Question

The pressure gradient's dimensions are

• A. ${\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}$
• B. ${\mathrm{ML}}^2{\mathrm{T}}^{-1}$
• C. ${\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}$
• D. ${\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}$

Answer 1

The correct option is A

${\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}$

1. The pressure gradient is denoted as $\frac{\mathrm{dp}}{\mathrm{dx}}$.
2. Pressure = force/ area , which has dimension as $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$.
3. $\mathrm{x}$ denotes the length, therefore, it has dimensions as $\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]$.
4. Pressure Gradient = $\frac{\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]}=\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}\right]$.

Therefore, Option A is the correct answer.