Tuesday, June 1, 2010

Pascal’s Law

Let me give you some introduction on pascal's law

The French scientist Blaise Pascal observed that the pressure in a fluid at rest is the same at all points if they are at the same height. This fact may be demonstrated in a simple way.
Fig : Proof of Pascal’s law. ABC-DEF is an element of the interior of a fluid at rest. This element is in the form of a right angled prism. The element is small so that the effect of gravity can be ignored, but it has been enlarged for the sake of clarity.

Figure shows an element in the interior of a fluid at rest. This element ABC-DEF is in the
form of a right-angled prism. In principle, this prismatic element is very small so that every
part of it can be considered at the same depth from the liquid surface and therefore, the effect
of the gravity is the same at all these points. But for clarity we have enlarged this element.
The forces on this element are those exerted by the rest of the fluid and they must be normal to
the surfaces of the element as discussed above. Thus, the fluid exerts pressures Pa, Pb and Pc on
this element of area corresponding to the normal forces Fa, Fb and Fc as shown in Fig. 10.2 on the faces BEFC, ADFC and ADEB denoted by Aa, Ab and Ac respectively. Then Fb sinθ = Fc, Fb cosθ = Fa (by equilibrium)Ab sinθ = Ac, Ab cosθ = Aa (by geometry)
Thus,Hence, pressure exerted is same in all directions in a fluid at rest. It again reminds us that like other types of stress, pressure is not a vector quantity. No direction can be assigned
to it. The force against any area within (or bounding) a fluid at rest and under pressure is
normal to the area, regardless of the orientation of the area.

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