A polymer solution is to be pumped at a rate of $3 \mathrm{gpm}$ through a horizontal $1 \mathrm{in}$. diameter pipe. The solution behaves as a power law fluid with a flow index of 0.5 , an apparent viscosity of $400 \mathrm{cP}$ at a shear rate of $1 \mathrm{~s}^{-1}$, and a density of $60 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$.

(a) What is the pressure gradient in $\mathrm{psi} / \mathrm{ft}$ ?

(b) What is the shear rate at the pipe wall and the apparent viscosity of the fluid at this shear rate?

(c) If the fluid were Newtonian, with a viscosity equal to the apparent viscosity from (b) above, what would the pressure gradient be?

(d) Calculate the Reynolds numbers for the polymer solution and for the above Newtonian fluid.