We can extend Prob. 5.18 to the case of laminar duct flow of a non-Newtonian fluid, for which the simplest relation for stress versus strain-rate is the power-law approximation:
r = c (dθ / dt)n
This is the analog of Eq. (1.23). The constant C takes the place of viscosity. If the exponent n is less than (greater than) unity, the material simulates a pseudo plastic (dilatant) fluid, as illustrated in Fig. 1.7. (a) Using the {MLT} system, determine the dimensions of C. (b) The analog of Prob. 5.18 for Power-law laminar triangular-duct flow is Q = fcn(C, Δp/L, b). Rewrite this function in the form of dimensionless Pi groups.