Repeat the previous problem without the assumption that the velocity in the heating section is negligible. The ratio of the flow area of the heating section to the chimney flow area is R.

Data From Problem 6.35

A fluid of density ρ₁ enters a chamber where the fluid is heated so that the density decreases to ρ₂ The fluid then escapes through a vertical chimney that has a height L. Neglecting friction and treating the flow processes as in-compressible except for the heating, determine the velocity, v, in the stack. The fluid velocity entering the heating chamber may be neglected, and the chimney is immersed in fluid of density ρ₁.

P2 P1 L2 Pi Heating section