While studying some texts on porous media, I came across the following statement: the flow is one-dimensional and incompressible, so has constant velocity.
Is it true always or did the author others suppositions that are not explicit?
Many thanks in advance for some clarification.
On
Maybe a bit more elaboration on the answer above. The continuity equation (conservation of mass) for incompressible flows is given by $$\nabla\cdot u = 0,$$ where $u$ is the fluid velocity. For the case of one dimensional flow, this boils down to $$\frac{\mathrm d u }{\mathrm dx}=0,$$ i.e., the fluid velocity is constant.
The answer provided by Matteo are all problems which have a dimensionality higher then 1. In real life one does not encounter truly one dimensional flows, your problem is a bit of an academic construct I think. If you would like a example which comes close, you could think of fully developed laminar flow trough a pipe with circular cross-section. The flow itself has a parabolic shape (Poiseuille flow, if you're familiar with this), but if you would look at the flow only at the centreline of the pipe, you would see that it is constant, and therefore the same at every position on the centreline.
I think also the flow has to pass through a pipe of constant measures. For example think about the river: here there are wirhlpool that change the velocity of water.