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As such, it depends on the substance or substances in the system, temperature, and pressure but not on the velocity gradient, which is the rate of shear or on the time parameter. We now apply the statement of conservation of energy to the fluid in the macroscopic flow system. A simple parabolic form of the velocity defect law can often be used over limited ranges: The velocity profiles in terms of the velocity defect laws are compared with experimental data in Fig. 6.17.

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K-1 ( Table 2.2) 41. μ= Viscosity In general, the viscosity of gases increases with temperature at low pressures while that of liquids usually decreases. For gases as rigid spheres and at low pressures ( < 10 atm), the variation of viscosity is related to the square root of temperature in absolute unit ( K or R). It is desired to use the result of Example 20.1-3 to dis- cuss the critical size of a system in which an "autocatalytic reaction" is occurring.

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The proportionality constant k is called the thermal conductivity. Equa- tion 17.7-4 can be derived from Eq. 17.7-3 by using some of the relations in Tables 17.7-1 and 2. The method of separation of variables gives the exact solution8 for the compositions in the two bulbs as in which y,, is the nth root of y tan y = N, and N = SL/V. The top of the trap is equipped with a clear or translucent section, such as nylon tubing, in order to observe the gas-liquid interface.

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At first the flow goes through a duct 0. rises vertically 1. 3-12.5 m. p = 850 kg/m3) will flow in the pipeline? For film condensation on a horizontal tube of diameter D, length L, and constant surface temperature To, the result of Nusselt3 may be written as Here w/L is the mass rate of condensation per unit length of tube, and it is understood that all the physical properties of the condensate are to be calculated at the film tempera- ture, Ti = :(T, + To). If the solution is sufficiently dilute, then Stokes’ law [Eq. (12.65)] can be assumed: fi = F,l U, = 6npBrp (14.76) where rp is the particle radius and pB is the viscosity of the surrounding fluid.

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The course requires no prior programming skills. This difference is that there are a number of possible mass transfer coefficients depending on the driving forces chosen. g molehec cm2 and g mole/sec cm2 atm. Wind is blowing horizontally at a velocity of 8.94 d s e c. Other analogies, such as von Karman 's and Prandtl 's, usually result in poor relations. If &in and Rmin are known, it is then possible (for any given reflux ratio R ) to determine the stages needed by using the graphical correlation shown in Figure 12-15.

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Review of first and second law principles; application to the properties of fluids and solutions; vapour liquid equilibria; the third law; applications to chemical equilibrium and chemical reactions. What is the maximum rate of slurry that can be handled? 14-54. Confirming the attack is critical, especially if it is the first reported chemical attack in the theater. Nevertheless, Pai’s equations yield a smooth profile with no discontinuities in slopes.

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Substituting and solving, we obtain With equal heat transfer (i.e., hLu values the same) Example 7-2 A polymer solution (n of 0.5; K at 90°F of 51-lb mass s e F 2 ft-I; viscosity activation energy of 14,900 Btu/lb mole) is fed into a 1-inch inside-diameter stainless steel tube (10 feet long) at a mass flow rate of 750 Ib masskour and a temperature of 90°F. Chemie, 108,385-426 (1860). 52 Chapter 2 Shell Momentum Balances and Velocity Distributions in Laminar Flow The results of this section are only as good as the postulates introduced at the begin- ning of the section-namely, that v, = v,(r) and p = p(z).

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The reaction releases heat at a uni- form volumetric rate S, throughout the reactor. Hydrotreatment of a kerosene fraction can convert aromatics into naphthenes, which are cleaner-burning compounds. You’ll likely work on a range of projects, from addressing consultancy questions for other clients to designing, commission and validating large pharmaceutical production and production facilities. Heat and Mass Transfer, 6,221-229, Eq. 20.2-51 with n, = 0, and K can be found by ihterpolating the function K(R, A) to R = A, and A = p/pQAB.

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Similar expressions can be written for the surface elements per- pendicular to the y- and z-axes. In the trans-Alaska (Alyeska) pipeline, drag reducing additives are injected to reduce pumping costs and to increase flow rates by 10 to 20 percent [BlO]. For exam- ple, for ideal gases p = pM/RT and RT P21 RT P2 1 d p = - 1 dp = - In - (ideal gases) (15.2-3) M PI M PI For incompressible liquids, p is constant so that 1 1,' dp = p (p2 - pl) (incompressible liquids) (15.2-4) For frictionless adiabatic flow of ideal gases with constant heat capacity, p and p are related by the expression pp-? = constant, in which y = kP/& as shown in Exarn- ple 11.4-6.

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The diffusivity in Eq. 24.4-7 can be estimated from Eq. 17.4-3 as in which Rp is the radius of a sphere having the volume of the protein molecule, ,uw is the sol- vent (water) viscosity, and fp is a hydrodynamic shape factor (that is, a correction factor to ac- count for the nonsphericity of the protein molecule). This course is not eligible for Credit/D/Fail grading. Both cases will be considered in this chapter. 5.1 CONVECTIVE FLUX CAUSED BY FORCED CONVECTION A convective flux contribution to the transfer of a property by forced convection must involve a flow velocity.