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# Lecture 7

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### Lecture 7

1. 1. Lecture 7 Fluid Mechanics II Muhammad Usman
2. 2. Venturimeter
3. 3. To calculate Discharge
4. 4. External Flows Past Bodies <ul><li>Applications </li></ul><ul><li>AERODYNAMICS </li></ul><ul><li>AUTOMOTIVES (CARS, TRUCKS, BICYCLES) </li></ul><ul><li>SUBMIRINES </li></ul>
5. 5. Wind tunnel Testing Shape of the body affects the flow characteristics
6. 6. Newton’s Law of Resistance <ul><li>The force exerted by a moving fluid on an immersed body is directly proportional to the rate of change of momentum due to the presence of the body. </li></ul><ul><li>Assumptions of this Law </li></ul><ul><li>The planes of the body are completely smooth. </li></ul><ul><li>The space around the body is completely filled with fluid. </li></ul><ul><li>The fluid has a large number of fine particles having mass but no diemension. </li></ul><ul><li>The fluid particles do not exert any influence on one another. </li></ul><ul><li>The body experiences impacts from all the particles in its path. </li></ul>
7. 7. Drag <ul><li>A fluid flowing past the surface of a body exerts a surface force on it. </li></ul><ul><li>Drag is the component of this surface force parallel to the flow direction. </li></ul>
8. 8. Lift <ul><li>Lift is the component of this force that is perpendicular to the oncoming flow direction. </li></ul><ul><li>Wall shear stress contribute little to the lift, most of the lift come from the surface pressure distribution. </li></ul><ul><li>Surface roughness is unimportant in terms of lift. </li></ul><ul><li>It denpends considerably on the shape of the body. </li></ul>
9. 9. Reynold’s Number <ul><li>It is the ratio of the inertia force on an element of fluid to the viscous force on an element. </li></ul><ul><li>Viscosity is measure of resistance to flow. </li></ul><ul><li>Most familiar flows are with high reynold’s number values. </li></ul>
10. 10. Boundry Layer <ul><li>A small rectangle particle begin to distort within the boundry layer because of velocity gradient with in the boundry layer. </li></ul><ul><li>At some distance from the boundry layer the flow changes to turbulent. </li></ul>
11. 11. Boundry Layer Thickness <ul><li>The thickness of the velocity boundary layer is normally defined as the distance from the solid body to a place where the velocity of flow is 99% of the freestream velocity (the surface velocity of an inviscid flow). </li></ul>
12. 12. Boundry Layer Velocity
13. 13. Boundry layer Parts
14. 14. Transition State <ul><li>Transition takes place at a distance x from the leading edge for flat plate is given by. </li></ul><ul><li>Re= 2 * 10 5 TO Re= 3 * 10 6 </li></ul>
15. 15. Pressure Gradient around the Boundry Layer
16. 16. Magnus Effect in a moving liquid <ul><li>The phenomenon of deviating the stream lines by rotating cylinder is known as magnus effect. </li></ul>
17. 17. Example 1 <ul><li>Air flowing into a 2-ft square duct with a uniform velocity of 10 ft/s forms a boundry layer as shown in the figure. The fluid with in the core region (outside the boundry layers) flows as if it were inviscid. From advanced calculations it is determined that for this flow the boundary layer displacement thickness is given by </li></ul><ul><li>s= 0.0070(x) 1/2 </li></ul><ul><li>Where x and s are in feet. Determine the velocity U=U(x) of the air within the duct but outside of the boundary layer. </li></ul>
18. 18. Example 2 <ul><li>A man weighting 750 N descends to the ground from an aeroplane with the help of a parachute against the resistance of air. The shape of the parachute is hemispherical of 2m diameter. Find the velocity of the parachute with which it comes down. Take specific weight of the air as 12 N/m 3 . </li></ul>
19. 19. Example 3 <ul><li>A truck having projected area of 6.5 square meters travelling at 72 km/hr has a total resistance of 1.6 kN. Out of this resistance 30 percent is due to rolling friction and 20 % is due to surface friction. The rest is due to drag. Calculate the coefficient of drag. Assume specific weight of air as 12 N/m 3 . </li></ul>
20. 20. Example 4 <ul><li>A flat plate 1.5m *1.5m moves at 45 km/hour in stationary air of specific weight 11.3 N/m3. If the coefficient of drag and lift are 0.15 and 0.75 respectively, Find </li></ul><ul><li>Lift force </li></ul><ul><li>Drag force </li></ul><ul><li>Resultant force </li></ul><ul><li>Power required to keep the plate in motion. </li></ul>
21. 21. Drag <ul><li>Friction Drag </li></ul><ul><li>Friction Drag is the function of wall shear stress and orientation of the surface. </li></ul><ul><li>Precise determination of shear stress along the surface of curved body is quite difficult. </li></ul><ul><li>Pressure Drag </li></ul><ul><li>Pressure drag is the fuction of magnitude of pressure and orientation of the surface element on which the pressure force acts. </li></ul>