed to relate the flow rate Q to the pressure drop measured by the manometer. This problem can he solved using the mechanical energy balance. In a well-made venturi, viscous losses are neghgihle, the pressure drop is entirely the result of acceleration into the throat, and the flow rate predicted neglecting losses is quite accurate. The inlet area is A and the throat area is a. 

The facdor K would be 1 in the case of full momentum recoveiy, or 0.5 in the case of negligible viscous losses in the portion of flow which remains in the pipe after the flow divides at a takeoff point (Denn, pp. 126-127). Experimental data (Van der Hegge Zijnen, Appl. Set. Re.s., A3,144-162 [1951-1953] and Bailey, ]. Mech. Eng. ScL, 17, 338-347 [1975]), while scattered, show that K is probably close to 0.5 for discharge manifolds. For inertiaUy dominated flows, Ap will be negative. For return manifolds the recovery factor K is close to 1.0, and the pressure drop between the first hole and the exit is given by... 

The primary cause of efficiency losses in an axial-flow turbine is the buildup of boundary layer on the blade and end walls. The losses associated with a boundary layer are viscous losses, mixing losses, and trailing edge losses. To calculate these losses, the growth of the boundary layer on a blade must be known so that the displacement thickness and momentum thickness can be computed. A typical distribution of the displacement and momentum thickness is shown in Figure 9-26. The profile loss from this type of bound-ary-layer build-up is due to a loss of stagnation pressure, which in turn is... 

Polymer High MW (>10,000) Tg usually < RT Physically crosslinks on cooling Strong Strength Hot tack Viscous loss —> peel force... 

In Eq. (4-29) jc is the distance traveled by the wave, and a is the absorption coefficient. Sound absorption can occur as a result of viscous losses and heat losses (these together constitute classical modes of absorption) and by coupling to a chemical reaction, as described in the preceding paragraph. The theory of classical sound absorption shows that a is directly proportional to where / is the sound wave frequency (in Hz), so results are usually reported as a//, for this is, classically, frequency independent. 

In terms of transient behaviors, the most important parameters are the fluid compressibility and the viscous losses. In most field problems the inertia term is small compared with other terms in Eq. (128), and it is sometimes omitted in the analysis of natural gas transient flows (G4). Equations (123) and (128) constitute a pair of partial differential equations with p and W as dependent variables and t and x as independent variables. The equations are hyperbolic as shown, but become parabolic if the inertia term is omitted from Eq. (128). As we shall see later, the hyperbolic form must be retained if the method of characteristics (Section V,B,1) is to be used in the solution. 

We can see that as the stress is applied the strain increases up to a time t = t. Once the stress is removed we see complete recovery of the strain. All the strain stored has been recovered. The material has the properties of an elastic solid. In order to achieve viscous flow we need to include an additional term, the viscous loss term. This is known as a Burger Body ... 

This equation is plotted as curve C in Figure 4.1. The form of equation 4.21 is somewhat similar to that of equations 4.16 and 4.17, in that the first term represents viscous losses which are most significant at low velocities and the second term represents kinetic energy losses which become more significant at high velocities. The equation is thus applicable over a wide range of velocities and was found by Ergun to correlate experimental data well for values of Rei/(l — e) from 1 to over 2000. 

Bill Magnetic drive viscous loss VISC LOSS N 13 kW... 

The frequency dependence of the moduli was measured by Mason et al. [7,8] and is shown in Fig. 4.3 for several values of <. In all cases, there is a plateau in G (, this extends over the full four decades of explored frequency, while for the lower 4>, the plateau is no longer strictly independent on co but reduces to an inflection point at G. In contrast, for all 4>, G" co) exhibits a shallow minimum, G". Mason et al. used G to characterize the elasticity and G" to characterize the viscous loss. 

The peak stress can be resolved into a component a0 cos S that is in place with the strain, related to the stored elastic energy and a component [Pg.200]

The following calculation as made for the Saline Water Project (6) shows the relation between pressure applied and production rate. The dominant factors are (1) the salt solution whose osmotic pressure must be overcome, (2) the pressure, as an energy source, (3) the diffusion of heat and (4) vapor as resistance factors, and (5) viscous losses within the cellophane capillaries. 

The vapor density, like the vapor pressure, can be used as a thermodynamic potential whose total change around a closed path is zero. According to this argument, the effect of the above five factors on vapor density can be mathematically expressed and summed to zero. Beginning at the product water outlet, move to salt water by adding M, compress the salt water to pressure p, and subject it to the thermal loss of latent heat transfer, the diffusion loss of mass transfer, and the viscous loss of pressure in cellophane and manifold passages. This returns the path to fresh water and a closed circuit. 

Experiments to distinguish between these two possibilities have often involved measurements of ultrasonic attenuation (ref. 5,9,31,32). The popularity of this approach derives in part from the fact that small impurities in liquids, such as suspended particles, have negligible influence on attenuation in comparison with even a very small concentration of microbubbles (ref. 9). (Microbubbles, in contrast to solid particles, appreciably increase the compressibility of a liquid, introducing forms of viscous losses and nonreversible energy exchanges that do not exist in the case of solid particles.) It is therefore of considerable interest that all fresh tap water samples measured by Turner (ref. 9) showed substantial and persistent abnormal (ultrasonic) attenuation, amounting to a minimum of 44% over that of distilled water it was concluded that this result stemmed from the presence of stabilized micron-sized bubbles. 

The last term is the rate of viscous energy dissipation to internal energy, Ev = jv <5 dV, also called the rate of viscous losses. These losses are the origin of frictional pressure drop in fluid flow. Whitaker and Bird, Stewart, and Lightfoot provide expressions for the dissipation function <5 for Newtonian fluids in terms of the local velocity gradients. However, when using macroscopic balance equations the local velocity field within the control volume is usually unknown. For such... 

Based on these experiments, a kind of flow-pattern map was proposed describing a region of laminar flow where viscous losses dominate, an intermediate region with secondary flow where inertial losses dominate (albeit still not turbulent) and a region of fully developed turbulent flow (see Figure 1.142) [151]. The transitional Reynolds number from the pure laminar to the secondary-flow regime increases with the ratio of bend length to hydraulic diameter. 

The first part of this equation is a viscous loss term and the second is an inertial loss term. For simple homogeneous porous media, S, can be written as... 

Here it will be assumed, as shown in Fig. 8.11, that the flow enters the channel through a smooth, convergent inlet in which the viscous losses are negligible. On the inlet plane of the channel, the velocity will consequently be uniform and equal to the mean velocity at any section of the channel, um. This is illustrated in Fig. 8.12. 

Enthalpy per unit mass Liquid depth Ratio of specific heats Kinetic energy of turbulence Power law coefficient Viscous losses per unit mass Length... 

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