B Can the same formula be used for both water and mercury manometers?

[AmirWG]

if we use a water manometer we get the pressure of the gas in manometer by using this forumla :
P_gas = P_atmosphere ± ρgh
and if we use the a mercury manometer we use this formula instead :
P_gas = P_atmosphere ± h
and here's my question :
why cannot we use the first formula in both of them , realistically we can get the same results if use the first formula in case of mercury manometer

 

[Nugatory]

They're the same formula, because the numerical value of the quantity $\rho{g}$ depends on our choice of units. If we choose to report the pressure in units of "inches of mercury" and use mercury as the working fluid, $\rho{g}$ is equal to one and we have the second formula.