FLUID PRESSURE AT A POINT

FLUID PRESSURE AT A POINT :
1) No pressure change in horizontal direction for fluid at rest. 2) Pressure in vertical direction is proportional to density, gravity and depth. Since θ was arbitrary, implies pressure at a point in a static fluid is independent of orientation.
or
]Consider a fluid at rest as shown in Fig. 2.2. From around the point of interest, P in the fluid let us pull out a small wedge of dimensions dx x dz x ds . Let the depth normal to the plane of paper be b. In some of the derivations we chose z to be the vertical coordinate. This is consistent with the use of z as the elevation or height in many applications involving atmosphere or an ocean. Let us now mark the surface and body forces acting upon the wedge.

The surface forces acting on the three faces of the wedge are due to the pressures, $ p_x$, $ p_z$ and $ p_n$ as shown. These forces are normal to the surface upon which they act. We follow the usual convention that compression pressure is positive in sign. We again remind ourselves that since the fluid is at rest there is no shear force acting. In addition we have a body force, the weight, W of the fluid within the wedge acting vertically downwards.

Summing the horizontal and the vertical forces we have,

$\displaystyle \Sigma F_x$ $\displaystyle =0;~ \texttt{ie.}, p_x ~ dz~b ~-~ p_n ~ b ~ ds ~ sin
\theta = 0$
$\displaystyle \Sigma F_z$ $\displaystyle =0;~ \texttt{ie.}, p_z ~ dx~b ~-~ p_n ~ b
~ ds ~ cos \theta~-~W ~~= ~~0$
$\displaystyle \texttt{i.e.,}$ $\displaystyle = p_z ~ dx~b ~-~ p_n ~ b ~ ds ~ cos \theta~-~{1 \over 2} \rho~g
~b ~dx~ dz ~~= ~~0$ (2.1)
know more about fluid pressure at apoint at :
https://www.youtube.com/watch?v=MPYZFemB-Go

https://www.youtube.com/watch?v=l-HAqS51Zgc

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