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Unformatted text preview: Chapter 15 Flow Over Bodies: Drag and Lift 15-1 Chapter 15 FLOW OVER BODIES: DRAG AND LIFT Drag, Lift, and Drag Coefficients of Common Geometries 15-1C The flow over a body is said to be two-dimensional when the body is too long and of constant cross- section, and the flow is normal to the body (such as the wind blowing over a long pipe perpendicular to its axis). There is no significant flow along the axis of the body. The flow along a body that possesses symmetry along an axis in the flow direction is said to be axisymmetric (such as a bullet piercing through air). Flow over a body that cannot be modeled as two-dimensional or axisymmetric is three-dimensional . The flow over a car is three-dimensional. 15-2C The velocity of the fluid relative to the immersed solid body sufficiently far away from a body is called the free-stream velocity , V . The upstream (or approach ) velocity V is the velocity of the approaching fluid far ahead of the body. These two velocities are equal if the flow is uniform and the body is small relative to the scale of the free-stream flow. 15-3C A body is said to be streamlined if a conscious effort is made to align its shape with the anticipated streamlines in the flow. Otherwise, a body tends to block the flow, and is said to be blunt . A tennis ball is a blunt body (unless the velocity is very low and we have creeping flow). 15-4C The formation of vapor cavities in regions of low pressure in liquid flow is called cavitation . It occurs at locations such as the constrictions in a valve or the tips of impeller blades where the pressure drops below vapor pressure due to high velocities. We try to avoid cavitation since it reduces performance, generates annoying vibrations and noise, and causes erosion, surface pitting, fatigue failure, and the eventual destruction of the components or machinery. 15-5C The force a flowing fluid exerts on a body in the flow direction is called drag . Drag is caused by friction between the fluid and the solid surface, and the pressure difference between the front and back of the body. We try to minimize drag in order to reduce fuel consumption in vehicles, improve safety and durability of structures subjected to high winds, and to reduce noise and vibration. 15-6C The force a flowing fluid exerts on a body in the normal direction to flow that tend to move the body in that direction is called lift . It is caused by the components of the pressure and wall shear forces in the normal direction to flow. The wall shear also contributes to lift (unless the body is very slim), but its contribution is usually small. 15-7C When the drag force F D , the upstream velocity V , and the fluid density are measured during flow over a body, the drag coefficient can be determined from A F C D D 2 2 1 V r = where A is ordinarily the frontal area (the area projected on a plane normal to the direction of flow) of the body. Chapter 15 Flow Over Bodies: Drag and Lift 15-2 15-8C When the lift force...
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