Pressure in Fluids and Atmospheric Pressure — Question 5

(a) As we know,

Pressure due to water column of height h = hρg

and

Pascal's law, states that the pressure exerted anywhere in a confined liquid is transmitted equally and undiminished in all directions throughout the liquid.

Hence,

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 = $\dfrac{\text h_\text m \text ρ_\text m}{\text ρ_\text w}$

Substituting the values, we get,

$\text h_\text w = (\dfrac{13.6}{1}) \times 70 \\[0.5em] \Rightarrow \text h_\text w = 952\ \text{cm} \\[0.5em] \Rightarrow \text h_\text w = 9.52\ \text{m} \\[0.5em]$

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.