I am confused about the some of the concepts behind fluid statics. Here is an example to illustrate this, using Pascal's barrel experiment.(adsbygoogle = window.adsbygoogle || []).push({});

Consider a cylindrical barrel with cross-sectional areaAand heightH. Now insert a straw of heighthand cross-sectional areaaso that the total of height of the barrel and straw ish + H. Assuming a fluid of uniform densityρ, the total weight of the fluid is

[tex] W = m_{tot}g = \rho V g = \rho g (ha + HA)[/tex]

If the barrel is sitting on a plank, then the magnitude of the normal forceNof the plank on the barrel is simplyN = W.

However, using a different method, I come up with a different result forN. By Pascal's equation, the gauge pressure at the bottom of the tank is

[tex] P_{bottom} = \rho g (h + H) [/tex]

Thus the force due to pressure acting on the bottom of the barrel is

[tex] F_P = P_{bottom}A = \rho g A (h + H) [/tex]

In order to balance this force, the normal forceNfrom the plank on the barrel must thus be equal toF, yet this is a different result then from before:_{P}N = W ≠ F._{P}= N

There must be some error in my reasoning here, but I cannot find it. Thanks a bunch for the help!

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# Fluid statics with Pascal's barrel

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