Equipment Design and Optimization - Plant Design and Economics - Chemical Engineering Previous Year Questions

Minimum input required to calculate the ‘blank diameter’ for a torispherical head is

The total cost (C_T) of an equipment in terms of the operating variables x and y is
\[ C_T = 2x + \frac{12000}{xy} + y + 5 \]
The optimal value of C_T, rounded to 1 decimal place, is ______.

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_pump = 48.13 q² μ / D⁴
The annual cost of the installed piping system per unit length of pipe is given by
C_piping = 45.92D
Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m³ s⁻¹ and μ is the viscosity of the liquid in Pa.s.
If the viscosity of the liquid is 20 × 10⁻³ Pa.s and the volumetric flow rate of the liquid is 10⁻³ m³ s⁻¹, the economic inner diameter of the pipe is _______ meter (round off to 3 decimal places).