Wall shear stress-flow characteristic curves and scale-up

4 Wall shear stress-flow characteristic curves and scale-up for laminar flow 

When data are available in the form of the flow rate-pressure gradient relationship obtained in a small diameter tube, direct scale-up for flow in larger pipes can be done. It is not necessary to determine the r-y curve with the true value of y calculated from the Rabinowitsch-Mooney equation (equation 3.20). 

Equation 3.17 shows that the flow characteristic is a unique function of the wall shear stress for a particular fluid  

In the case of a Newtonian fluid, substituting y = — -i//x in equation 3.17 and evaluating the integral gives 

Recall that the wall shear rate for a Newtonian fluid in laminar flow in a tube is equal to —8w/d,. In the case of a non-Newtonian fluid in laminar flow, the flow characteristic is no longer equal to the magnitude of the wall shear rate. However, the flow characteristic is still related uniquely to tw because the value of the integral, and hence the right hand side of equation 3.17, is determined by the value of tw. 

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