Dimensional Analysis
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Dimensional Equation
In the equation below x has a dimension of length and t has a dimension of time
\[
\begin{gather}
x=a\operatorname{e}^{-bt}\cos \left(\theta +b^{2}ct\right)
\end{gather}
\]
determine the dimensions of the quantities a, b, c, and θ.
The equation that describes the movement of a viscous fluid in one dimension is given by
\[
\begin{gather}
\rho \frac{dv}{dt}=-{\frac{dp}{dx}}+\eta \frac{d^{2}v}{cx^{2}}
\end{gather}
\]
where ρ is the density, v is the velocity, t is the time, p is the
pressure, and η is the viscosity. Determine the dimension of viscosity η.
During the presentation of a project on an acoustic system, a student forgot the expression of the
intensity of a sound wave. However, using intuition, he concluded that the average intensity (I) is a
function of the amplitude of the air movement (A), the frequency (f), the air density
(%rho;), and the speed of sound (c), obtaining at the expression
\( I=A^{x}.f^{y}.\rho ^{z}.c \).
Considering the fundamental quantities, mass, length, and time, find the values of the exponents x,
y, and z.
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Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .