Tomato catsup with 10 Pa sn consistency coefficient and 0.8 flow behaviour index is flowing in a pipe. Generalized coefficient of viscosity of catsup, in Pa sn is
GATE AG - 2012,
Answer: B
The generalized coefficient of viscosity is 6.93 Pa sn.
For pipe flow of a power-law fluid the Metzner-Reed approach first converts the consistency coefficient K into the pipe-flow coefficient K', then forms the generalized viscosity \(\gamma = K' 8^{\,n-1}\) that appears in the generalized Reynolds number:
\[ \begin{aligned} K' &= K\left(\frac{3n+1}{4n}\right)^{n} \\ &= 10\left(\frac{3.4}{3.2}\right)^{0.8} = 10.50 \\ \gamma &= K' 8^{\,n-1} \\ &= 10.50 \times 8^{-0.2} \\ &= 10.50 \times 0.660 = 6.93 \end{aligned} \]
Stopping at K' gives 10.5, which is not offered; the other options do not follow from K = 10 and n = 0.8 by these relations.
Please log in or register to report this question.