A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given by
\[
C_{\text{pump}} = \frac{48.13 q^2 \mu}{D^4}
\]
The annual cost of the installed piping system per unit length of pipe is given by
\[
C_{\text{piping}} = 45.92 D
\]
Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m\(^3\)s\(^{-1}\) and \(\mu\) is the viscosity of the liquid in Pa.s. If the viscosity of the liquid is \(20 \times 10^{-3}\) Pa.s and the volumetric flow rate of the liquid is \(10^{-4}\) m\(^3\)s\(^{-1}\), the economic inner diameter of the pipe is \(\underline{\hspace{1cm}}\) meter (round off to 3 decimal places).
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Correct Answer: 0.014
Solution and Explanation
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