Solution

Since we need the Q — (—Ap) relation to solve this problem, such a relationship will be first derived using the generalised approach outlined in Section 3.2.4. For laminar flow in circular pipes, the Ellis fluid model is given as:

Substituting equation (3.24) into equation (3.21) followed by integration and rearrangement gives:

Note that in the limit of ti/2 ! 1, i.e. for Newtonian fluid behaviour, this equation reduces to the Hagen-Poiseuille equation. Now substituting the numerical values:

A trial and error procedure gives rw = 3412 Pa

i.e. the pressure drop across the pipe will be 5.46 MPa.

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