Question

1. Calculate the height of a water column which will exert on its base the same pressure as the 70 cm column of mercury. Density of mercury is 13.6 g cm^-3.
2. Will the height of the water column in part (a) change if the cross-section of the water column is made wider?

Answer 1

(a) As we know,

Pressure due to water column of height h = hρg 

Pressure due to water column = Pressure due to mercury column

Hence, h_w ρ_w g = h_m ρ_m g

Given, h_m = 70 cm, ρ_m = 13.6 g cm^-3, ρ_w = 1 g cm^-3 

From the above formula, we get,

h_w = `("h"_"m" rho_"m")/rho_"m"`

Substituting the values, we get,

h_w = `(70 xx 13.6)/1`

h_w = 952 cm

∴ h_w = `952/100` = 9.52 m

Hence, height of a water column = 9.52 m

(b) No, if the cross-section of the water column is made wider, the height of the water column will be unaffected.