A non-Newtonian fluid, described by the power law model, is flowing through a thin slit between two parallel planes of width W, separated by a distance H. The slit is inclined upward at an angle to...

A non-Newtonian fluid, described by the power law model, is flowing through a thin slit between two parallel planes of width W, separated by a distance H. The slit is inclined upward at an angle to the horizontal.

(a) Derive an equation relating the volumetric flow rate of this fluid to the pressure gradient, slit dimensions, and fluid properties.

(b) For a Newtonian fluid, this solution can be written in dimensionless form as

                             f ¼ 24=NRe;h

where the Reynolds number, NRe;h, is based upon the hydraulic diameter of the channel. Arrange your solution for the power law fluid in dimensionless form, and solve for the friction factor, f.

(c) Set your result from (b) equal to 24=NRe;h and determine an equivalent expression for the power law Reynolds number for slit flow.