Consider the hydrodynamic flow of nitrogen at \(400 \mathrm{~K}\) through the porous diaphragm described in Example 1.24. It is desired to achieve a superficial gas velocity through the diaphragm of \(0.28 \mathrm{~kg}\) of \(\mathrm{N}_{2} / \mathrm{m}^{2} \cdot \mathrm{s}\) by increasing the upstream pressure while maintaining the downstream pressure constant at \(0.1 \mathrm{~atm}\). Calculate the upstream pressure required.

Data From Example 1.24:-

A porous carbon diaphragm 25.4 mm thick of average pore diameter 0.01 cm allowed the flow of nitrogen at the rate of 0.05 m³ (measured at 300 K and 1 atm)/m²-s with a pressure difference across the diaphragm of 500 Pa. The temperature was 300 K and the downstream pressure 0.1 atm. The viscosity of nitrogen at 300 K is 180 μP.

(a) Estimate the value of the viscous flow parameter, B0, for this solid.

(b) Calculate the nitrogen flow to be expected at 400 K with the same pressure
difference. At 400 K, the viscosity of nitrogen is 220 μP.