A 4 meter tall reactor vessel contains a bubbly solution of ethyl alcohol and hy

Question

A 4 meter tall reactor vessel contains a bubbly solution of ethyl alcohol and hydrogen gas at moderate pressure. The small gas bubbles slowly expand as the bubbles rise toward the top of the reactor. Assume the fraction of the volume occupied by the bubbles varies linearly from 10% at the bottom to 50% at the top. The hydrogen bubbles are small and move slowly enough to be considered static. The hydrogen gas density is negligible. Surface tension is negligible. The process is not isothermal. Given: At the top location (0): p_0 = 50 kPa, gauge. Find the gauge pressure at the center & the bottom, p_1 = & p_2 (kPa) Plot the pressure variation vs elevation (p as a function of z): p(z) vs z

Explanation / Answer

gauge pressure inversely proportional to the radius or the area of bubble

when the bubble was at bottom position it has less radius so max gauge pressure

so, gauge pressure at bottom is = 5x50kPa = 250kPa [ 5 times because the area was 5 times less]

and similarly at centre = 3x50 = 150kPa [remember 4 meter tall, we can figure out five point from top to bottom as 50kpa, 100kpa, 150kpa,200 kpa, 250kPa]

and P vs Z will be staright line [but decreasing]

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