Drag Force

6 Key excerpts on "Drag Force"

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  Aerodynamics & its Applications

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  For high velocities — or more precisely, at high Reynolds numbers — 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 more-or-less 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). Drag at high velocity Explanation of drag by NASA. ____________________ WORLD TECHNOLOGIES ____________________ 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: where is the force of drag, is the density of the fluid, is the speed of the object relative to the fluid, is the reference area, is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car) The reference area A is often defined as the area of the orthographic projection of the object — on a plane perpendicular to the direction of motion — e.g. for objects with a simple shape, such as a sphere, this is the 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.

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  Advanced Transport Phenomena

  Analysis, Modeling, and Computations

  • P. A. Ramachandran(Author)
  • 2014(Publication Date)
  • Cambridge University Press

    (Publisher)

  Drag is a macroscopic property, since it provides the total force. The above relation shows how the drag is related to microscopic or local forces. For complex shapes the Drag Force is correlated in an empirical manner using the drag coefficient, C D . This is defined as Total Drag Force = C D A p ρ v 2 / 2 Here v is the fluid approach velocity and A p is the projected area of the body. The drag coefficient is similar to the friction factor for internal flows. The lift force Similarly the component of the surface force in a direction perpendicular to flow is called the lift force: Total lift force = A e y · [ n · ( ˜ τ − p ˜ I ) ] dA 179 4.4 Drag and lift forces In practice it is convenient to use the lift coefficient values: Total lift force = C L A p ρ v 2 / 2 An application of the Drag Force is for particle settling in a liquid, which is shown below. Particle settling velocity Consider a particle settling in a liquid. Systems of this type are encountered in filtration, sedimentation, etc. The system is characterized by the balance of gravity, pressure forces, and viscous forces. The pressure force is usually included as the buoyancy term. Hence the gravity + pressure (or buoyancy) force on the system is equal to v p g (ρ p − ρ l ) . Here v p is the volume of the particle equal to ( 4 / 3 )π R 3 for a spherical particle. The viscous force is usually represented by using a drag coefficient. Viscous forces = C D A p 1 2 ρ l v 2 t where v t is the relative velocity of the liquid and the solid and is equal to terminal veloc-ity since the movement of the liquid phase is usually small. The area A p is taken as the projected area in the direction of flow and is equal to π R 2 for spherical particles.

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  Fluid Mechanics for Civil and Environmental Engineers

  • Ahlam I. Shalaby(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  D in the theoretical expression for the Drag Force,

  F D

  = (

  F P

  +

  F f

  ) s

  = ( Δ p A

  ) s

  =

  (

  ρ

  v 2

  2

  A +

  τ w

  L

  R h

  A

  )

  s

  in the integral form of the momentum equation is sought in terms of velocity, v and a flow resistance coefficient. This is accomplished by using dimensional analysis in order to derive an empirical expression for the Drag Force,

  FD

  as a function of the velocity, v , which involves the definition of a drag coefficient,

  CD

  that represents the flow resistance and is empirically evaluated. Thus, the momentum theory is supplemented with dimensional analysis in order to derive an expression for the Drag Force,

  FD

  for external flow. Thus, for the derivation of the Drag Force,

  FD

  , in addition to the inertia force,

  FI

  and the pressure force,

  FP

  (causes the viscous force for turbulent flow,

  FV = τA

  , which is represented by the Drag Force,

  FD

  ), other forces including the viscous force for laminar flow,

  FV

  = τA = μvL ; the elastic force,

  FE

  ; and the gravity force,

  FG

  also play an important role in the external fluid flow. Additionally, other physical quantities include the absolute surface roughness, ɛ and the geometry,

  Li

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  An Introduction to Mathematics for Engineers

  Mechanics

  • Stephen Lee(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  Forces and Newton’s laws of motion Nature to him was an open book. He stands before us, strong, certain and alone. Einstein on Newton 2.1 Force diagrams The picture shows a crate of medical supplies being dropped into a remote area by parachute. What forces are acting on the crate of supplies and the parachute? One force which acts on every object near the earth’s surface is its own weight . This is the force of gravity pulling it towards the centre of the earth. The weight of the crate acts on the crate and the weight of the parachute acts on the parachute. The parachute is designed to make use of air resistance . A resistance force is present whenever a solid object moves through a liquid or gas. It acts in the opposite direction to the motion and depends on the speed of the object. The crate also experiences air resistance, but to a lesser extent than the parachute. Other forces are the tensions in the guy lines attaching the crate to the parachute. These pull upwards on the crate and downwards on the parachute. All these forces can be shown most clearly if you draw force diagrams for the crate and the parachute. 2 Figure 2.1: Forces acting on the crate Figure 2.2: Forces acting on the parachute Force diagrams are essential for the understanding of most mechanical situations. A force is a vector: it has a magnitude, or size, and a direction. It also has a line of action . This line often passes through a point of particular interest. Any force diagram should show clearly ● the direction of the force ● the magnitude of the force ● the line of action. In figures 2.1 and 2.2 each force is shown by an arrow along its line of action. The air resistance has been depicted by a lot of separate arrows but this is not very satisfactory. It is much better if the combined effect can be shown by one arrow. When you have learned more about vectors, you will see how the tensions in the guy lines can also be combined into one force if you wish.

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  Aerodynamics of Road Vehicles

  From Fluid Mechanics to Vehicle Engineering

  • Wolf-Heinrich Hucho(Author)
  • 2013(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  If each detail's contribution to drag could be defined and then minimized, a vehicle with the minimum aerodynamic drag would be obtained, but the high degree of interaction between parts limits the success of this procedure (section 4.4.4.1). Cars with very low aerodynamic drag cannot be designed piecemeal, but require total consideration of the drag phenomenon. Different explanations of drag have been based on • the physical causes • the local origin • the effect upon the surrounding field. Consistent application of each of these methods leads to the correct result, but errors often appear when partial arguments from the three categories are mixed with one another. One example of this is the induced drag, as is shown in this section. The physical causes of aerodynamic drag can be investigated by comparing the actual, frictional (viscous) flow with the ideal, friction-free (non-viscous) flow and breaking down the drag into its pressure and frictional components. The occurrence of both components is explained in Fig. 4.13. The surrounding flow field generates a pressure and shear stress distribution around the vehicle. At points where the flow is opposed by a high pressure increase, it tends to separate from the contour. This phenomenon is explained in section 2.3.3, Fig. 2.7. In the example in Fig. 4.13 it is assumed, for the sake of simplicity, that separation occurs only at the rear end of the vehicle. As a consequence the pressure distribution there deviates from that in non-viscous flow. If the pressure is plotted against the width of the vehicle, as shown upper right in Fig. 4.13, it becomes evident that this change in the pressure distribution is highly significant for the origin of drag. The shear stresses at the wall decrease with increasing boundary layer thickness, and fall to zero at the separation point.

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  Physics of Force and Friction (Concepts and Applications)

  • (Author)
  • 2014(Publication Date)
  • Academic Studio

    (Publisher)

  Friction Force diagram for block on ground. Arrows are vectors indicating directions and magnitudes of forces. W is the force of weight, N is the normal force, F is an applied force, and F f is the force of kinetic friction which is equal to the coefficient of kinetic friction times the normal force. Since the magnitude of the applied force is greater than ________________________ WORLD TECHNOLOGIES ________________________ the magnitude of the force of kinetic friction opposing it, the block is accelerating to the left. Friction is the force resisting the relative motion of solid surfaces, fluid layers, or material elements sliding against each other. It may be thought of as the opposite of slipperiness. There are several types of friction: • Dry friction resists relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction between non-moving surfaces, and kinetic friction between moving surfaces. • Fluid friction describes the friction between layers within a viscous fluid that are moving relative to each other. • Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. • Skin friction is a component of drag, the force resisting the motion of a solid body through a fluid. • Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation. When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic conse-quences, as illustrated by the use of friction between pieces of wood to start a fire. Another important consequence of many types of friction can be wear, which may lead to performance degradation and/or damage to components. Friction is a component of the science of tribology. Friction is not a fundamental force but occurs because of the electromagnetic forces between charged particles which constitute the surfaces in contact.

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