Fluid Dynamic Drag

8 Key excerpts on "Fluid Dynamic Drag"

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  eBook - ePub

  Sports Biomechanics

  The Basics: Optimising Human Performance

  • Prof. Anthony J. Blazevich(Author)
  • 2017(Publication Date)
  • Bloomsbury Sport

    (Publisher)

  CHAPTER 13 FLUID DYNAMICS – DRAG We know that aerodynamics is very important in cycling but how can we determine the optimum aerodynamic body position on a bike? By the end of this chapter you should be able to:

  • Explain the concept of drag and differentiate between different types of drag

  • Describe the factors influencing drag and how we might manipulate them to improve sporting performance

  • Design experiments to assess the impact of body position or equipment modifications on drag and subsequent performance

  We need to find out what factors affect drag so that we can highlight a number of probable ‘best aerodynamic positions’, then test them. Factors affecting drag

  We’ve all noticed that it is harder to run, ride or project an implement such as a football into a strong wind. The reason is that in these circumstances the drag force is increased. Drag occurs when molecules of a fluid (‘fluid’ refers to any moveable medium, including air) collide with an object and take energy away from it. As you learned in Chapter 9 , all moving objects have kinetic energy. If energy is taken from them their mass or velocity must decrease. It is rare for mass to be reduced so normally an object loses velocity.

  The loss of energy from the object to the fluid can be visualised in two ways. The theoretically correct way is to assume that the fluid moving towards an object is ordered into smooth, parallel layers, that is, it is not being mixed around. This is laminar flow, as shown in Figure 13.1 . The fluid has a certain amount of energy, which remains constant. But as it passes an object, the fluid changes direction and therefore velocity (remember, velocity is a vector quantity, so it changes if either the speed or the direction is altered) and so gains energy. The energy gained by the fluid is always equal to the energy lost from the object because (as you already know) energy cannot be created or destroyed. This non-laminar flow is also called turbulent flow

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  Elements of Friction Theory and Nanotribology

  • Enrico Gnecco, Ernst Meyer(Authors)
  • 2015(Publication Date)
  • Cambridge University Press

    (Publisher)

  Part IV Lubrication 22 Drag in a viscous fluid The friction force on an object moving in a viscous fluid (so-called ‘drag’) has a completely different character from the friction on the same object sliding on a solid substrate. The parasitic drag is ‘tuned’ by the shape of the object (‘form drag’) and also by the contact between the fluid and the surface of the body (‘skin friction’). In a first approximation the parasitic drag is proportional to the square of the velocity. Furthermore, the lift force created on a streamlined body such as a wing can also cause friction (‘induced drag’). Here, we will introduce the most important expressions for the drag forces. The corresponding derivations can be found in textbooks on advanced fluid dynamics such as [176]. The wave drag caused by the shock waves formed at transonic and supersonic speed will be not discussed. 22.1 The Navier–Stokes equation The motion of an incompressible viscous fluid is described by the Navier–Stokes equation [230, 323] ρ  ∂ v ∂ t + v · ∇ v  = −∇ p + η∇ 2 v, (22.1) where ρ and v are the density and velocity of the fluid, p is the pressure and η is the dynamic viscosity. 1 Equation (22.1) is obtained from the Newton equation with the addition of a diffusing viscous term. Typical values for the viscosity of various fluids at room temperature are listed in Table 22.1. A brief discussion on the viscosity of gases, as estimated with the kinetic theory, is presented in Appendix B. Equation (22.1) is accompanied by the equation of continuity ∇ · v = 0, 1 The ratio of the dynamic viscosity to the fluid density is the kinematic viscosity ν = η/ρ. 243 244 Drag in a viscous fluid Table 22.1 Typical values of dynamic viscosity (in mPa·s) Fluid η Air 0.017 Water 0.9 Ethanol 1.2 Mercury 1.5 Glycerol 1.2 × 10 3 which simply states that the mass of the fluid is conserved. Furthermore, appro- priate boundary conditions must be satisfied.

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  Fluid Mechanics for Civil and Environmental Engineers

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

    (Publisher)

  R , but dependent on the Mach number,

  M = C =

  v

  E v

  ρ

  =

  v a

  c

  ,

  where c is the sonic velocity; thus, the elastic force (compressibility effects) will play an important role. The gravity force will play an important role if there is a wave action at the free surface; thus, the definition of the drag coefficient,

  CD

  will be dependent on F ; such examples include ships and open channel flow-measuring devices/structures such as weirs and spillways.

  Finally, one may note that dimensional analysis yields a nonstandard form of the drag coefficient,

  CD

  , using inertia force,

  FI

  in its definition, which yields the corresponding expression for the drag force,

  FD

  as follows:

  F D = C D ρ v 2 L 2 = C D ρ v 2 A	(7.27)

  If however, one considers the fact that inertia force,

  FI

  = ρv 2 A may be further defined as the dynamic (pressure) force,

  Fdynpres

  = ρv 2 A/ 2, then the drag coefficient,

  CD

  would be defined as follows. The practical application of the expression for the drag force,

  FD

  (given by Equation 7.26 ) is accomplished by the application of the principle of conservation of momentum and the definition of the dynamic pressure term, ρv 2 / 2. The inertia force,

  FI

  term in Equation 7.26

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  An Introduction to Mechanical Engineering: Part 2

  • Michael Clifford(Author)
  • 2014(Publication Date)
  • CRC Press

    (Publisher)

  (3) We must choose the fabric of the swimming costume carefully to achieve these objectives: a smooth fabric where we want laminar flow, and a rough fabric in certain parts of the costume to promote turbulence. Learning summary By the end of this section you should have learnt: 3 viscous fluid does not slip at a solid wall surface. This is called the non-slip condition of flow motion; 3 the boundary layer is a thin fluid layer near a solid wall surface, where the velocity is less than the freestream velocity; 3 the momentum thickness signifies the loss of momentum in the boundary layer due to skin-friction drag; 3 the displacement thickness is a measure of mass flow deficit in the boundary layer; 3 the boundary layer equations are a simplified form of the Navier–Stokes equations; 3 flow separation occurs over a curved surface when the static pressure increases in the flow direction. Fluid dynamics 19 1.4 Drag on immersed bodies Pressure drag While the friction drag D fric results from the viscous action of fluids on the body surface, the pressure drag D pres comes from the static pressure distribution around the body, mainly due to boundary-layer separation. The total drag acting on immersed bodies in incompressible flows, therefore, consists of the friction drag and the pressure drag. We can write D tot (total drag) 5 D fric (friction drag) 1 D pres (pressure drag) (1.48) The relative importance of D pres to D fric depends on the body shape as well as the Reynolds number. When the immersed bodies are streamlined, the friction drag dominates the total drag. When the non-streamlined bodies (bluff bodies) are placed in a fluid flow, however, the total drag is dominated by the pressure drag, and the contribution of the friction drag is usually negligible.

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  Design Principles of Ships and Marine Structures

  • Suresh Chandra Misra(Author)
  • 2015(Publication Date)
  • CRC Press

    (Publisher)

  Looking at the drag in a different way, the total resistance to forward motion is the sum of the longitudinal components of stresses tangential to the surface (friction), R F , and normal to the surface (pressure), R P : R R R T F P = + . The viscosity of water also alters the pressure distribution around the hull and thereby causes an increase in the pressure resistance. The part of the pressure resistance due to the viscosity around a 3D form is called the viscous pressure resistance R VP given by R R R R R VP V F P W = -= -Then, R R R R R R R R R R R T V W F VP W F VP W F P = + = + + = + + = + ( ) ( ) The viscous pressure resistance is usually a small component of the total resistance. However, if the hull is excessively curved at the stern and there are large waterline or but-tock line slopes or discontinues, the flow separates from the hull surface and gives rise to eddies or vortices. This results in a significant increase in the viscous pressure resistance. The additional resistance due to separation of flow and the generation of eddies is called separation drag or eddy resistance. The frictional resistance R F is the sum total of the frictional resistance of a 2D surface of infinite aspect ratio (surface of zero pressure gradient), R F 0 , and an additional component due to the 3D effect on friction, commonly known as friction form effect, and taking k as the form factor, R F = (1 + k ) R F 0 . When the waves generated by the ship have high wave slope, like in full form ships moving even at slow speed, waves break and the drag is manifested as viscous resistance. Thus, if one measured the energy content of the wake behind the ship experimentally, the drag would consist of the normal viscous resistance and the drag due to wave breaking, and the remaining part of the total drag can be mea-sured by estimating the energy content in the waves, which is known as wave pattern resistance.

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  An Introduction to Mechanical Engineering, SI Edition

  • Jonathan Wickert, Jonathan Wickert, Kemper Lewis(Authors)
  • 2016(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 6.7 Lift Force 257 ▸ ▸ 6.7 Lift Force S imilar to drag, the lift force is also produced by the relative motion between a solid object and a fluid. While the drag force acts in parallel to the direction of the fluid’s flow, the lift force acts in perpendicular to it. For instance, in the context of the airplane shown in Figure 6.27, the high-speed flow of air around the wings generates a vertical lift force F L that balances the plane’s weight. Four forces are shown acting on the aircraft in flight: the plane’s weight w , the thrust F T produced by its jet engines, the lift F L produced by the wings, and the drag F D that opposes the motion of the plane through the air. In steady level flight, those forces balance to keep the plane in equilibrium: the engines’ output overcomes wind resistance, and the wings’ lift supports the weight of the aircraft. Lift force is important not only for aircraft wings and other flight control surfaces, but also for the design of propeller, compressor, and turbine blades; ship hydrofoils; and the body contours of commercial and racing automobiles. The area of mechanical engineering that encompasses the interaction between structures and the air flowing around them is called aerodynamics . When engineers are performing aerodynamic analysis of drag and lift forces, invariably they make approximating assumptions with respect to geometry and the behavior of the fluid. For instance, neglecting a fluid’s viscosity or compressibility Aerodynamics Example 6.9 | continued Because this is less than one, we have confirmed that it was acceptable to apply Equation (6.16). Had we found otherwise, we would have discarded this prediction, and instead applied Equation (6.14) with the graph of Figure 6.23 for C D .

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  Introduction to Chemical Engineering Fluid Mechanics

  • William M. Deen(Author)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  1 In Part II we will show how to calculate forces such as drag from a knowledge of the pressure and velocity fields near an object. Our focus at present is the use of experimental results. Drag coefficient A quantity with the dimension of stress is obtained by dividing the drag force ( F D ) by an area. In drag calculations it is customary to employ the projected area of the object ( A ⊥ ). Imagine the shadow of an opaque object on a screen. If the screen is perpendicular to the direction of flow, A ⊥ is the area of the shadow. For a sphere of diameter D , the shadow would be a circle of area A ⊥ = π D 2 / 4. A disk of diameter D whose surfaces are perpendicular to the flow, and a cylinder of diameter D with an end-on orientation, each 1 For objects less symmetric than that in Fig. 3.1 , the fluid-dynamic force might have additional components. The y component would be called a lift force. Although lift is crucial for certain applications, such as airfoil design, we are concerned here only with drag. 55 Drag, particles, and porous media Figure 3.2 Drag coefficients for spheres and disks. The curves are fits to a large body of experimental data. The line labeled “Stokes” is the prediction for spheres given by Eq. (3.2-2) . have that same projected area. For a cylinder of length L whose axis is perpendicular to the flow, the shadow would be a rectangle of area A ⊥ = DL . A dimensionless group could be constructed by dividing F D / A ⊥ by either the vis-cous or the inertial stress scale. As with the friction factor for pipe flow ( Chapter 2 ), the conventional reference stress is ρ U 2 / 2. Dimensional analysis indicates that the dimen-sionless stress for an object of a given shape and orientation is a function only of the Reynolds number. Thus, C D (Re) = 2 F D ρ U 2 A ⊥ (3.2-1) where C D is the drag coefficient . For spheres, disks, or cylinders the customary length scale in Re is the diameter.

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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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