Question

(i) Calculate the height of a water column which will exert on its base the same
Pressure as the 70 cm column of mercury.
(ii) Will the height of the water column change if the cross-section of the water column is made wider?

Answer 1

(i) we know pressure exerted by a liquid column of height h, density p is P = h x px g.
The pressure exerted by a mercury column of height 70 cm.
Density of mercury = 13.6 g/cc = 1.36 x 10⁴kg/m³.
P_mercury = 0.7 x 1.36 x 10⁴ x 9.8 = 9.32 x 10⁴ Nm^-2.

Let the height of the water column = hm.
Density of water = 1g/cc = 10³ kg/m³.
P_water = h x 10³ x 9.8 = 9.8h x 103 Nm^-2,
Now put P_mercury = P_water
9.8 h x 10³ = 9.32 x 10⁴

h = 93.2/9.8 = 9.52 m.

So, 9.52 m height of water column would exert the same pressure on its base as 70 cm column of mercury.

(ii) The height of the water column would not change if the cross-section of the water column is made wider.