Chapter%202%20Stresses

# Chapter%202%20Stresses - Fluid Mechanics II Stress in a...

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Fluid Mechanics II. Stress in a Fluid 2.1 Surface Forces and Body Forces * Imaging a surface S separating some part of the fluid: F -F Fig. 2.1 Imaginary surface S separating the body of fluid S The portion of the fluid close to the surface on its two sides exerts forces F & -F on each other -- action & reactions -- Newton’s 3 rd law of motion. They are internal forces . Since they act across a surface that is imagined to separate the fluid, they are also called surface forces . * Body forces are those that act through the WHOLE BODY of the fluid without physical contact. They are proportional to the volume or mass of the fluid, such as gravitational force and electromagnetic force. 1

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2.2 Concept of Stress and the State of Stress at a Point * Consider a plane surface S n drawn through some point p in a fluid with a normal n . There are a resultant force F and moment M acting on S n . n F M S p Fig. 2.2 Force F and moment M on a surface S n at a point op. n The stress at p across S n is defined as σ n = n S F . (2.1) In orthogonal coordinates (x 1 , x 2 , x 3 ), the stress σ n can be written in various forms as σ n = σ n1 e 1 + σ n2 e 2 + σ n3 e 3 = ( σ n1 , σ n2 , σ n3 ) = σ nj e j (2.2) where e j is the unit vector in the x j -direction. * In many applications of interest, the stress components parallel and normal to a given surface S n are desired. Thus σ n is a written as, σ n = σ nm e n + σ nt e t + σ ns e s (2.3) e n = the unit vector of n , e t , e s = two mutually perpendicular unit vectors on S n that are normal to n , 2
σ nm = normal tensile stress on S n along the direction of n . σ

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Chapter%202%20Stresses - Fluid Mechanics II Stress in a...

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