Determine if the following equation is dimensionally correct:
$v = \sqrt{\dfrac{P}{\rho}}$
where $h =$ height, $S =$ surface tension, $\rho =$ density, $P =$ pressure, $V =$ volume, $\eta =$ coefficient of viscosity, $\nu =$ frequency and $I =$ moment of inertia.

Question

Determine if the following equation is dimensionally correct:

v = \sqrt{\dfrac{P}{\rho}}

where

h =

height,

S =

surface tension,

\rho =

density,

P =

pressure,

V =

volume,

\eta =

coefficient of viscosity,

\nu =

frequency and

I =

moment of inertia.

Quantrex Academy · Accepted Answer

Correct answer: D. The equation is dimensionally correct.

The dimensions of the left-hand side (velocity,

v

) are:

[v] = [L T^{-1}]

The dimensions of the terms on the right-hand side are:
Pressure,

P = \dfrac{\text{Force}}{\text{Area}} = \dfrac{[M L T^{-2}]}{[L^2]} = [M L^{-1} T^{-2}]

Density,

\rho = \dfrac{\text{Mass}}{\text{Volume}} = \dfrac{[M]}{[L^3]} = [M L^{-3}]

Substituting these into the right-hand side expression:

\sqrt{\dfrac{P}{\rho}} = \sqrt{\dfrac{[M L^{-1} T^{-2}]}{[M L^{-3}]}} = \sqrt{[L^2 T^{-2}]} = [L T^{-1}]

Since the dimensions of the left-hand side are equal to the dimensions of the right-hand side, the equation is dimensionally correct.

Determine if the following equation is dimensionally correct: v =...