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2fluidStatics-print

# 2fluidStatics-print - Chap 2 Fluid Statics Considering...

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First Prev Next Last Go Back Full Screen Close Quit Chap 2 Fluid Statics Considering Newton’s second law, d ( mv ) dt = F The goal of this chapter: d ( mv ) dt = 0 Fluid statics Solid body acceleration (special case) Can be converted to statics by using a moving frame of reference No relative motion of adjacent fluid layers, Shear stresses are zero.

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First Prev Next Last Go Back Full Screen Close Quit 2.1 Force, Stress, Pressure at a Point 2.1.1 Body Force A body force creates its effect on the parcel by action through a distance (no contact is needed), such as electric-magnetic and gravity forces. Gravity force δ G = g δm = ρ g δV where, ρ g , is f V = lim δV 0 δ F δV body force intensity
First Prev Next Last Go Back Full Screen Close Quit 2.1.2 Surface Force A surface force exists by virtue of direct contact between fluid parcel.

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First Prev Next Last Go Back Full Screen Close Quit An equivalent system of resultant forces acting on the area of contact between the surrounding particle and the central particle
First Prev Next Last Go Back Full Screen Close Quit Consider one of the contact areas, say between parcels 1 and 6. Unit direction vectors s 1 , s 2 are tangent to the point of contact. s 1 , s 2 define a plane. And the unit normal ( n ) to the surface area is defined relative to the plane.

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First Prev Next Last Go Back Full Screen Close Quit Area is a vector quantity and the surface areas are rotating and changing with time, it is extremely difficult to keep track of the area vector. It is convenient to define an intensive representation called stress. normal stress σ n = lim A 0 Δ F n Δ A shear stress τ ss 1 = lim A 0 Δ F s 1 Δ A τ ss 2 = lim A 0 Δ F s 2 Δ A
First Prev Next Last Go Back Full Screen Close Quit Too many local coordinates s 1 , s 2 , n , Each local stress σ n , τ ss 1 , τ ss 2 is a vector. Global coordinates are more convenient. In ( x, y, z ) , three orthogonal plane, in each plane, three orthogonal components tensor. ¯ ¯ τ = σ xx σ yx σ zx τ xy σ yy σ zy τ xz τ yz σ zz First subscript: axis to which the action plane is perpendicular. Second subscript: stress component direction.

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First Prev Next Last Go Back Full Screen Close Quit Bulk Stress and pressure p = - ¯ σ = - 1 3 ( σ xx + σ yy + σ zz ) Positive normal stress is defined as positive away from the surface. Positive shear stress is defined by right-hand screw rule (xy gives +z, yx gives -z). Pressure is defined to be positive towards the center of mass of the surface it acts upon.
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2fluidStatics-print - Chap 2 Fluid Statics Considering...

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