Flow rate calculations

Pipecalc 2.0, Gulf Publishing Company, Houston, Texas. Note Pipecalc 2.0 will calculate the compressibility factor, minimum pipe ID, upstream pressure, downstream pressure, and flow rate for Panhandle A, Panhandle B, Weymouth, AGA, and Colebrook-White equations. The flow rates calculated in the above sample calculations will differ slightly from those calculated with Pipecalc 2.0 since the viscosity used in the examples was extracted from Figure 5, p. 147. Pipecalc uses the Dranchuk et al. method for calculating gas compressibility. 

The old, tedious, but quite reliable method is to measure the supply flow by the bag method. A tightly rolled plastic bag empty of air at the commencement of the test is pressed on the terminal with all the supply air passing into the bag. The filling time of the bag is measured and the flow rate calculated based on this information. The bag volume has to be determined in advance by a special measurement. Finally, the characteristic pressure difference method, menrumed above, can also be applied to supply terminals. 

Fig. 7. Experimental flow rates plotted vs. theoretical flow rates calculated using the Hagen-Poiseuille equation. The 100 data points include flow rates calculated using five different solvents, four different tube lengths and five different values of overpressure (see Supporting information for data used to generate this plot). The dashed lines indicate the variation expected if the inner diameter was 25% less (1 0.32) or 25% more (1 2.44) than the claimed value.

An important application of Bernoulli s equation is in flow measurement, discussed in Chapter 8. When an incompressible fluid flows through a constriction such as the throat of the Venturi meter shown in Figure 8.5, by continuity the fluid velocity must increase and by Bernoulli s equation the pressure must fall. By measuring this change in pressure, the change in velocity can be determined and the volumetric flow rate calculated. 

In Example 10.2, the range of pressure in the supply tank is specified and a more convenient method of calculation is to split the pressure range into a number of increments. After calculating the mass flow rate, the mass remaining in the tank is determined from the pressure at the end of the increment and hence the required time may be determined. A small refinement is to base the flow rate calculation on the mean pressure in the increment rather than on that at the beginning. 

To indicate the error introduced by the simplification of Eq. (28), the values of bubble volume at different flow rates calculated by both Eqs. (28) and (29) have been presented in Table II. The simplification is seen to give rise to errors of 10 to 30 %, hence restricting the use of Eq. (29) to cases where only approximate values are needed. 

Figure 7.18 Ratio of the rotational flow rate calculated using the generalized Newtonian method to the rotational flow calculated using the numerical method as a function of screw diameter...

Rotational flow and pressure flow rate calculations for the screw geometry and process conditions are performed for the injection-molding process in the same manner as for an extrusion process. Since the plasticator of an injection-molding process is not a continuous process, the instantaneous rate must be calculated based on the time that the screw is actually rotating. The instantaneous rate is the rate that is compared to the calculated flow rates for the screw. The instantaneous specific rate is calculated as follows ... 

Since flow is frame indifferent, then the transformed flow rate calculation for rate can be calculated using the above Eq. A7.51. The flow rate is obtained by integrating the z-direction velocity of the area as follows ... 

Care should be taken when using the HEM to size downstream disposal equipment. It may result in the flow rate being underestimated and the disposal system being undersized. It may be better to use a slip flow model in such cases. An alternative approach would be the application of an appropriate safety factor to a flow rate calculated using the HEM (see 7.2 (b)). 

TABLE 1-SUPERFICIAL MASS FLOW RATE CALCULATIONS... 

Since the influence of walls on the U and V flow components disappears upon the separation of the order of 8 from a solid wall, inaccuracy of the scheme cannot have an essential influence on the flow rate calculations. Equations (4.32) may have an explicit solution within some limited time interval when the flow from a point runner is still radial, while the flow front is circular. This filling pattern is realized up to the moment when the radius of a free boundary R(t) will become equal to B/2 (see Fig. 11). Such a filling regime we shall refer to as the first stage of filling the formulae of 4.2 with some minor corrections (for details see 36)) are applicable to this stage the corrections arise mainly due to the fact that the radial flow occurs in... 

Fig. 7. kf versus linear flow rate calculated for BSA adsorption to fluidized controlled pore glass after Rowe (A, Eq. 19, Ref. 74) and after Fan et al. ( , Eq. 20, Ref. 75). Physical data of adsorbent average particle diameter 200 pm, average particle density 1240 kg/m3, BSA diffusion coefficient in solution 7.3-10 11 m2/s, bed expansion calculated according to Richardson and Zaki, U, and n estimated according to Eqs. (3-5)... 

In the liquid flow rate calculation, one-dimensional flow is assumed however, it is acknowledged this is not true in the vicinity of the bubbles (especially at their leading and trailing edges) where the relative velocity between the bubbles and the liquid phase creates a complex liquid motion that is far from one dimensional. 

Now, for convenience, we assume that the barrel surface is stationary and that the upper and lower plates representing the screws move in the opposite direction, as shown in Fig. 6.57, but for flow rate calculations, it is the material retained on the barrel rather than that dragged by the screw that leaves the extruder. We assume laminar, isothermal, steady, fully developed flow without slip on the walls of an incompressible Newtonian fluid. We distinguish two flow regions marked in Fig. 6.57 as Zone I and Zone II. In the former, the flow is between two parallel plates with one plate moving at constant velocity relative to... 

Based on the most recent set of temperatures and total flow rates, calculate the component vapor rates using the tridiagonal matrix method. Find the component liquid rates by l j = Ay i>y,... 

The flow rate should be checked regularly and this can be achieved by fitting a graduated pipette on the reservoir side of the pump. Medium can be drawn into the pipette using a syringe, and the flow rate calculated from the time taken for a set volume of medium to be withdrawn. 

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