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PHYSICS-IC Another common unit used for pressure is atm (atmosphere) which is approximately equal to air pressure at sea level. 1 atm = 101.325 kPa and the dimensions, [PJ= M'LT If the card used is very small so that we can neglect the difference in depth of the fluid over the surface and if the fluid is in static condition, F is independent of orientation of the surface at the same location.This observation is made by Pascal. In a static fluid, pressure at a point is unique and is same in all the directions at that point. From this statement, we can conclude that pressure in a static fluid is a scalar PAsure is always quantity. Force due to pressure is always perpendicular to the surface of contact, Force due to tormal to the Variation of Pressure in a static fluid antact surface Let us consider a container filled with water. Density of water can be taken as uniform through out the container.Let A and B be two points inside the water located at the same level. Consider a thin fluid element located between A and B as shown in the Fig. 2.2(a). Now, let us apply Newton's law of motion to the clements. It is clear that the acceleration of the clement is zero. From the surrounding fluid, the net vertical fluid contact force must balance its weigght. PS' and PS' act on the element as shown; where 'S' is the area of cross- section of the clement. As the net horizontal force on the element is also zero, P,S = P,S or P, =P, Therefore, when the fluid is at rest, the points Fig. 2.2(a) located on the same horizontal level and within a given fluid, must have equal pressures. Now, let us take A & B on a veitical line as shown. Separation between A&B is h'. Again, consider a thin water clement located between A&B and apply Newton's B law of motion to it Fig. 2.3(n) The vertical pressure forces 1P,S' and 'PS must balance the weight of the element. where, m-Shp Fig. 2.2(b) PS+ mg- PS (or) P,S+ (Shpg - PS : P = P, + hpg The above expression can also be written as pressure gradient P-P. Pg, or in dp =P8= constant. (p density assumed to be constant) differential form dh In other words, when density is constant, pressure increases linearly with depu Fig. 2.3(b) Now, let h, & h, be the depths of A and B from the free surface. Then, applying the above relation, P- P, +hpg and P=P, +hpg where P, is atmospheric pressure. The pressure difference between hydrostaric pressure and atmosphenic pressut is called gauge-pressure, Fig. 2.3(c) gauge pressure a P-P-hpg 44 ELITE SERIES for Sri Chaltanya Jr. ICON Stude