Pressure gradient parameter

A17 This cell contains a specified value of the nondimensional pressure-gradient parameter,... 

The cell A 17 refers to the pressure-gradient parameter, with the needed to identify the fact that it is always in column A and thus not shifted relatively with dragging commands that will follow. The cells D 14 and D 15 refer to rows containing the values of fj-1/2 and rj+1/2. Here the is needed to fix the row reference in subsequent dragging operations. That is, the values of fj-1/2 and rJ+1/2 are always in rows 14 and 15, but the columns must be allowed to change in a relative dragging operation. Cells C17 and E17 refer to the values of the axial velocity in the adjacent cells (i.e., uj-1 and uj+i). 

A18 This spreadsheet has been designed to solve the Couette-Poiseuille problem for several values of the pressure-gradient parameter at once. In this case, cell A18 has been programmed to have the value =A17+2. Thus each row has a pressure-gradient parameter that is two greater than the one above it. 

A8 - B8 Cell A8 contains the name PP, which is defined to have the value in cell B8, representing the nondimensional pressure-gradient parameter P. At this point a number is simply entered in to cell B8 for a particular problem. However, as we will discuss in more detail later, the number will be involved in an iteration process seeking a particular value of P for a given aspect ratio a. 

If the problem were being done for a specific value of the pressure-gradient parameter in dimensional terms, the problem would be solved once the spreadsheet has completed its iterations. The correct velocities would be contained in each of the cells. However, for the... 

There is only one value of the pressure-gradient parameter (cell B8) for which this constraint will be satisfied. Therefore, a further iteration must be accomplished to determine the correct value of P for the given aspect ratio a. 

D8 - E8 Cell E8 contains the value of the nondimensional group /Re, which is essentially the desired general solution to this problem. For every value of the aspect ratio a, entered in cell Al, there will be a corresponding value of /Re. Given a value of a, the value of /Re in cell E8 will be correct when the pressure-gradient parameter in cell B8 is chosen such that mean velocity in cell E9 is 1. Referring to Eq. 4.87, we have... 

The spreadsheet could be programmed to use the TOOLS-SOLVER function to automate the selection of the pressure-gradient parameter, cell B8, to drive the mean nondi-mensional velocity to 1.0. However, our experience in using this spreadsheet is that the iteration proceeds more efficiently if one simply guesses the value of the parameter and watches the value for the calculated mean velocity in cell E9. Making a series of successively more accurate guesses in cell B8 could be used to solve the problem for a new aspect ratio in just a few seconds. Furthermore it is fun to watch the iterations spin by ... 

Kays and associates (K2) have correlated their turbulent boundary layer data to produce the A+ correlation shown in Fig. 4. There Po is the stream ise pressure-gradient parameter... 

For similar flows, the pressure gradient parameter expressed as follows must be constant ... 

Pressure Gradient Parameter, n/1016-Pq, where Pq is the Minimum Pressure in mb... 

FIGURE 6 The cyclogensis classification (top panel) is based on the minimum pressure of winter storms in the Gulf of Mexico. The bottom panel shows the number of storms studied, the relationship between the pressure gradient parameter and the reported maximum winds, while the vertical bars are the standard deviations. [Reprinted with permission from Hsu, S. A. (1993). Mariners Weather Log 37(2), 4.]... 

Here, A=APRIi2mL R/V) is the dimensionless pressure gradient parameter, which may be positive or negative depending on whether the pressure gradient assists (cases la and Ila in Fig. 1) or opposes (cases Ib and Ilb in Fig. I) the drag of the moving cylinder. 

Some examples of calculated pressure gradients are shown in Figure 5.12 in which solids concentration is a parameter. Experimental points are given, with separate designations for each concentration band. The difference between experimental and predicted value does not generally exceed about 15 per cent. 

A general case of heat transfer under the conditions of combined action of electro-osmotic forces and imposed pressure gradient was considered by Chakra-borty (2006). The analysis showed that in this case the Nusselt number depends not only on parameters z and S, but also on an additional dimensionless group, which is a measure of the relative significance of the pressure gradient and osmotic forces. 

The solubility of the solute (in this case, quartz) is a function of both pressure and temperature. Pressure could be in theory be used as the controlling parameter rather than temperature. However, it is difficult to design an apparatus with a pressure gradient, whereas obtaining a temperature gradient is fairly easy. 

The pressure drop through packed columns, and the flooding conditions, can be estimated from the generalized correlation of Leva (1992), shown in Fig. 13-5. The pressure gradient in millimeters of water per meter of packed height is the parameter on the curves, and interpolation is usually necessary to determine the pressure drop (note that the pressure... 

Over the range of Martinelli parameter of practical importance (0.1 Martinelli-Nelson correlation predicts a frictional pressure gradient approximately twice that predicted by the homogeneous model. 

---