ch14 - Chapter 14 Fluids In this chapter we will explore...

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Chapter 14 Fluids In this chapter we will explore the behavior of fluids. In particular we will study the following: Static fluids: Pressure exerted by a static fluid Methods of measuring pressure Pascal’s principle Archimedes’ principle, buoyancy Real versus ideal Fluids in motion: fluids Equation of continuity Bernoulli’s equation (14 - 1)
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As the name implies a fluid is defined as a substance that can flow. Fluids conform to the boundaries of any container in which they are placed. A fluid cannot exert a force tangential to its Fluids. surface. It can only exert a force perpendicular to its surface. Liquids and gases are classified together as fluids to contrast them from solids. In crystalline solids the constituent atoms are organized in a rigid three dimensional regular array known as the "lattice". Density: Consider the fluid shown in the figure. It has a mass and volume . The density (symbol ) is defined as the ratio of m V ρ 3 the mass over the volume. If the fluid is homogeneous the above equati SI unit on has : k the fo / : g rm m m V m V = = Δ m Δ V m V = (14 - 2)
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Consider the device shown in the insert of the figure which is immersed in a fluid filled vessel. The device can measure the normal force exerted on its piston from the compression of the spr F Pressure 2 ing attached to the piston. We assume that the piston has an area . The pressure exerted by the f N The SI unit luid on the for pressure is is known as the pasca pisto is defin l m ed ( as: A p F p A = 2 5 2 symbol: Pa). Other units are the atmosphere (atm), the torr, and the lb/in . The atm is defined as the average pressure of the atmosphere at sea level 1 atm = 1.01 10 Pa = 760 Torr = 14.7 lb/in Expe × rimentally it is found that the pressure p at any point inside the fluid has the same value regardless of the orientation of the cylinder. The assumption is made that the fluid is at rest. F p A = (14 - 3)
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1 2 Consider the tank shown in the figure. It contains a fluid of density at rest. We will determine the pressure difference between point 2 and point 1 whose y-coordinates are a p p y ρ - Fluids at rest 1 nd , respectively. Consider a part of the fluid in the form of a cylinder indicated by the dashed lines in the figure. This is our "system" and its is at equilibrium. The equilibrium condition is: y 2 1 2 1 1 1 2 2 1 0 Here and are the forces exerted by the rest of the fluid on the bottom and top faces of the cylinder, respectively. Each face has an area . , , ynet F F F mg F F A F p A F p A m V A y = - - = = = = = - ( 29 ( 29 ( 29 ( 29 2 2 1 1 2 2 1 1 2 1 2 1 2 If we substitute into the equilibrium conditon we get: 0 If we take 0 and then and The equation above takes the form: o o y p A p A gA y y p p g y y y h y p p p p p p gh - - - = - = - = = - = = = + o p p gh = + ( 29 ( 29 2 1 1 2 p p g y " o p p - Note : gauge pressure
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ch14 - Chapter 14 Fluids In this chapter we will explore...

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