Question

If the atmospheric pressure on the surface of an oil tank (sp. gr. 0.8) is $ 0.1 \, \text{kg/cm}^2 $, the pressure at a depth of $ 2.5 \, \text{m} $, is

• A. 1 metre of water
• B. 2 metres of water
• C. 3 metres of water
• D. 3.5 metres of water

Hint:

To convert pressure from one fluid to another, use specific gravity: $$ h_{\text{water = h_{\text{fluid \times \text{Sp. Gr. $$

Answer 1

The Correct Option is C

Step 1: Use hydrostatic pressure formula.
Total pressure at a depth $ h $ in a fluid: $$ P = P_{\text{atm}} + \rho g h $$ Given:
Atmospheric pressure $ P_{\text{atm}} = 0.1 \, \text{kg/cm}^2 $
Specific gravity of oil = 0.8 → $ \rho = 0.8 \times 1000 = 800 \, \text{kg/m}^3 $
Depth $ h = 2.5 \, \text{m} $
$ g = 9.81 \, \text{m/s}^2 $
Convert atmospheric pressure to head of water:
$$ 1 \, \text{kg/cm}^2 = 10 \, \text{metres of water} \Rightarrow 0.1 \, \text{kg/cm}^2 = 1 \, \text{metre of water} $$ Now compute pressure due to oil: $$ \text{Head due to oil} = \frac{\rho_{\text{oil}}}{\rho_{\text{water}}} \times h = 0.8 \times 2.5 = 2 \, \text{metres of water} $$ Total pressure head: $$ P_{\text{total}} = 1 + 2 = 3 \, \text{metres of water} $$
Step 2: Select the correct option.
The pressure at 2.5 m depth is equivalent to: $$ \boxed{3 \, \text{metres of water}} $$