First approximation design methods:Empirical relationships

Empirical relationships

It will be seen from Equations (18.4) to (18.6) that, for a given material and pipeline, there are only a limited number of variables relating the main conveying parameters. Of these the conveying air temperature will be known and either the material flow rate required, pipeline bore to be used, or conveying line pressure drop available will be specified. This means that there are only four variables in these equations.

It will be possible to provide solutions to Equations (18.4)–(18.6), therefore, if two further relationships can be provided. These will, by necessity, be empirical, and so the accuracy of any expressions developed will depend upon the accuracy of the empirical relationships used.

Conveying line inlet air velocity

The conveying line inlet air velocity, C1, to be employed is a value that should be known with a high degree of certainty. The value depends very much upon the material to be conveyed, although for dilute phase conveying it will be in a fairly narrow range of val- ues, and is generally expressed in terms of the minimum value of conveying air velocity for the material.

For dilute phase conveying the minimum value of conveying air velocity, Cmin, will almost certainly be above 10 m/s. For cement and similar materials it is about 10–11 m/s, and for fine fly ash and similar materials it is about 11–12 m/s. For granular alumina it

First approximation design methods-0359

is about 13–14 m/s and for granulated sugar approximately 16 m/s, the value depend- ing mainly upon mean particle size, particle shape and particle size distribution.

Design would generally be based on a conveying line inlet air velocity, C1, 20 per cent greater than the minimum conveying air velocity:

First approximation design methods-0360

Solids loading ratio

An approximate relationship between pressure drop and solids loading ratio, for dilute phase conveying, is presented in Figure 18.1. This is an alternative way of plotting test data for a material, such as that presented in Figure 11.6, but is rarely done because it is of limited use. The relationship is based upon the assumption that the curves on Figure 18.1 are equi-spaced with respect to conveying line pressure drop. When con- veying test data is plotted in this manner it is surprising how many materials approxi- mate to this relationship in dilute phase flow. A mathematical expression for this is:

First approximation design methods-0361

where !lpc is the conveying line pressure drop (kN/m2) and !lpa, the air only pressure drop (kN/m2).

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