Is there a meaningful physical concept of $distance * velocity$?
Came across something analogous in computer science and was wondering if there was any physical analogue.
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$\begingroup$ In units this can be transformed to [mechanical-power/acceleration] = $m^2/s$ $\endgroup$– user78217Feb 15, 2017 at 16:37
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3 Answers
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In diffusion equations, the diffusion coefficient typically has a dimensionality of $\mathrm{L^2T^{-1}}$.
For instance, the heat equation is typically written in this form:
$$ \frac{\partial u}{\partial t}-\alpha\nabla u=0, $$
where $u$ is temperature and $\alpha$ is the thermal diffusivity. The thermal diffusivity is defined as:
$$ \alpha=\frac{k}{\rho c_p}, $$
where $k$ is the thermal conductivity of the medium, $\rho$ is the mass density and $c_p$ is the specific heat capacity. The SI unit of thermal diffusivity is $\mathrm{m^2/s}$.
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$\begingroup$ Although this does have the dimensionality of $distance*time$ you didn't really explain if there's an actual physical analogue. You gave a dimensional analogue, I don't see that as the same thing. Your answer doesn't seem to address distance or time specifically. $\endgroup$– JMacFeb 15, 2017 at 21:26
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$\begingroup$ @JMac I sort of see your point (although I think you mean $distance*velocity$). I think there is a "physical analogue" in the sense you mean, but it may seem a little contrived. We also only know that OP wants an analogue to a quantity that is a distance multiplied with a velocity. We don't know what the distance or the velocity represent or why it's meaningful to multiply them. Without more information I think there isn't much point in going further than dimension analysis to check for analogousness. $\endgroup$– jkejFeb 15, 2017 at 23:12
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Angular momentum for a unit mass. Angular momentum is: $$ L= r × (mv) $$
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This could also be thought of as an "area speed" (in lack of a better word). For instance if you are painting a wall and $d$ is the width of your brush, and $v$ is the speed you are moving the brush with, the area you would cover per unit time would be $d\cdot v$. I wouldn't say that this is a commonly used physical quantity though.