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16-September-2008 16:15:17 - Drag physics Redirected from Air resistance An object moving through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. Shown is a sphere in Stokes flow, at very low Reynolds number. An object moving through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. Shown is a sphere in Stokes flow, at very low Reynolds number. In fluid dynamics, drag sometimes called fluid resistance is the force that resists the movement of a solid object through a fluid a liquid or gas. The most familiar form of drag is made up of friction forces, which act parallel to the object's surface, plus pressure forces, which act in a direction perpendicular to the object's surface. For a solid object moving through a fluid, the drag is the component of the net aerodynamic or hydrodynamic force acting in the direction of the movement. The component perpendicular to this direction is considered lift. Therefore drag acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust. In astrodynamics, depending on the situation, atmospheric drag can be regarded as inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit. Types of drag are generally divided into three categories: parasitic drag, lift-induced drag, and wave drag. Parasitic drag includes form drag, skin friction, and interference drag. Lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or planing hulls. Wave drag occurs when a solid object is moving through a fluid at or near the speed of sound in that fluid. The overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation. Assuming a constant drag coefficient, drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid mass density, the cross sectional area of the specified item, and the square of the velocity. Wind resistance is a layman's term used to describe drag. Its use is often vague, and is usually used in a relative sense e.g., A badminton shuttlecock has more wind resistance than a squash ball. Contents 1 Stokes' drag 2 Drag at high velocity 2.1 Power 2.2 Velocity of falling object 2.3 Transonic and supersonic drag 3 See also 4 References 4.1 Inline 4.2 General 5 External links Stokes' drag The equation for viscous resistance or linear drag is appropriate for small objects or particles moving through a fluid at relatively slow speeds where there is no turbulence i.e. low Reynolds number, Re 1.1 In this case, the force of drag is approximately proportional to velocity, but opposite in direction. 1 The equation for viscous resistance is: \mathbfF_d = - b \mathbfv \, where: \mathbf b is a constant that depends on the properties of the fluid and the dimensions of the object, and \mathbfv is the velocity of the object. When an object falls from rest, its velocity will be vt = \frac\rho-\rho_0Vgb\left1-e^-bt/m\right which asymptotically approaches the terminal velocity \mathbf v_t = \frac\rho-\rho_0Vgb . For a given \mathbf b , heavier objects fall faster. For the special case of small spherical objects moving slowly through a viscous fluid and thus at small Reynolds number, George Gabriel Stokes derived an expression for the drag constant, b = 6 \pi \eta r\, where: \mathbf r is the Stokes radius of the particle, and \mathbf \eta is the fluid viscosity. For example, consider a small sphere with radius \mathbf r = 0.5 micrometre diameter = 1.0 µm moving through water at a velocity \mathbf v of 10 µm/s. Using 10-3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water. Drag at high velocity Main article: Drag equation The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity i.e. high Reynolds number, R_e ~1000 , also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L^2 \ in place of A \ L\, being some length. The force on a moving object due to a fluid is: \mathbfF_d= -1 \over 2 \rho v^2 A C_d \mathbf\hat v see derivation where \mathbfF_d is the force of drag, \mathbf \rho is the density of the fluid Note that for the Earth's atmosphere, the density can be found using the barometric formula. It is 1.293 kg/m3 at 0 °C and 1 atmosphere., \mathbf v is the speed of the object relative to the fluid, \mathbf A is the reference area, \mathbf C_d is the drag coefficient a dimensionless constant, e.g. 0.25 to 0.45 for a car, and \mathbf\hat v is the unit vector indicating the direction of the velocity the negative sign indicating the drag is opposite to that of velocity. The reference area A is related to, but not exactly equal to, the area of the projection of the object on a plane perpendicular to the direction of motion i.e., cross sectional area. Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given. The reference for a wing would be the plane area rather than the frontal area. Power The power required to overcome the aerodynamic drag is given by: P_d = \mathbfF_d \cdot \mathbfv = 1 \over 2 \rho v^3 A C_d Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph 80 km/h may require only 10 horsepower 7.5 kW to overcome air drag, but that same car at 100 mph 160 km/h requires 80 hp 60 kW. With a doubling of speed the drag force quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work resulting in displacement over a fixed distance is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power. It should be emphasized here that the drag equation is an approximation, and does not necessarily give a close approximation in every instance. Thus one should be careful when making assumptions using these equations. Velocity of falling object Main article: Terminal velocity The velocity as a function of time for an object falling through a non-dense medium is roughly given by a function involving a hyperbolic tangent: vt = \sqrt \frac2mg\rho A C_d \tanh \leftt \sqrt\fracg \rho C_d A2 m \right \, In other words, velocity asymptotically approaches a maximum value called the terminal velocity: v_t = \sqrt \frac2mg\rho A C_d \, For a potato-shaped object of average diameter d and of density Ï?obj terminal velocity is about v_t = \sqrt gd \frac \rho_obj \rho \, For objects of water-like density raindrops, hail, live objects - animals, birds, insects, etc. falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to v_t = 90 \sqrt d, For example, for human body \mathbf d ~ 0.6 m \mathbf v_t ~ 70 m/s, for a small animal like a cat \mathbf d ~ 0.2 m \mathbf v_t ~ 40 m/s, for a small bird \mathbf d ~ 0.05 m \mathbf v_t ~ 20 m/s, for an insect \mathbf d ~ 0.01 m \mathbf v_t ~ 9 m/s, for a fog droplet \mathbf d ~ 0.0001 m \mathbf v_t ~ 0.9 m/s, for a pollen or bacteria \mathbf d ~ 0.00001 m \mathbf v_t ~ 0.3 m/s and so on. Actual terminal velocity for very small objects pollen, etc is even smaller due to the viscosity of air. Terminal velocity is higher for larger creatures, and thus more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This explains why small animals can fall from a large height and not be harmed. Transonic and supersonic drag The general form of the high speed equation applies fairly well even at speeds approaching or exceeding the speed of sound, however, the Cd factor varies with speed, in a way dependent on the nature of the object. In general, above Mach 0.85 the drag coefficient climbs to a value several times higher at Mach 1.0, and then comes down again at higher speeds, tending to a value perhaps 30% higher than that at subsonic speeds. This is due to the creation of shockwaves which generates wave drag. See also Added mass Aerodynamic force Angle of attack Boundary layer Coandă effect Drag coefficient Drag-resistant aerospike Gravity drag Keulegan-Carpenter number Parasitic drag Ram pressure Reynolds number Stall flight Stokes' law Terminal velocity References Inline ^ Drag Force General Serway, Raymond A.; Jewett, John W. 2004. Physics for Scientists and Engineers 6th ed.. Brooks/Cole. ISBN 0-534-40842-7. Tipler, Paul 2004. Physics for Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics 5th ed.. W. H. Freeman. ISBN 0-7167-0809-4. Huntley, H. E. 1967. Dimensional Analysis. Dover. LOC 67-17978. External links Educational materials on air resistance Aerodynamic Drag and its effect on the acceleration and top speed of a vehicle. Retrieved from http://en..org/wiki/Drag_physics Categories: Aerodynamics | Fluid dynamics Views Article Discussion this page History Personal tools Log in / create account Navigation Main page Contents Featured content Current events Random article Search Go Search Interaction Community portal Recent changes Contact Donate to Help Toolbox What links here Related changes Upload file Special pages Printable version Permanent link Cite this page Languages ÄŒesky Dansk Deutsch Español Français Italiano עברית Nederlands Polski Português РуÑ?Ñ?кий SlovenÅ¡Ä?ina Suomi Svenska Türkçe УкраїнÑ?ька ä¸æ–‡ This page was last modified on 30 July 2008, at 23:57
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