Pressure In Fluids

Question

A diver descends to a depth of 20 m below the surface of a lake where water density is 1000 kg/m³; what is the gauge pressure exerted by the water column at that depth? (Take g = 10 m/s²)

RankGuru · Accepted Answer

NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids) shows that the gauge pressure due to a column of liquid at depth $h$ is $P = ho g h$, arising from the weight of the fluid above pressing down on the deeper layers. This is the pressure in excess of atmospheric pressure. Substituting $ho = 1000\ 	ext{kg/m}^3$, $g = 10\ 	ext{m/s}^2$ and $h = 20\ 	ext{m}$ gives $P = 1000 	imes 10 	imes 20 = 2 	imes 10^5\ 	ext{Pa}$. The option $1 	imes 10^5$ uses half the depth. The option $2 	imes 10^6$ misplaces a power of ten. The option $4 	imes 10^5$ 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 $1 	imes 10^5\ 	ext{Pa}$ 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 $ho g h$, namely $	ext{kg/m}^3 	imes 	ext{m/s}^2 	imes 	ext{m}$, correctly reduce to $	ext{N/m}^2$ or pascals, confirming the result. This also explains why divers must equalise pressure as they descend.

Pressure In Fluids

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