Question 9.9: Non-Newtonian Fluid Flow A non-Newtonian fluid that can be ......
Non-Newtonian Fluid Flow
A non-Newtonian fluid that can be described by a power law model for which n is 0.2 and k is 5 (kPa s)^n is to be pumped through a pipe of length 10 m and inside diameter of 20 mm. Determine the radius required for another pipe of 20 m in length to carry the fluid at the same rate with the same pressure drop.
The rate of flow for the non-Newtonian fluid is given by the generalised Equation 9.34:
{\dot{Q}}={\frac{\pi n}{3n+1}}{\left({\frac{\Delta p}{2k L}}\right)}^{\frac{1}{n}}{R^{\frac{3n+1}{n}}} (9.36)
For the two pipes with the same pressure drop and flow rate, it follows that
\frac{R_1^{\frac{3n+1}{n} }}{L_1^{\frac{1}{n} }} =\frac{R_2^{\frac{3n+1}{n} }}{L_2^{\frac{1}{n} }} (9.37)
The new pipe radius is therefore
R_{2}=R_{1}\left({\frac{L_{2}}{L_{1}}}\right)^{\frac{1}{3n+1}}=0.01\times\left({\frac{20}{10}}\right)^{\frac{1}{1.6}}=0.015\,\mathrm{m} (9.38)
that is, a required inside pipe diameter of 30 mm.