Question
Define pressure. State its SI and CGS units and dimensions.
✓
Answer
Definition : The pressure at a point in a fluid in hydrostatic equilibrium is defined as the normal force per unit area exerted by the fluid on a surface of infinitesimal area containing the point.
Thus, the pressure, $\mathrm{p}=\lim _{\Delta A \rightarrow 0} \frac{F}{\Delta A}$
where $\mathrm{F}$ is the magnitude of the normal force on a surface of area $\Delta \mathrm{A}$. The pressure is defined to be a scalar quantity.
SI unit: the pascal (Pa), $1 \mathrm{~Pa}=1 \mathrm{~N} \cdot \mathrm{m}^{-2}$
CGS unit: the dyne per square centimetre $\left(\mathrm{dyn} / \mathrm{cm}^2\right)$
Dimensions : $[\mathrm{p}]=[\mathrm{F}]\left[\mathrm{A}^{-1}\right]=\left[\mathrm{MLT}^{-2}, \mathrm{~L}^{-2}\right]$
$=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
Thus, the pressure, $\mathrm{p}=\lim _{\Delta A \rightarrow 0} \frac{F}{\Delta A}$
where $\mathrm{F}$ is the magnitude of the normal force on a surface of area $\Delta \mathrm{A}$. The pressure is defined to be a scalar quantity.
SI unit: the pascal (Pa), $1 \mathrm{~Pa}=1 \mathrm{~N} \cdot \mathrm{m}^{-2}$
CGS unit: the dyne per square centimetre $\left(\mathrm{dyn} / \mathrm{cm}^2\right)$
Dimensions : $[\mathrm{p}]=[\mathrm{F}]\left[\mathrm{A}^{-1}\right]=\left[\mathrm{MLT}^{-2}, \mathrm{~L}^{-2}\right]$
$=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$
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