Question

If the gauge pressure at the bottom of a water tank is $2.7\text{kPa}$, then what is the depth of the water in the tank?
[Take $g=10{\text{m/s}}^2$]

• A. $0.27\text{cm}$
• B. $2.7\text{cm}$
• C. $27\text{cm}$
• D. $270\text{cm}$

Answer 1

The correct option is C $27\text{cm}$

We know that,
Guage pressure= Absolute pressure-Atmospheric pressure
Let, atmospheric pressure be $P_o$ and height of water in the tank is $h$.

Now, absolute pressure at bottom of the tank $=P_o+\rho gh$
So, Guage pressure $=P_o+\rho gh-P_o=\rho gh$
Therefore,
$2.7\times {10}^3=1000\times 10\times h$
[$\because \rho =1000{\text{kg/m}}^3$ for water]
$\Rightarrow h=0.27\text{m}=27\text{cm}$