Module-6_Fluid-Dynamics111112222333.pptx

Fluid Dynamics

1. Fluids in Motion How does blood flow dislodge plaque from an artery? Why can a strong wind cause the roof to blow off a house? Why do people snore? © 2014 Pearson Education, Inc.

2. Fluids moving across surfaces: Qualitative analysis How does air blowing over the top of a beach ball lift and support the ball? We must compare the forces that stationary air exerts on a surface to the forces exerted on the surface by moving air. We can deduce the direction of the net force due to air pressure exerted on different sides of the ball. © 2014 Pearson Education, Inc.

3. Observational experiment © 2014 Pearson Education, Inc.

4. Observational experiment © 2014 Pearson Education, Inc.

5. Testing experiments © 2014 Pearson Education, Inc.

6. Testing experiments © 2014 Pearson Education, Inc.

7. Bernoulli ' s principle Bernoulli ' s principle has many important applications, including fluid-flow implications in biological systems such as blood through blood vessels. © 2014 Pearson Education, Inc.

8. Snoring A snoring sound occurs when air moving through the narrow opening above the soft palate at the back of the roof of the mouth has lower pressure than nonmoving air below the palate. The normal air pressure below the soft palate, where the air is not moving, pushes the palate closed. When airflow stops, the pressures equalize and the passage reopens. © 2014 Pearson Education, Inc.

9. Flow rate and fluid speed Flow rate is defined as the volume V of fluid that moves through a cross section of a pipe divided by the time interval Δ t during which it moved: The SI unit of flow rate is m 3 /s. © 2014 Pearson Education, Inc.

10. Relationship between flow rate and speed of the moving fluid The darkened volume of fluid passes a cross section of area A along the pipe. The back part of this fluid volume has, in effect, moved forward to this position. The fluid flow rate is: This leads to: © 2014 Pearson Education, Inc.

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12. Continuity equation The flow rate past cross section 1 will equal that past cross section 2. v 1 is the average speed of the fluid passing cross section A 1 and v 2 is the average speed of the fluid passing cross section A 2 . © 2014 Pearson Education, Inc.

13. Causes and types of fluid flow Fluid flow is caused by differences in pressure. When the pressure in one region of the fluid is lower than the pressure in another region, the fluid tends to flow from the higher-pressure region toward the lower-pressure region. For example, large masses of air in Earth ' s atmosphere move from regions of high pressure into regions of low pressure. © 2014 Pearson Education, Inc.

14. Streamline flow and turbulent flow Streamline flow: Every particle of fluid that passes a particular point follows the same path as particles that preceded it. Turbulent flow: Characterized by agitated, disorderly motion. © 2014 Pearson Education, Inc.

15. Bernoulli ' s equation Bernoulli ' s equation is the quantitative version of Bernoulli ' s principle: © 2014 Pearson Education, Inc.

16. Bernoulli ' s equation © 2014 Pearson Education, Inc.

17. Using Bernoulli bar charts to understand fluid flow © 2014 Pearson Education, Inc.

18. Viscous fluid flow Previously, we assumed that fluids flow without friction. We assumed no interaction either between the fluid and the walls of the pipes it flows in, or between the layers of the fluid. This assumption is not reasonable in many processes. When we cannot neglect this friction inside the fluid, we call the fluid " viscous. " © 2014 Pearson Education, Inc.

19. Factors that affect fluid flow rate Pressure difference: How hard the fluid is pushed forward. Radius r of the tube: It is more difficult to push fluid through a tube of tiny radius. Length of the tube: A long tube offers more resistance to flow. Fluid type: Some property of a fluid that characterizes its "thickness" or "stickiness" should affect the flow. © 2014 Pearson Education, Inc.

20. Factors that affect fluid flow rate A pump that produces an adjustable pressure, thereby causing fluid to flow through tubes of different radii and lengths, allows us to test parameters that affect fluid flow rate. © 2014 Pearson Education, Inc.

21. Viscosity If we use the same pressure difference to push different fluids through the same tube, we find that the fluids have different flow rates. Water flows faster than oil; oil flows faster than molasses. The quantity that measures this effect on flow rate is called the viscosity of the fluid. Flow rate is proportional to viscosity. © 2014 Pearson Education, Inc.

22. Poiseuille ' s law The pressure difference is related to the resistance of the fluid to the flow and to the net push on the fluid related to the flow rate Q . © 2014 Pearson Education, Inc.

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24. Viscosities of some liquids and gases © 2014 Pearson Education, Inc.

25. Limitations of Poiseuille ' s law: Reynolds number © 2014 Pearson Education, Inc.

26. Blowing the roof off a house Roofs can be blown from houses during tornadoes or hurricanes. How does that happen? On a windy day, the air inside the house is not moving, whereas the air outside the house is moving very rapidly. The air pressure inside the house is greater than the air pressure outside, creating a net pressure against the roof and windows that pushes outward. © 2014 Pearson Education, Inc.

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28. Dislodging plaque The physical principles of a roof being lifted from a house also explain how plaque can become dislodged from the inner wall of an artery. The plaque may block a considerable portion of the area where blood normally flows. The kinetic energy density is much greater in the constricted area. This pressure differential could cause the plaque to be pulled off the wall and tumble downstream, causing a blood clot. © 2014 Pearson Education, Inc.

29. Example 11.7 Blood flows through the unobstructed part of a blood vessel at a speed of 0.50 m/s. The blood then flows past a plaque that constricts the cross-sectional area to one-ninth the normal value. The surface area of the plaque parallel to the direction of blood flow is about 0.60 cm 2 = 6.0 x 10 –5 m 2 . Estimate the net force that the fluid exerts on the plaque. © 2014 Pearson Education, Inc.

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31. Measuring blood pressure The air is slowly released from the cuff, decreasing the pressure. When the pressure in the cuff is equal to the systolic pressure, blood starts to squeeze through the artery past the cuff. The flow is intermittent and turbulent and causes a sound heard with the stethoscope. When the pressure decreases to less than the diastolic pressure, the artery is continually open and blood flow is laminar and makes no sound. © 2014 Pearson Education, Inc.

32. Drag force Now we focus on solid objects moving through a fluid. Examples: a swimmer moving through water, a skydiver falling through the air, and a car traveling through air The fluid in these and in other cases exerts a resistive drag force on the object moving through the fluid. So far we have been neglecting this force in our mechanics problems. © 2014 Pearson Education, Inc.

33. Laminar drag force and Stokes ' s law If an object moves relatively slowly through a fluid, the water flows around the object in streamline laminar flow, with no turbulence. However, the fluid does exert a drag force on the object. The equation expressing this relationship is called Stokes ' s law: © 2014 Pearson Education, Inc.

34. Reynolds number An equation can be used to decide whether the flow of a fluid past an object is laminar or turbulent: If the Reynolds number is more than 1, the flow is turbulent and we cannot use Stokes ' s law. In the case of turbulent flow, we use this equation: © 2014 Pearson Education, Inc.

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