Calculation of flow rate-pressure drop relationship for

3 Calculation of flow rate-pressure drop relationship for laminar flow using r-y data 

If the T-y relationship can be accurately represented by a simple algebraic expression, such as the power law, over the required range then this may be used to substitute for y in equation 3.17, allowing the integral to be evaluated analytically. Both these methods are illustrated in Example 3.2. 

Using the viscometric data given in Table 3.3 calculate the average velocity for the material flowing through a pipe of diameter 37 mm when the pressure gradient is 1.1 kPa/m. 

Note that the above table gives absolute values of y and r. 

It is necessary to evaluate the integral from r = 0 to t = 10.18 Pa. This can be done by calculating r2y for each of the values given in the table and plotting r2 against t. The area under the curve between r = 0 and t = 10.18 Pa can then be measured. An alternative, which will be used here, is to use a numerical method such as Simpson s rule. This requires values at equal intervals of r. 

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