Lecture 6
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The document discusses concepts related to fluid mechanics including: 1) Two examples of centrifugal pump problems calculating speed, vane angle, and work done per KN of water given pump specifications like diameters and flow velocities. 2) Two problems calculating work done per KN of water for centrifugal pumps operating at given speeds and with given diameters and flow velocities. 3) Discussions of concepts like Newton's law of resistance, lift and drag forces on objects in fluid flow, Reynolds number, boundary layers, and boundary layer thickness.
Lecture 6
- 1. Lecture 6 Fluid Mechanics II Muhammad Usman
- 2. Example 1 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 Speed of impeller in r.p.m. Work done per KN of water
- 3. Example 2 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.
- 4. Problem 1 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.
- 5. Problem 2 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 Vane angle at inlet Work done per kN of water.
- 6. Newton’s Law of Resistance 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.
- 7. Assumptions for the Law The planes of the body are completely smooth. The space around the body is completely filled with fluid. The fluid has a large number of fine particles having mass but no diemension. The fluid particles do not exert any influence on one another. The body experiences impacts from all the particles in its path.
- 8. Lift and Drag A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. Drag is the component of this surface force parallel to the flow direction.
- 9. Reynold’s Number It is the ratio of the inertia force on an element of fluid to the viscous force on an element. Viscosity is measure of resistance to flow. Most familiar flows are with high reynold’s number values.
- 10. Boundry Layer A small rectangle particle begin to distort within the boundry layer because of velocity gradient with in the boundry layer. At some distance from the boundry layer the flow changes to turbulent.
- 11. Boundry Layer Thickness 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).