|MadSci Network: Physics|
For uniform flow, the thing to look at is Bernoulli's equation. A
fairly good introduction to this can be found in "Fundamentals of Physics,"
by Halliday, Resnick, and Walker. It's in chapter 15 of the 5th edition.
In essence, for steady flow of an incompressible fluid, the quantity
For a pool of uniform depth, moving with uniform speed, v is the same everywhere. The isobars therefore must be horizontal, as changes in the quantity d*g*y are balanced by changes in P.
If the pool has a non-uniform depth, however, the situation changes. Say that the fluid is moving left or right. With a non-uniform depth, the fluid speed must change (assuming steady flow). The pressure will also change from left to right, so as to keep the same value of Bernoulli's constant, and so the isobars will no longer be horizontal, and will curve in a way that depends upon the shape of the pool.
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