Drag Force
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Drag (physics) From Wikipedia, the free encyclopedia (Redirected from Drag force) Jump to: navigation, search
An object falling through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal to force of gravity pulling it down. In fluid dynamics, drag is the force that resists the movement of a solid object through a fluid (a liquid or gas). Drag is made up of friction forces, which act in a direction parallel to the object's surface (primarily along its sides, as friction forces at the front and back cancel themselves out), plus pressure forces, which act in a direction perpendicular to the object's surface. For a solid object moving through a fluid or gas, the drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. (Forces perpendicular to this direction are considered lift). It therefore 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.
Contents [hide] ●
●
●
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1 Details 2 General drag 3 Drag at low velocity ; Stokes' Drag 4 Drag at high velocity ● 4 . 1 P o w e r ● 4 . 2 V e l o c i t
[edit] Details Types of drag are generally divided into three categories: parasitic drag, liftinduced 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 only in the aviation perspective of drag. Beyond these two kinds of drag there is a third kind of drag, called wave drag, that occurs when the solid object is moving through the 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 density, the cross sectional area of your specified green 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).
[edit] General drag Fluid mechanics is one of the most complicated subjects in physics, and so people have found many approximations to avoid such complexities. The drag equation and viscous resistance equation below are two such approximations. In general, the force of drag experienced by an object moving through a fluid can be expressed by: where an is some constant for every value of n that relates to the properties of the fluid and the object, and v is the velocity, and is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity).
Generally, the value of an decreases as n becomes larger.
[edit] Drag at low velocity; Stokes' Drag The equation for viscous resistance is appropriate for small objects or particles moving through a fluid at relatively slow speeds. In this case, the force of drag is approximately proportional to velocity, but opposite in direction. [1] The equation for viscous resistance is: where: b is a constant that depends on the properties of the fluid and the dimensions of the object, and v is the velocity of the object. When an object falls from rest, its velocity will be which asymptotically approaches the terminal velocity vt = mg / b. For a certain 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 coefficient, where: r is the Stokes radius of the particle, and η is the fluid viscosity. For example, consider a small sphere with radius r = 1 micrometre moving through water at a velocity v of 10 µm/s. Using 103 as the dynamic viscosity of water in SI units, we find a drag force of 0.2 pN. This is about the drag force that a bacterium experiences as it swims through water.
[edit] Drag at high velocity The Drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity. The equation is attributed to Lord Rayleigh, who originally used in place of (L being some length). The force on a moving object due to a fluid is: see derivation where Fd is the force of drag,
ρ is the density of the fluid (Note that for the Earth's atmosphere, the density can be found using the barometric formula), v is the velocity of the object relative to the fluid, A is the reference area, Cd is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car), and 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.
[edit] Power The power required to overcome the aerodynamic drag is given by: 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 a work 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.
[edit] Velocity of falling object Main article: Terminal velocity The velocity as a function of time for an object falling through a nondense medium is roughly given by a function involving a hyperbolic tangent:
In other words, velocity asymptotically approaches a maximum value called the Terminal velocity:
With all else (gravitational acceleration, density, crosssectional area, drag constant, etc.) being equal, heavier objects fall faster. For potatoshaped bof average diameter d and of density ρobj terminal velocity is about
For objects of waterlike density (raindrops, hail, live objects animals, birds, incects, etc) falling in air near surface of Earth at sea level terminal velocity is roughly equal For example, for human body (d~0.6 m) vt ~70 m/s, for a small animal like a cat (d~0.2
m) vt ~40 m/s, for a small bird (d~0.05 m) vt ~20 m/s, for an insect (d~0.01 m) vt ~9 m/s, for a fog droplet (d~0.0001 m) vt ~0.9 m/s, for a pollen or bacteria (d~0.00001 m) vt ~0.3
m/s and so on. Actual terminal velocity for very small objects (pollen, etc) is even smaller due to viscosity of air.
As can be seen, terminal velocity for grownup human and large animals is deadly on impact, but for small animals and birds can be survivable, and for insects not deadly at all. It is known that sometimes even small babies surfive fall fatal for a grownup which can be explained by their smaller terminal velocity.
An object falling through a gas or liquid experiences a force in direction opposite to its motion. Terminal velocity is achieved when the drag force is equal to force of gravity pulling it down. In fluid dynamics, drag is the force that resists the movement of a solid object through a fluid (a liquid or gas). Drag is made up of friction forces, which act in a direction parallel to the object's surface (primarily along its sides, as friction forces at the front and back cancel themselves out), plus pressure forces, which act in a direction perpendicular to the object's surface. For a solid object moving through a fluid or gas, the drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. (Forces perpendicular to this direction are considered lift). It therefore 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.
Contents [hide] ●
●
●
●
1 Details 2 General drag 3 Drag at low velocity ; Stokes' Drag 4 Drag at high velocity ● 4 . 1 P o w e r ● 4 . 2 V e l o c i t
[edit] Details Types of drag are generally divided into three categories: parasitic drag, liftinduced 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 only in the aviation perspective of drag. Beyond these two kinds of drag there is a third kind of drag, called wave drag, that occurs when the solid object is moving through the 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 density, the cross sectional area of your specified green 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).
[edit] General drag Fluid mechanics is one of the most complicated subjects in physics, and so people have found many approximations to avoid such complexities. The drag equation and viscous resistance equation below are two such approximations. In general, the force of drag experienced by an object moving through a fluid can be expressed by: where an is some constant for every value of n that relates to the properties of the fluid and the object, and v is the velocity, and is the unit vector indicating the direction of the velocity (the negative sign indicating the drag is opposite to that of velocity).
Generally, the value of an decreases as n becomes larger.
[edit] Drag at low velocity; Stokes' Drag The equation for viscous resistance is appropriate for small objects or particles moving through a fluid at relatively slow speeds. In this case, the force of drag is approximately proportional to velocity, but opposite in direction. [1] The equation for viscous resistance is: where: b is a constant that depends on the properties of the fluid and the dimensions of the object, and v is the velocity of the object. When an object falls from rest, its velocity will be which asymptotically approaches the terminal velocity vt = mg / b. For a certain 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 coefficient, where: r is the Stokes radius of the particle, and η is the fluid viscosity. For example, consider a small sphere with radius r = 1 micrometre moving through water at a velocity v of 10 µm/s. Using 103 as the dynamic viscosity of water in SI units, we find a drag force of 0.2 pN. This is about the drag force that a bacterium experiences as it swims through water.
[edit] Drag at high velocity The Drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity. The equation is attributed to Lord Rayleigh, who originally used in place of (L being some length). The force on a moving object due to a fluid is: see derivation where Fd is the force of drag,
ρ is the density of the fluid (Note that for the Earth's atmosphere, the density can be found using the barometric formula), v is the velocity of the object relative to the fluid, A is the reference area, Cd is the drag coefficient (a dimensionless constant, e.g. 0.25 to 0.45 for a car), and 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.
[edit] Power The power required to overcome the aerodynamic drag is given by: 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 a work 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.
[edit] Velocity of falling object Main article: Terminal velocity The velocity as a function of time for an object falling through a nondense medium is roughly given by a function involving a hyperbolic tangent:
In other words, velocity asymptotically approaches a maximum value called the Terminal velocity:
With all else (gravitational acceleration, density, crosssectional area, drag constant, etc.) being equal, heavier objects fall faster. For potatoshaped bof average diameter d and of density ρobj terminal velocity is about
For objects of waterlike density (raindrops, hail, live objects animals, birds, incects, etc) falling in air near surface of Earth at sea level terminal velocity is roughly equal For example, for human body (d~0.6 m) vt ~70 m/s, for a small animal like a cat (d~0.2
m) vt ~40 m/s, for a small bird (d~0.05 m) vt ~20 m/s, for an insect (d~0.01 m) vt ~9 m/s, for a fog droplet (d~0.0001 m) vt ~0.9 m/s, for a pollen or bacteria (d~0.00001 m) vt ~0.3
m/s and so on. Actual terminal velocity for very small objects (pollen, etc) is even smaller due to viscosity of air.
As can be seen, terminal velocity for grownup human and large animals is deadly on impact, but for small animals and birds can be survivable, and for insects not deadly at all. It is known that sometimes even small babies surfive fall fatal for a grownup which can be explained by their smaller terminal velocity.
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