Question

Pressure gradient has the same dimensions as that of

• A. velocity gradient
• B. potential gradient
• C. energy gradient
• D. None of these

Answer 1

Answer: (D)

Pressure gradient = $\frac{△p}{△x}=\frac{N/m^2}{m}$
$\therefore Dimensionsof\left(\frac{△p}{△x}\right)=\frac{[ML{T}^{-2}]/[L^2]}{[L]}$
= $[M{L}^{-2}{T}^{-2}]$
Dimension of velocity gradient
= $[-\frac{△v}{△x}]=\frac{m/s}{m}=\frac{[L{T}^{-1}]}{[l]}$
= $[M^0{L}^0{T}^{-1}]$
Dimensions of potential gradient
= $(-\frac{△V}{△x})=\frac{△W/Q}{△x}$
= $\frac{[ML{T}^{-2}][L]}{[AT][L]}$
= $[ML{T}^{-3}{A}^{-1}]$b
Energy gradient = $\frac{△E}{△x}=\frac{Nm}{m}$
$\therefore$ Dimensions of $\left(\frac{△p}{△x}\right)=\frac{[ML{T}^{-2}]/[L]}{[L]}$
= $[ML{T}^{-2}]$
As observed from above results, we see that none of the dimensions are same as of pressure gradient.