Question

What is the intensity of pressure in the following SI units, when specific gravity of mercury is 13.6 and the intensity of pressure is 400 KPa?
1. 0.3 bar or 4.077 m of water or 0.299 m of Hg
2. 4 bar or 5.077 m of water or 0.399 m of Hg
3. 0.3 bar or 5.077 m of water or 0.599 m of Hg
4. 4 bar or 40.77 m of water or 2.99 m of Hg

Answer 1

Correct Answer - Option 4 : 4 bar or 40.77 m of water or 2.99 m of Hg

Concept:

The intensity of pressure is given by P = ρ × g × h

Where, ρ = density of the fluid, and h = is the height of liquid column

1 bar = 10⁵ pa

Calculation:

Given, specific gravity of mercury = 13.6, Pressure = 400 KPa

So 400 KPa = 400 × 10³ Pa

\(400\;KPa = \frac{{\left( {400 \times {{10}^3}} \right)}}{{{{10}^5}}}\;bar = 4\;bar\)

Now pressure in terms of mercury column

∵ P = ρ × g × h

400 × 10³ = 13.6 × 1000 × 9.81 × h

\(h = \frac{{400}}{{13.6 \times 9.81}} = 2.99\;m\)

i.e. 2.99 m of Hg

Again Pressure in terms of water column

∵ P = ρgh

400 × 10³ = 1000 × 9.81 × h

h = \(\frac{{400}}{{9.81}} = 40.77\;m\)

i.e. 40.77 m of water