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# Lecture 6

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### Lecture 6

1. 1. Lecture 6 Fluid Mechanics II Muhammad Usman
2. 2. Example 1 <ul><li>A centrifugal pump has external and internal impeller diameters as 600 mm and 300 mm respectively. The vane angle at inlet and outlet are 30° and 45°respectively. The water enters the impeller at 2.5 m/s, the velocity of flow is constant through the impeller is constant. Find </li></ul><ul><li>Speed of impeller in r.p.m. </li></ul><ul><li>Work done per KN of water </li></ul>
3. 3. Example 2 <ul><li>Calculate vane angle at the inlet of a centrifugal pump impeller having 200 mm diameteer at inlet and 400 mm diameter at outlet. The impeller vanes are set back at angle of 45° to the outer rim, and the entry of the pump is radial. The pump runs at 1000 r.p.m and velocity of flow through the impeller is constant at 3 m/s. Also calculate the work done per kN of water and the velocity as well as direction of the water at outlet. </li></ul>
4. 4. Problem 1 <ul><li>A centrifugal pump has external and internal diameters of 300 mm and 150 mm respectively. The vane angles of inlet and outlet are 30° and 25° respectively and the pump runs at 1450 r.p.m. If the velocity of flow through the pump is constant, find the work done per kN of water. </li></ul>
5. 5. Problem 2 <ul><li>A centrifugal pump having external and internal diameters as 750 mm and 400 mm respectively is operating at 1000 r.p.m. The vanes are curved back at 35° to the tangent at outlet. If the velocity of flow is constant at 6 m/s, find </li></ul><ul><li>Vane angle at inlet </li></ul><ul><li>Work done per kN of water. </li></ul>
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>
7. 7. Assumptions for the Law <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>
8. 8. Lift and Drag <ul><li>A fluid flowing past the surface of a body exerts a surface force on it. </li></ul><ul><li>Lift is the component of this force that is perpendicular to the oncoming flow direction. </li></ul><ul><li>Drag is the component of this surface force parallel to the flow direction. </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 at which the viscous flow velocity is 99% of the freestream velocity (the surface velocity of an inviscid flow). </li></ul>