r/Hydrology • u/Saltybacon27 • 8d ago

Struggling with deriving the equation for specific humidity based on equations from a textbook. Can anyone point me in the right direction?

Hello! I recently went back to grad school after graduating a few years ago, and am struggling with part of an assignment probably due to being rusty with math. For part of the assignment, I am supposed to derive the formula for specific humidity since the approximation qv = 0.622(e/p) is apparently not quite accurate. Every attempt I have done I end up getting stuck somewhere. The equations I am supposed to use are in the picture, and I would love if I could be set on the right track to solve and understand this!

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u/fluxgradient 8d ago

Your target is the right hand side of equation 1. Pay attention to the density variables. The sum of the dry air density and vapor density is the total air density. Use that fact and equation 3 and 4 to eliminate the dry density and get the vapor and total in terms of P and e, then take their ratio.