Question

The density of mercury changes approximately linearly with temperature as

ρ_Hg = 13595 − 2.5 T kg/ m³ T in Celsius

so the same pressure difference will result in a manometer reading that is influenced by temperature. If a pressure difference of 100 kPa is measured in the summer at 35°C and in the winter at −15°C, what is the difference in column height between the two measurements? 

Answer 1

The manometer reading h relates to the pressure difference as

∆P = ρ L g ⇒ L = ∆P/ρg

The manometer fluid density from the given formula gives

ρ_su = 13595 − 2.5 × 35 = 13507.5 kg/m³

ρ_w = 13595 − 2.5 × (−15) = 13632.5 kg/m³

The two different heights that we will measure become