MadSci Network: Physics

Re: What do isobars look like in a hydrostatic medium(say a pool)?

Date: Wed Oct 25 13:50:55 2000
Posted By: Stephen Murray, Physicist
Area of science: Physics
ID: 971895066.Ph

Hi Giulio,

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

P + 0.5 * d * v2 + d*g*y = constant
In the above, P is the pressure of the fluid, d is the mass density, v is the speed with which the fluid is moving, g is the acceleration of gravity, and y is height above some, arbitrary, reference point.

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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