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ObjectiveDiscuss the application of Newton’s second law to fluid flows.Explain the development, uses, and limitations of the Bernoulli equation.Use the Bernoulli equation (stand-alone or in combination with the continuity equation) to solve simple flow problems.Apply the concepts of static, stagnation, dynamic, and total pressures.11/5/2012
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Newton’s Second Law As a fluid particle moves from one location to another, it usually experiences an acceleration or deceleration. According to Newton’s second law of motion, the net force acting on the fluid particle under consideration must equal its mass times its acceleration F ma11/5/2012
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Bernoulli Equation 1 p V2 z constant along streamline 2 Apply Bernoulli Equ between two points 1 2 1 2 p1 V1 z1 p2 V2 z2 2 2 This is the celebrated Bernoulli equation—a very powerful tool in fluid mechanics. In 1738. To use it correctly we must constantly remember the basic assumptions used in its derivation: 1. Viscous effects are assumed negligible 2. The flow is assumed to be steady 3. The flow is assumed to be incompressible 4. The equation is applicable along a streamline.11/5/2012
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Bernoulli Equation Example 1 Consider the flow of air around a bicyclist moving through still air with velocity as is shown in Fig. Determine the difference in the pressure between points 1 and 2. 1 2 1 2 p1 V1 z1 p2 V2 z2 2 2 1 sloution : p2 p1 V1211/5/2012 2
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Bernoulli EquationExample 2 A stream of water of diameter d =0.1 m flows steadily from a tank of diameter D=1.0 m as shown in Fig. Determine the flowrate, Q, needed from the inflow pipe if the water depth remains constant, h = 2.0 m.11/5/2012
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Bernoulli EquationExample 3 Air flows steadily from a tank, through a hose of diameter D = 0.03 m and exits to the atmosphere from a nozzle of diameter d = 0.01 m as shown in Fig. The pressure in the tank remains constant at 3.0 kPa (gage) and the atmospheric conditions are standard temperature and pressure. Determine the flowrate and the pressure in the hose. T1=15o11/5/2012
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Bernoulli Equation • Example 4 Water is flowing from a hose attached to a water main at 400 kPa gage (Fig. below). A child places his thumb to cover most of the hose outlet, causing a thin jet of of high speed water as can be seen from Fig. If the hose held upward what is the maxmuinm height that the jet could achieve?11/5/2012
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