Taking a car for example. Can I say that since the cross sectional area for air flow above the car is larger than that below it, the velocity of the air above is higher than the air below? Or would that be an invalid application of the continuity equation because the flow of air ahead of the car separates into 2 flows (one above the car and one below it)?
1 Answer
$\begingroup$
$\endgroup$
The only assumption in the full continuity equation is that the flow is a continuum; that is, that the mean free path of the individual molecules is much smaller than the "smallest significant characteristic dimension of the problem" (Fox and McDonald). Continuity is just a statement of conservation of mass, so as long as you're accounting for the same fluid in your continuum you can apply continuity no matter how many times or places the flow splits.
Flow over a car is really no different than flow in pipes that branch out to go over and under it. However, in this case, the "pipes" have surfaces bounded by streamlines instead of by some physical barrier. You'd need to select these streamtubes carefully to get meaningful results, because you want the average properties across the tubes to be representative of the flow within them. For complicated flow problems such as this, CFD or experiment is used when the accuracy of results is important.
