I need a concise definition of a fluid flux and an accompanying example. I've never taken a single physics course before, but I'm required to understand this concept so I can do the calculations for a Complex Analysis class.


The flux through a surface is the amount of fluid that crosses the surface in a flow per unit time at any one instant. If the velocity field is $v(x)$, and the surface is S, it is the integral over the surface

$$\int_S v \cdot n $$

where n is the normal to the surface. This is the general definition of flux of a vector field, applied to the special case of the velocity field.


Suppose the velocity field is

$$ v_x = \omega y $$ $$ v_y = - \omega x $$ $$ v_z = 0 $$

This is the fluid rigidly rotating with angular frequency $\omega$. Suppose you want the flux through the surface defined by $0<x<L$, $0<z<L$ at $y=0$ at the instant the fluid has this velocity profile. This has a normal in the y-direction, so the integral is of the y-component of the velocity over the surface:

$$ \int_0^L \int_0^L -x dx dz = L\int_0^L x dx = - L^2 {\omega L\over 2}$$

  • $\begingroup$ I just want to mention Gauss (divergence) theorem here. Which for close surface $S$ convert in a volume integral. $\endgroup$ – Bernhard Apr 28 '12 at 7:18

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.