# Rational Psychrometric Formulae/Appendix No. 1

Rational Psychrometric Formulae by Willis H. Carrier
Appendix No. 1

APPENDIX No. 1

PROOF OF FORMULA [1]

${\displaystyle {\text{Per cent humidity}}={\frac {e_{1}}{e'_{2}}}={\frac {D_{2}}{D'_{2}}}}$

71In this formula ${\displaystyle e_{1}}$ is the pressure of saturated vapor corresponding to the dew point ${\displaystyle T_{1}}$, and ${\displaystyle e'_{2}}$ is the vapor pressure at saturation corresponding to temperature ${\displaystyle T_{2}}$. It also follows that

${\displaystyle D_{2}=D'_{2}\times {\frac {e_{1}}{e'_{2}}}}$

At constant pressure

[30]

${\displaystyle {\frac {D_{2}}{D_{1}}}={\frac {T_{1}}{T'_{2}}}}$, or ${\displaystyle D_{2}={\frac {D_{1}T_{1}}{T_{2}}}}$

Also if it is assumed ${\displaystyle {\frac {pv}{T}}}$ is constant, i.e., ${\displaystyle {\frac {e}{DT}}}$ is constant for saturated water vapor (not exactly correct),

${\displaystyle {\frac {e_{1}}{D_{1}T_{1}}}={\frac {e'_{2}}{D'_{2}t_{2}}}}$

Therefore

[31]

${\displaystyle {\frac {e_{1}}{e'_{2}}}={\frac {D_{1}T_{1}}{D'_{2}t_{2}}}}$

But substituting ${\displaystyle D_{2}}$ for its value in [30]

${\displaystyle {\frac {e_{1}}{e'_{2}}}={\frac {D_{2}}{D'_{2}}}={\text{per cent of isothermal saturation}}}$