### Pressure drag equation

Drag coefficients are dimensionless similarity parameters for describing the drag of flowed around bodies. Learn more about them in this article. When a body moves through a fluid or a fluid flows around a body, drag forces act on the body. These generally have two causes:. These two mechanisms have already been explained in detail in the article on Parasitic drag.

Therefore, theses mechanisms will only be briefly summarized in the following.

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On the one hand, due to the viscosity of the fluid, frictional forces act on the skin of the bodyresulting in a so-called skin friction drag. The decisive factor here is the shear stress acting on the surface of the body. Skin friction drag is caused by wall shear stresses that act between the fluid and the body surface due to the viscosity! On the other hand, the body is affected by different static pressure forces.

If a flow around a body accelerates, the static pressure decreases, i. Conversely, deceleration of the fluid leads to an increase in static pressure at the expense of kinetic energy. The different pressures that arise around the body also lead to a drag. This is also known as pressure drag or form drag. The pressure drag has its cause in the different static pressures, which act on the body due to the conservation of energy! Both types of drag skin friction drag and pressure drag then form the macroscopically observable drag of a body.

### Drag coefficient (friction and pressure drag)

This overall drag is also referred to as parasitic drag or just drag. Friction drag, pressure drag and parasitic drag can each be expressed with dimensionless parameters. These quantities are also known as drag coefficients. The meaning of these coefficients is quite analogous to other dimensionless similarity parameters such as Reynolds numberPrandtl numberNusselt numberSchmidt numberLewis numberetc. The drag coefficients serve the purpose of describing flows independently of the size of the system.

In this way, for example, the knowledge gained about the drag from a car model in a wind tunnel can be transferred to the real vehicle. The friction drag coefficient is used for the characterization of the friction drag which is caused by shear stresses. Note that both quantities have the same unit and the quotient is therefore dimensionless. The friction drag coefficient can thus be interpreted as dimensionless wall shear stress. If you take the square root of the quotient of shear stress and density, this quotient also has the dimension of a velocity.

The shear velocity is not a velocity in the true sense of the word, it is simply called that because this quantity has the same dimension as a velocity. The shear velocity influences not only the drag coefficient but also the thickness of the viscous sublayer.

In the case of a flat plate, the growth of the boundary layer is accompanied by a decrease in the velocity gradient at the wall. This results in a decrease of the wall shear stress and thus a reduction of the friction. The friction drag coefficient is therefore by no means a constant quantity, but depends on local conditions.

For a plate with flow around both sides, the frictional force is obviously twice as high, since the frictional force acts on both sides:. In the article on boundary layers it was shown that the thickness of a laminar boundary layer is inversely proportional to the root of the local Reynolds number:.

This influence is now directly evident in the friction drag coefficients for laminar flow. For a turbulent flow, however, the relationship is the following:.Form drag known also as pressure drag arises because of the shape and size of the object. The pressure drag is proportional to the difference between the pressures acting on the front and back of the immersed body, and the frontal area.

This causes, that there can be a pressure difference between surfaces of the object. The general size and shape of the body are the most important factors in form drag. In general, bodies with a larger presented geometric cross-section will have a higher drag than thinner bodies. As can be seen from the figure, the drag force arises from the difference between the pressures acting on the front and back of the immersed body.

For this force can be calculated for this case simply using the definition of pressure as:. Since the head loss is roughly proportional to the square of the flow rate in most engineering flows, the total drag coefficient can be determined by simply adding the friction and pressure drag coefficients:.

## Drag equation

Reactor Physics and Thermal Hydraulics: J. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed. Lamarsh, A.

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Baratta, Introduction to Nuclear Engineering, 3d ed. Glasstone, Sesonske. Thermodynamics in Nuclear Power Plant Systems. Modern Fluid Dynamics. White Frank M. See above: Drag.Form drag known also as pressure drag arises because of the shape and size of the object.

The pressure drag is proportional to the difference between the pressures acting on the front and back of the immersed body, and the frontal area.

This causes, that there can be a pressure difference between surfaces of the object. The general size and shape of the body are the most important factors in form drag. In general, bodies with a larger presented geometric cross-section will have a higher drag than thinner bodies.

As can be seen from the figure, the drag force arises from the difference between the pressures acting on the front and back of the immersed body. For this force can be calculated for this case simply using the definition of pressure as:. Since the head loss is roughly proportional to the square of the flow rate in most engineering flows, the total drag coefficient can be determined by simply adding the friction and pressure drag coefficients:.

We hope, this article, Form Drag — Pressure Draghelps you. If so, give us a like in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.

The drag force arises from the difference between the pressures acting on the front and back of the immersed body. Thermal Engineering. Reactor Physics and Thermal Hydraulics: J. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed. Lamarsh, A. Baratta, Introduction to Nuclear Engineering, 3d ed. Glasstone, Sesonske. Thermodynamics in Nuclear Power Plant Systems. Modern Fluid Dynamics. White Frank M. See also: Drag. What is Parasitic Drag - Definition.In fluid dynamicsthe drag equation is a formula used to calculate the force of drag experienced by an object due to movement through a fully enclosing fluid.

The equation is:. The equation is attributed to Lord Rayleighwho originally used L 2 in place of A with L being some linear dimension. The reference area A is typically defined as the area of the orthographic projection of the object on a plane perpendicular to the direction of motion.

For non-hollow objects with simple shape, such as a sphere, this is exactly the same as a cross sectional area. For other objects for instance, a rolling tube or the body of a cyclistA may be significantly larger than the area of any cross section along any plane perpendicular to the direction of motion. Airfoils use the square of the chord length as the reference area; since airfoil chords are usually defined with a length of 1, the reference area is also 1.

Aircraft use the wing area or rotor-blade area as the reference area, which makes for an easy comparison to lift. Airships and bodies of revolution use the volumetric coefficient of drag, in which the reference area is the square of the cube root of the airship's volume. 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. For sharp-cornered bluff bodieslike square cylinders and plates held transverse to the flow direction, this equation is applicable with the drag coefficient as a constant value when the Reynolds number is greater than The equation is easier understood for the idealized situation where all of the fluid impinges on the reference area and comes to a complete stop, building up stagnation pressure over the whole area.

No real object exactly corresponds to this behavior. C D is the ratio of drag for any real object to that of the ideal object. In practice a rough un-streamlined body a bluff body will have a C D around 1, more or less. Smoother objects can have much lower values of C D.

The equation is precise — it simply provides the definition of C D drag coefficientwhich varies with the Reynolds number and is found by experiment. When flow velocity is doubled, for example, not only does the fluid strike with twice the flow velocity, but twice the mass of fluid strikes per second.

Therefore, the change of momentum per second is multiplied by four. Force is equivalent to the change of momentum divided by time. This is in contrast with solid-on-solid frictionwhich generally has very little flow velocity dependence.

Here the pressure P d is referred to as dynamic pressure due to kinetic energy of fluid experiencing relative flow velocity u.

## What is Form Drag – Pressure Drag – Definition

This is defined in similar form as kinetic energy equation:. The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved — under some conditions — are the:.

That this is so becomes apparent when the drag force F D is expressed as part of a function of the other variables in the problem:. This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, f a is some as-yet-unknown function that takes five arguments. Now the right-hand side is zero in any system of units; so it should be possible to express the relationship described by f a in terms of only dimensionless groups.

The most appropriate are the Reynolds number, given by. The original law is then reduced to a law involving only these two numbers. Because the only unknown in the above equation is the drag force F Dit is possible to express it as. Dimensional analysis thus makes a very complex problem trying to determine the behavior of a function of five variables a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number. If the fluid is a gas, certain properties of the gas influence the drag and those properties must also be taken into account.

Those properties are conventionally considered to be the absolute temperature of the gas, and the ratio of its specific heats. These two properties determine the speed of sound in the gas at its given temperature.

The Buckingham pi theorem then leads to a third dimensionless group, the ratio of the relative velocity to the speed of sound, which is known as the Mach number.Pls, WG gib Haida.

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