Chapter 2_sec.2.1_2.11

Chapter 2_sec.2.1_2.11 - Sections 2.1-2.11 Fluid Mechanics...

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Sec. 2.1-2.11 1 Sections 2.1-2.11 Fluid Mechanics EM 3313
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Sec. 2.1-2.11 2 What’s the Point? •Con te x t – In the previous chapter, we learned that fluids at rest must have zero shear stress. We called the nonzero normal stress the hydrostatic pressure. • Motivation – There are many problems of interest to engineers in which the fluid velocity is zero, e.g., atmospheric pressure distributions, manometers, forces on submerged surfaces, and buoyancy-related applications. • Learning objective – Demonstrate the ability to solve problems of fluid statics, using concepts of forces, moments and hydrostatic pressure
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Sec. 2.1-2.11 3 2.1 Pressure at a Point • Consider forces acting on wedge – fluid with no relative motion – Body force (gravity) – Surface forces only • No shear stresses () s z s y y s z y s y z s z z y s y y p p p p z y x y a p p y a p p a z y x z y x s x p y x p F a z y x s x p z x p F m = = + = = = = = = = 0 , , 2 2 2 2 cos 2 sin δδ δ γρ ρ γθ ρθ a F p is independent of direction θ . For fluid in motion, p is average of three values p is a normal stress
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Sec. 2.1-2.11 4 2.2 Basic Eq. Pressure Field • Pressure force on a fluid element – Consider forces acting on two opposing faces of a cube • Similar expressions for the other directions – The total net force due to pressure – The pressure force per unit volume due to the pressure gradient is – Pressure causes a net force on a fluid element when it varies spatially z y x y p z x y y p p z x y y p p F y δδ δ = + = 2 2 z y x p z y x z p y p x p p −∇ = + + = k j i F p z y x p −∇ = F
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Sec. 2.1-2.11 5 2.2 Basic Eq. Pressure Field (cont) • Gravity force • Applying N2L – equation of motion for a fluid with zero shear stress k k F z y x W g δ γδ = = a k a k a F F a F ργ δδ ρδ = = = + = p z y x z y x z y x p m m g p
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Sec. 2.1-2.11 6 2.3 Pressure Var. Fluid at Rest • Zero acceleration • Incompressible (constant density) () z p p
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This note was uploaded on 08/21/2008 for the course EM 3313 taught by Professor Thompson during the Spring '08 term at Mississippi State.

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Chapter 2_sec.2.1_2.11 - Sections 2.1-2.11 Fluid Mechanics...

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