Pressure In Fluids

NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids) shows that the gauge pressure due to a column of liquid at depth $h$ is $P=\rho gh$, arising from the weight of the fluid above pressing down on the deeper layers. This is the pressure in excess of atmospheric pressure. Substituting $\rho =1000{\text{kg/m}}^3$, $g=10{\text{m/s}}^2$ and $h=20\text{m}$ gives $P=1000\times 10\times 20=2\times 10^5\text{Pa}$. The option $1\times 10^5$ uses half the depth. The option $2\times 10^6$ misplaces a power of ten. The option $4\times 10^5$ doubles the depth incorrectly. Note that this formula gives the gauge pressure, the excess over atmospheric pressure; the total or absolute pressure would add the atmospheric value of about $1\times 10^5\text{Pa}$ acting on the lake surface. As a plausibility check, this gauge pressure of about 2 atmospheres at 20 m matches the well-known rule that water pressure rises by roughly one atmosphere for every 10 m of depth, and the units of $\rho gh$, namely ${\text{kg/m}}^3\times {\text{m/s}}^2\times \text{m}$, correctly reduce to ${\text{N/m}}^2$ or pascals, confirming the result. This also explains why divers must equalise pressure as they descend.