Drag (physics) - Citizendia

An object moving through a gas or liquid experiences a force in direction opposite to its motion. In Physics, a force is whatever can cause an object with Mass to Accelerate. Terminal velocity is achieved when the drag force is equal in magnitude but opposite in direction to the force propelling the object. A free falling object achieves its terminal velocity when the downward force of gravity ( Fg)equals the upward force of drag ( Fd) Shown is a sphere in Stokes flow, at very low Reynolds number. "Globose" redirects here See also Globose nucleus. A sphere (from Greek σφαίρα - sphaira, "globe Stokes flow (named after George Gabriel Stokes) is a type of Fluid flow where advective inertial forces are small compared with viscous In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio

In fluid dynamics, drag (sometimes called resistance) is the force that resists the movement of a solid object through a fluid (a liquid or gas). Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of This page is about the physical properties of gas as a state of matter 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. Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface For a solid object moving through a fluid, the drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the movement. Fluid dynamics is the sub-discipline of Fluid mechanics dealing with fluid flow: Fluids ( Liquids and Gases in motion In Physics, a force is whatever can cause an object with Mass to Accelerate. Forces perpendicular to this direction are considered lift. In the context of a Fluid flow relative to a body the lift force is the component of the Aerodynamic force that is Perpendicular to the flow It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust. Thrust is a reaction force described quantitatively by Newton 's Second and Third Laws.

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. Orbital mechanics or astrodynamics is the application of Celestial mechanics to the practical problems concerning the motion of Rockets and other Spacecraft Space launch is the earliest part of a Flight that reaches space.

Types of drag are generally divided into three categories:

parasitic drag,
lift-induced drag, and
wave drag. Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid In Aerodynamics, lift-induced drag, induced drag, vortex drag, or sometimes drag due to lift, is a drag force that occurs whenever Wave drag is an Aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft and blade tips moving at high-subsonic and supersonic

Parasitic drag includes form drag, skin friction, and interference drag. Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid 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. WING "ESPN 1410" is a commercial AM radio station in Dayton Ohio operating with 5000 watts at 1410 kHz with studios offices and transmitter located on David The lifting body is an Aircraft configuration where the body itself produces lift. A hull is the body of a Ship or Boat. It is a central concept in floating vessels as it provides the Buoyancy that keeps the vessel from sinking Wave drag occurs when a solid object is moving through a fluid at or near the speed of sound in that fluid. Wave drag is an Aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft and blade tips moving at high-subsonic and supersonic Sound is a vibration that travels through an elastic medium as a Wave.

The overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units The drag coefficient ( Cd, Cx or Cw) is a Dimensionless quantity that describes how streamlined an In Fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to a Fluid that it is moving Assuming a constant drag coefficient, drag will vary as the square of velocity. In Physics, velocity is defined as the rate of change of Position. 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. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve.

Wind resistance or air 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). Badminton is a racquet sport played by either two opposing players (singles or two opposing pairs (doubles who take positions on opposite halves of a rectangular court A shuttlecock' is a high- drag Projectile used in the sport of Badminton. Squash is a racquet sport that was formerly called squash racquets, a reference to the "squashable" soft ball used in the game (compared with the

1 Stokes' drag
2 Drag at high velocity
- 2.1 Power
- 2.2 Velocity of falling object
3 See also
4 References
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, $R e < 1$ ). In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio ^[1] In this case, the force of drag is approximately proportional to velocity, but opposite in direction. [1] The equation for viscous resistance is:

$\mathbf{F}_d = - b \mathbf{v} \,$

where:

$\mathbf{} b$ is a constant that depends on the properties of the fluid and the dimensions of the object, and

$\mathbf{v}$ is the velocity of the object.

When an object falls from rest, its velocity will be

$v(t) = \frac{mg}{b}\left(1-e^{-bt/m}\right)$

which asymptotically approaches the terminal velocity $\mathbf{} v_t = \frac{mg}{b}$ . 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. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code Sir George Gabriel Stokes 1st Baronet FRS ( 13 August 1819 &ndash 1 February 1903) was a mathematician and physicist The Stokes radius, Stokes-Einstein radius, or Hydrodynamic radius R H, named after George Gabriel Stokes, is

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. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. 09 pN. This is about the drag force that a bacterium experiences as it swims through water.

Drag at high velocity

The Drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i. In Fluid dynamics, the drag equation is a practical formula used to calculate the force of drag experienced by an object due to a Fluid that it is moving FLUID ( F ast L ight '''U'''ser '''I'''nterface D esigner is a graphical editor that is used to produce FLTK Source code e. high Reynolds number, $R_e > ~1000$ ), also called quadratic drag. In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio The equation is attributed to Lord Rayleigh, who originally used $L^2 \$ in place of $A \$ (L being some length). John William Strutt 3rd Baron Rayleigh OM (12 November 1842 &ndash 30 June 1919 was an English Physicist who with William Ramsay, discovered The force on a moving object due to a fluid is:

$\mathbf{F}_d= -{1 \over 2} \rho v^2 A C_d \mathbf{\hat v}$ ^{see derivation}

where

$\mathbf{F}_d$ 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. In Physics, a force is whatever can cause an object with Mass to Accelerate. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Temperature and layers The temperature of the Earth's atmosphere varies with altitude the mathematical relationship between temperature and altitude varies among five The barometric formula, sometimes called the exponential atmosphere or Isothermal Atmosphere, is a Formula used It is 1. 293 kg/m³ at 0 °C and 1 atmosphere. The Standard atmosphere is an international reference pressure defined as 101325 Pa and formerly used as unit of Pressure (symbol atm ),

$\mathbf{} v$ 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. Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of Area is a Quantity expressing the two- Dimensional size of a defined part of a Surface, typically a region bounded by a closed Curve. The drag coefficient ( Cd, Cx or Cw) is a Dimensionless quantity that describes how streamlined an In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units 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). In Mathematics, a unit vector in a Normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length

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). In Geometry, a cross section is the intersection of a body in 2-dimensional space with a line or of a body in 3-dimensional space with a plane etc 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:

$P_d = \mathbf{F}_d \cdot \mathbf{v} = {1 \over 2} \rho v^3 A C_d$

Note that the power needed to push an object through a fluid increases as the cube of the velocity. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for 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. In Physics, mechanical work is the amount of Energy transferred by a Force. 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:

$v(t) = \sqrt{ \frac{2mg}{\rho A C_d} } \tanh \left(t \sqrt{\frac{g \rho C_d A}{2 m}} \right) \,$

In other words, velocity asymptotically approaches a maximum value called the terminal velocity:

$v_{t} = \sqrt{ \frac{2mg}{\rho A C_d} } \,$

For a potato-shaped object of average diameter d and of density ρ_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. A free falling object achieves its terminal velocity when the downward force of gravity ( Fg)equals the upward force of drag ( Fd) In Mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular functions An asymptote of a real-valued function y=f(x is a curve which describes the behavior of f as either x or y goes to infinity A free falling object achieves its terminal velocity when the downward force of gravity ( Fg)equals the upward force of drag ( Fd) ) 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. Crickets, family Gryllidae (also known as "true crickets" are Insects somewhat related to Grasshoppers and more closely related to katydids This explains why small animals can fall from a large height and not be harmed.

References

^ Drag Force

Serway, Raymond A. Aerodynamic force is the resultant force exerted on a body by the air (or some other gas in which the body is immersed and is due to the relative motion between the body and the fluid In Physics, ram pressure is a pressure exerted on a body which is moving through a Fluid medium Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid In Fluid mechanics, added mass or virtual mass is the Inertia added to a system because an accelerating or decelerating body must move some Volume Angle of attack ( AOA, \alpha Greek letter alpha) is a term used in Aerodynamics to describe the Angle between the A drag-reducing aerospike is a device used to reduce the forebody pressure drag of blunt bodies at Supersonic speeds In Astrodynamics and Rocketry, gravity drag (or gravity losses) is the difference between the Delta-v expended and the actual change in speed For other uses see Stall. In Aerodynamics, a stall is a sudden reduction in the lift forces generated by an Airfoil A free falling object achieves its terminal velocity when the downward force of gravity ( Fg)equals the upward force of drag ( Fd) In Physics and Fluid mechanics, a boundary layer is that layer of Fluid in the immediate vicinity of a bounding surface The Coandă effect ('kwandə is the tendency of a Fluid jet to stay attached to an adjacent curved surface that is very well shaped. The drag coefficient ( Cd, Cx or Cw) is a Dimensionless quantity that describes how streamlined an In Fluid mechanics and Heat transfer, the Reynolds number \mathrm{Re} is a Dimensionless number that gives a measure of the Ratio In 1851, George Gabriel Stokes derived an expression now known as Stokes' law, for the frictional force — also called Drag force — exerted on ; 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.

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