Chp3_331

Chp3_331 - FLUID STATICS 3 Hydrostatics 3.1 Hydrostatic...

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FLUID STATICS 3. Hydrostatics 3.1. Hydrostatic pressure Fluid mechanics is the study of fluid in motion. special case: NO motion at all. Fluid statics - determine the stress field. * The force/stress on any given surface immersed in a fluid at rest , is always perpendicular (normal) to the surface. Recall that by definition, a fluid moves and deforms when subjected to shear stress and, conversely, a fluid that is static (at rest) is not subjected to any shear stress. Otherwise it'll move τ σ * At any given point in a fluid at rest, the normal stress is the same in all directions (hydrostatic pressure) 9
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Proof : Consider a small, wedged-shaped fluid element. Fluid is in equilibrium, so F = 0 Let the element be sufficiently small so that we can assume that the stress is constant on any surface (uniformly distributed). F 1 = 1 A 1 ; F 2 = 2 A 2 ; F 3 = 3 A 3 m =   V - fluid density ; V = 1 / 2 x y z - element volume Look at the side view F x = 0 F 1 cos - F 2 = 0 1 A 1 cos - 2 A 2 = 0 1 y( z/cos  cos - 2 y z = 0 1 = 2 10
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F z = 0 F 1 sin + m . g = F 3 1 A 1 sin + V g = 3 A 3 1 ( x /sin  y sin + 1 / 2 g x y z = 3 x y 1 + 1 / 2 g z = 3 Shrink the element down to an infinitesimal point, so that z 0, then 1 = 3 1 = 2 = 3 Notes : Normal stress at any point in a fluid in equilibrium is the same in all directions. This stress is called hydrostatic pressure. Pressure has units of force per unit area. F = PA [N/m 2 ] The objective is to find the stress field in a given body of fluid, namely to find the pressure at any point in a fluid at rest. 11
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3.2. Vertical distribution of pressure Look at a large tank of liquid Take a small element of fluid in a convenient shape Force balance: (P+dP) A + g A dy = P A dP/dy = - g Negative sign indicates that P decreases as y increases. For a constant density fluid, we can integrate for
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This note was uploaded on 09/08/2010 for the course AME 331 taught by Professor Zohar during the Fall '08 term at Arizona.

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Chp3_331 - FLUID STATICS 3 Hydrostatics 3.1 Hydrostatic...

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