Consider a gas atmosphere with pressure distributionp(z)=p0(1−2πtan−1(z/H))" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space:...

Consider a gas atmosphere with pressure distributionp(z)=p0(1−2πtan−1(z/H))" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">p(z)=p0(1−2πtan−1(z/H))p(z)=p0(1−2πtan−1(z/H))

where z is the vertical coordinate and H is a constant length scale. Determine the vertical profile ofρ" role="presentation" style="display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ρρ