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