- #1
e(ho0n3
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Let's say there is a U-shaped tube, both ends of the tube open, filled with some fluid. The fluid is still because the atmospheric pressure pushing on both openings of the tube are the same.
Suppose the column of fluid, when streched into a straight-tube, measures x. Given any cross-section of the fluid in the tube, the pressure on it measures 0. Let's look at this in detail:
Consider a cross-section of fluid at some distance h below the surface of the fluid. The pressure on one side of the fluid is
[tex]P_0 + \rho h g[/tex]
where [itex]P_0[/itex] is the atmospheric pressure and [itex]\rho[/itex] is the density of the fluid. The pressure on the other side is
[tex]P_0 + \rho (x - h) g[/tex]
Since the pressure on both sides are equal, equating the two equations above yields h = x - h. This, of course, is only possible if the cross-section is in the middle of the tube (h = x/2). Hmm...did I miss something here?
Suppose the column of fluid, when streched into a straight-tube, measures x. Given any cross-section of the fluid in the tube, the pressure on it measures 0. Let's look at this in detail:
Consider a cross-section of fluid at some distance h below the surface of the fluid. The pressure on one side of the fluid is
[tex]P_0 + \rho h g[/tex]
where [itex]P_0[/itex] is the atmospheric pressure and [itex]\rho[/itex] is the density of the fluid. The pressure on the other side is
[tex]P_0 + \rho (x - h) g[/tex]
Since the pressure on both sides are equal, equating the two equations above yields h = x - h. This, of course, is only possible if the cross-section is in the middle of the tube (h = x/2). Hmm...did I miss something here?