# Distance times Velocity

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.

• In units this can be transformed to [mechanical-power/acceleration] = $m^2/s$ – user78217 Feb 15 '17 at 16:37

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 $\mathrm{m^2/s}$.

• 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. – JMac Feb 15 '17 at 21:26
• @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. – jkej Feb 15 '17 at 23:12

Angular momentum for a unit mass. Angular momentum is: $$L= r × (mv)$$

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.