Example Flow Calculation

Two new LDPE resins are proposed to be processed on a similar extruder as described in the example in Section 1.5.1. The extruder here is configured with a downstream gear pump such that the discharge pressure for the extruder is targeted at 7 MPa. The resin manufacturer has provided viscosity data in the form of a viscosity relationship  

Note that the relationship contains an absolute value of the shear rate since it can be either positive or negative. The manufacturer has supplied parameters for the proposed 0.8 dg/min (190 °C, 2.16 kg) Ml resin and a lower viscosity resin with an Ml of 2 dg/min. The viscosity equation parameters are provided in Table 7.1. 

The target discharge temperature for the extrusion is 240 °C, and the maximum screw speed is 130 rpm (N = 2.167 rev/s). What will be the expected production rates for both resins at 130 rpm At 240 °C the melt density of the resins is 735 kg/mT As presented in Sections 1.4 and 7.4, the net flow in the extruder is the difference between the rotational flow and the flow induced by the pressure gradient Qp. The data in Table 7.2 was calculated from the example in Section 1.5.1 and Table 7.1  

The rotational flow rate is calculated using the data in Table 7.2 and Eq. 1.13 as follows  

This is the rate that the screw can produce at 130 rpm with no pressure gradient in the channel. Because both resins are LDPE and at the same temperature of 

---

Example 2 Calculation of Kremser Method For the simple absorber specified in Fig. 13-44, a rigorous calculation procedure as described below gives results in Table 13-9. Values of were computed from component-product flow rates, and corresponding effective absorption and stripping factors were obtained by iterative calculations in using Eqs. (13-40) and (13-41) with N = 6. Use the Kremser method to estimate component-product rates if N is doubled to a value of 12. 

Example 4 Calculation of the BP Method Use the BP method with the SRK eqiiation-of-state for K values and enthalpy departures to compute stage temperatures, interstage vapor and hqiiid flow rates and compositions, and rehoiler and condenser duties for the light-hydrocarhon distdlation-coliimn specifications shown in Fig. 13-51 with feed at 260 psia. The specifications are selected to obtain three products, a vapor distillate rich in Cri and C3, a vapor side-stream rich in n-C4, and a bottoms rich in n-C and n-Cg. 

Example 5 Calculation of the SR Method Use the SR method with the PR equation of state for K values and enthalpy departures. The oil was taken as n-dodecane. To compute stage temperatures and interstage vapor and hquid flow rates and compositions for ahsorher-column specifications shown in Fig. 13-52. Note that a secondary ahsorher oil is used in addition to the main ahsorher oil and that heat is withdrawn from the seventh theoretical stage. 

Example 8 Calculation of Rate-Based Distillation The separation of 655 lb mol/h of a bubble-point mixture of 16 mol % toluene, 9.5 mol % methanol, 53.3 mol % styrene, and 21.2 mol % ethylbenzene is to be earned out in a 9.84-ft diameter sieve-tray column having 40 sieve trays with 2-inch high weirs and on 24-inch tray spacing. The column is equipped with a total condenser and a partial reboiler. The feed wiU enter the column on the 21st tray from the top, where the column pressure will be 93 kPa, The bottom-tray pressure is 101 kPa and the top-tray pressure is 86 kPa. The distillate rate wiU be set at 167 lb mol/h in an attempt to obtain a sharp separation between toluene-methanol, which will tend to accumulate in the distillate, and styrene and ethylbenzene. A reflux ratio of 4.8 wiU be used. Plug flow of vapor and complete mixing of liquid wiU be assumed on each tray. K values will be computed from the UNIFAC activity-coefficient method and the Chan-Fair correlation will be used to estimate mass-transfer coefficients. Predict, with a rate-based model, the separation that will be achieved and back-calciilate from the computed tray compositions, the component vapor-phase Miirphree-tray efficiencies. 

As another example of calculation and dimensioning of pneumatic conveying systems we consider an ejector shown in Fig. 14.20. In fluidized bed combus tion systems a part of the ash is circulated with the hot flue gas. The task of the ejector, is to increase the pressure of the circulating gas to compensate the pressure losses of the circulation flow. The motivation for using an ejector, rather than a compressor, is the high temperature of the flue gas. The energy... 

Once a specific heat exchanger is chosen, the flow per tube is known, so it is possible to use the correlations of Chapter 2 to calculate a more precise overall heat transfer coefficient (U). An example of calculation of U is given in Chapter 5. 

A typical example of calculation of the thermal coefficient of performance for forced convection of air is shown in Fig. 2.69. COP surfaces are presented for the maximum and least material aluminum heat sink configurations in the design flow space between 0.01-0.04 m /s and 20-80 Pa. 

If AW AW the process of finding a linear-mixture basis can be tedious. Fortunately, however, in practical applications Nm is usually not greater than 2 or 3, and thus it is rarely necessary to search for more than one or two combinations of linearly independent columns for each reference vector. In the rare cases where A m > 3, the linear mixtures are often easy to identify. For example, in a tubular reactor with multiple side-injection streams, the side streams might all have the same inlet concentrations so that c(2) = = c(iVin). The stationary flow calculation would then require only AW = 1 mixture-fraction components to describe mixing between inlet 1 and the Nm — I side streams. In summary, as illustrated in Fig. 5.7, a turbulent reacting flow for which a linear-mixture basis exists can be completely described in terms of a transformed composition vector ipm( defined by... 

Example 1 Calculation of Rotational and Pressure Flow Components... 

Example 2 Flow Calculations for a Properly Operating Extruder... 

An impurities analytical procedure should be described adequately so that any qualified analyst can readily reproduce the method. The description should include the scientific principle behind the procedure. A list of reagents and equipment, for example, instrument type, detector, column type, and dimensions, should be included. Equipment parameters, for example, flow rate, temperatures, run time, and wavelength settings, should be specified. How the analytical procedure is carried out, including the standard and sample preparations, the calculation formulae, and how to report results, should be described. A representative chromatogram with labeled peak(s) should be included in the procedure. 

Fig. 3. Like a photoelectrochemical cell, such a powder includes sites for photo-induced oxidation and reduction, but no external current flow accompanies these transformations. Photoactivity is also maintained as the size of the particle decreases to the colloidal range although the absorption characteristics, the quantum efficiency of charge separation, and the kinetics of interfacial electron transfer may be influenced by the particle size. On sufficiently small particles, for example, the calculated space-charge width necessary for effective band bending may exceed the dimensions of the particle.

Boundary conditions In CFD frequently the fact is ignored that suitable boundary conditions are required at all flow boundaries. This is a major difficulty, for example, when calculating viscoelastic flow properties. We do not know the stages through which a fluid element has passed on entry into the computational domain. 

It is instructive to consider steady fluid flow (sometimes called Poiseuille flow) in a thin capillary tube. This example has many purposes it provides (1) a model flow calculation, (2) an illustration of how velocity profiles arise, (3) an explanation of the nature of flow in capillary chromatography, and (4) a foundation for capillary flow models of packed beds. 

By means of method of visualization with the help of acoustic waves [1,2] we could get the microstructure images of steel samples on different depths from the surface. The analysis of acoustic images gave the possibility to calculate the dimensions of grains, to observe their transformation in the period of time or under external influences. In accordance with the theory of Hall - Peach there were defined the strength characteristics, for example flow limit ( Go,2) of the materials under study. The significance obtained o0 2 is in proper correspondence with values that are table one for the type of steel under consideration. 

Some examples illustrative of discounted cash-flow calculations taken from the literature are as follows ... 

Corrosion economics and corrosion management forms the theme of the fifth chapter. Discounted cash flow calculations, depreciation, the declining balance method, double declining method, modified accelerated cost recovery system and present worth calculation procedures are given, together with examples. In the second part, corrosion management, including the people factor in corrosion failure is briefly presented. Some of the expert systems presently available in the literature are briefly discussed. 

Since minerals form ions in solution, they increase the electrical conductivity of the solution. Conversely, water that is low in dissolved ions has higher resistance to current flow. For example, the calculated resistivity of chemically pure water is 18.3 million Cl (megohms) over a distance of 1 cm at 25°C. In fact, 18 Mfl-cm is the upper limit of current water-purification technology. 

Example 2 Discounted-cash-flow calculations based on continuous interest compounding and continuous cash Row. Using the discount factors for continuous interest and continuous cash flow presented in Tables 5 to 8 of Chapter 7, determine the continuous discounted-cash-flow rate of return r for the example presented in the preceding section where yearly cash flow is continuous. The data follow. 

Related Calculations. Where in-line equalization basins are used, additional damping of the BOD mass-loading rate can be obtained by increasing the volume of the basins. Although the flow to a treatment plant was equalized in this example, flow equalization would be used, more realistically, in locations with high infiltration or inflow or peak stormwater flows. 

---