Determine if the following equation is dimensionally correct:
$V = \dfrac{\pi P r^4 t}{8 \eta l}$
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 = \dfrac{\pi P r^4 t}{8 \eta l}

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: C. The equation is dimensionally correct.

The dimensions of the terms are evaluated as follows:

[V] = [L^3]

[P] = [M L^{-1} T^{-2}]

[r] = [L]

[t] = [T]

[\eta] = [M L^{-1} T^{-1}]

[l] = [L]

Substituting these dimensions into the right hand side of the given equation:

\dfrac{[M L^{-1} T^{-2}] [L^4] [T]}{[M L^{-1} T^{-1}] [L]} = \dfrac{[M L^3 T^{-1}]}{[M L^0 T^{-1}]} = [L^3]

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

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