Drag Coefficient Report

7/23/2019 Drag Coefficient Report

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INTRODUCTION

In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the

drag or resistance of an object in a fluid environment such as air or water. It is used in the drag

equation where lower drag coefficient indicates the object will have less aerodynamic or

hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

figure 1: Measured drag Coefficient

The drag coefficient of any object comprises the effects of the two basic contributors to fluid

dynamic drag: skin friction and form drag. The drag coefficient of a lifting airfoil orhydrofoil also

includes the effects oflift-induced drag.

The drag coefficient of a complete structure such as an aircraft also includes the effects

ofinterference drag.

The drag equation:

is essentially a statement that the drag force on any object is proportional to the density of the

fluid and proportional to the square of the relative speed between the object and the fluid.
http://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Skin_frictionhttp://en.wikipedia.org/wiki/Form_draghttp://en.wikipedia.org/wiki/Airfoilhttp://en.wikipedia.org/wiki/Hydrofoilhttp://en.wikipedia.org/wiki/Lift-induced_draghttp://en.wikipedia.org/wiki/Interference_draghttp://en.wikipedia.org/wiki/Drag_(physics)http://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Skin_frictionhttp://en.wikipedia.org/wiki/Form_draghttp://en.wikipedia.org/wiki/Airfoilhttp://en.wikipedia.org/wiki/Hydrofoilhttp://en.wikipedia.org/wiki/Lift-induced_draghttp://en.wikipedia.org/wiki/Interference_draghttp://en.wikipedia.org/wiki/Drag_(physics)http://en.wikipedia.org/wiki/Forcehttp://en.wikipedia.org/wiki/Speed


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Cd is not a constant but varies as a function of speed, flow direction, object position, object size,

fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of

the object are incorporated into a dimensionless quantity called the Reynolds numberor .

is thus a function of . In compressible flow, the speed of sound is relevant and is also a

function ofMach number .

For a certain body shape the drag coefficient only depends on the Reynolds number ,

Mach number and the direction of the flow. For low Mach number , the drag coefficient

is independent of Mach number. Also the variation with Reynolds number within a practical

range of interest is usually small, while for cars at highway speed and aircraft at cruising speed

the incoming flow direction is as well more-or-less the same. So the drag coefficient can

often be treated as a constant.

For a streamlined body to achieve a low drag coefficient the boundary layeraround the body

must remain attached to the surface of the body for as long as possible, causing the wake to be

narrow. A high form drag results in a broad wake. The boundary layer will transition from

laminar to turbulent providing the Reynolds numberof the flow around the body is high enough.

Larger velocities, larger objects, and lowerviscosities contribute to larger Reynolds numbers.

For other objects, such as small particles, one can no longer consider that the drag

coefficient is constant, but certainly is a function of Reynolds number. At a low Reynolds

number, the flow around the object does not transition to turbulent but remains laminar, even up

to the point at which it separates from the surface of the object. At very low Reynolds numbers,without flow separation, the drag force is proportional to instead of ; for a sphere this is

known as Stokes law. Reynolds number will be low for small objects, low velocities, and high

viscosity fluids.

Figure 2: Flow past a Circular Cylinder at various Reynolds Numbers, continued
http://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Kinematic_viscosityhttp://en.wikipedia.org/wiki/Length_scalehttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Boundary_layerhttp://en.wikipedia.org/wiki/Wakehttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Stokes_lawhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Kinematic_viscosityhttp://en.wikipedia.org/wiki/Length_scalehttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Boundary_layerhttp://en.wikipedia.org/wiki/Wakehttp://en.wikipedia.org/wiki/Reynolds_numberhttp://en.wikipedia.org/wiki/Viscosityhttp://en.wikipedia.org/wiki/Stokes_law


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Figure 3 :Flow past a Circular Cylinder at various Reynolds Numbers

A equal to 1 would be obtained in a case where all of the fluid approaching the object is

brought to rest, building up stagnation pressure over the whole front surface. The top figure

shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the

left of it shows equal pressure across the surface. In a real flat plate the fluid must turn around

the sides, and full stagnation pressure is found only at the center, dropping off toward the edges

as in the lower figure and graph. Only considering the front size, the of a real flat plate wouldbe less than 1; except that there will be suction on the back side: a negative pressure (relative

to ambient). The overall of a real square flat plate perpendicular to the flow is often given as

1.17. Flow patterns and therefore for some shapes can change with the Reynolds number

and the roughness of the surfaces.
http://en.wikipedia.org/wiki/Stagnation_pressurehttp://en.wikipedia.org/wiki/Stagnation_pressure


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THEORY

It is a general experience that a body meets some resistance when it is forced to move through

a fluid especially liquid, such as difficulty to walk in water because of the much greater

resistance it present rather than air.

It is found that drag coefficient much convenient to work with dimensionless unit as it a function

of Reynolds number. The part of drag that is directly to wall shear stress is called skin friction

drag(or friction drag)as it caused by frictional effects, and the part is directly due pressure is

known as pressure drag(known as form drag due to strong dependence on the form or the

shape of the body).

Drag coefficient:


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Friction drag coefficient:

Pressure drag coefficient:

When the friction and pressure drag coefficients or forces are presented, total drag coefficients

or drag force can be determined. The drag force is the net force exerted by a fluid on a body in

the direction of flow due to the combined effects of wall shear and pressure forces.

Total drag coefficients;

Total drag force;

The contribution of friction drag is less at higher Reynolds number or might negligible at very

high Reynolds number due to pressure drag. While at low Reynolds number, especially highly

streamlined bodies case such as airfoils, is due to friction drag, bodies with larger surface area

result a larger friction drag, since friction drag is proportional to the surface area.

The pressure drag is proportional to the frontal area and to the difference between the pressure

acting on the front and back of the immersed body. The pressures drag most significant when

the velocity of the fluid is too high for the fluid to follow the curve of the body, and at some point,the fluids break away from the body and create a very low pressure region in the back, in this

case, due to large pressure difference between front and back sides of the body.


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Consideration of the physical factors which influence the drag force leads to the listing of the

following as principal variables:

FD the drag force on the sphere

D the diameter of the sphere

u the free stream velocity of the fluid

the density of the fluid

the viscosity of the fluid

Therefore, the following may be written:

),,,,(

= uDfFD (0)

or, supplying some constants,

.dcba

D uCDF = (0)

Using the mass-length-time systems of units and substituting the proper dimensions,

.32

dcb

a

LT

M

L

M

T

LL

T

ML

= (0)

Since the dimensions must be the same on both sides of the equation, the exponents must be

the same for each unit. Thus,

For M: dc+=1

For L: dcba += 31

For T: .2 db=

Solving these equations in terms ofd,

.1;2;2 dcdbda ===

Thus,

.122 dddd

D uCDF

= (0)


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Now, grouping variables according to exponents,

,22

d

D

DuuCDF

=

(0)

where

Du is a dimensionless group called the Reynolds number. Regrouping, this equation

can be rewritten in the general form

( ),Re22

fuD

FD =

(0)

that effectively reduces the number of variables to two dimensionless groups, which are, in turn,

functions of density, viscosity, diameter, and velocity. By varying any one or more of these

parameters, a correlation between the two groups can be formed.

An expression for the drag force on a body is usually given in the form

c

DDg

uACF

2

2

=

(0)

where,

CD is a dimensionless drag coefficient,

A is the frontal area of the body exposed to the flow (D2/4 for a sphere),

gcis the gravitational constant which allows the left hand side to be expressed in units of

force.

This expression can be related to equation 0 by solving for the drag coefficient:

( ).Re82

222f

uD

gF

uA

gFC cDcDD =

==

(0)

Therefore, the drag coefficient itself is a function of the Reynolds number.

Based on experiments on to measure drag coefficient of sphere


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Calculation of air density

Assuming ideal gas conditions, the density of air can be calculated using

=

Where R is the gas constant for air, R= 53.34

Calculation of velocity pressure from manometer reading

P= h

Calculation of free stream air velocity

By neglecting compressibility effects, the free stream air velocity can be derived from the

Bernoulli equation as:

Calculation of Reynolds number

The Reynolds number based on the sphere diameter is defined by the equation

Re =


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OBJECTIVE

To measure drag coefficient of sphere as a function of reynolds number.

DISCUSSION

TYPE OF DRAG COEFFICENT MEASUREMENT

Cylinder

A water tunnel is used to analyze the effects of fluid flow over a cylinder. As the water circulates

through the closed-loop system, the cylinder obstructs the path of the fluid flow causing the

water to deviate from its otherwise uninterrupted flow path. The uniform velocity profile of the

flow becomes non-uniform as the fluid passes by the cylinder. The drag caused by the cylinder

can be calculated through two different methods: control surface analysis consisting of pressure

measurements around the cylinder, and control volume analysis consisting of velocity

measurements taken before and after the cylinder. These experimentally obtained pressure and

velocity measurements provide the necessary data required to find the coefficient of drag of the

cylinder for this experiment. With these two methods of obtaining the drag coefficient, the fluid

flow around the cylinder can be observed, analyzed, and compared.

Sphere

The Handbuch values are based on experiments with falling or fixed spheres; and differences in

drag for rising and falling spheres have been previously observed by Hes selberg and Birkeland


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and others. It thus seems that the flow around a rising sphere is somehow different from that

around a falling one.

EXAMPLE OF EXPERIMENT

Description of Experimental Setup

Figure 1 Low speed wind tunnel

A manually controlled variable speed wind tunnel similar to that shown in Figure 1 was used in

this experiment. The wind tunnel was equipped with an integral force balance which measured

both drag and lift forces and a multistation manometer tube bank to measure the velocity of the

air stream. A separate pitot tube was used to verify the calibration of the built-in manometer. A

mercury barometer was used to measure the atmospheric pressure and a thermometer was

used to measure the air temperature.

APPARATUS


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1. Flotek 250 wind tunnel located in the Mechanical Engineering Laboratory (S/N FT250-2784)

2. 2.5-inch diameter smooth calibration sphere wind tunnel accessory

3. Pitot tube and differential manometer (Property tag BSW365-22984)

4. Mercury barometer fixed to the wall near the wind tunnel.

5. Mercury thermometer (Sargent brand, no tag or serial number)

APPLICATION

Drag coefficients are used in the calculation of particle terminal settling velocity of solids and

therefore used where the suspension or settling of solids particle will occur in chemical unit

operations. There are hundred of correlations relating the drag coefficient to the particle

Reynolds number and some form of measure of the particle shape (i.e sphericity). The particle

terminal settling velocity in turn can be used to calculate the hindered settling velocity, so it can

be used to help design solid-liquid mixers, clarifiers, thickeners, slurry transport in pipe

(i.e design a slurry pump), solid-liquid filters, it can also be used to design pneumatic transport

lines to name but a few. It can be used to help design unit operations where solid -fluid (liquid or

gas) will need to be mixed, transported or separated.

This topic is under the Fluid Mechanics branch. The drag force can be applied in many

things with regard for chemical engineering. for example, in a stream of air Oxygen can beabsorbed by another media, now knowing the drag force for air that will indicate along with

diffusion rate of Oxygen into the media how much Oxygen has been transferred also. To

calculate the temperature profile for some application that uses air as a cooling media, drag

force can be used. In separation drag force will tell how much component A has moved a long

with component B depending on the drag force of B.

ADVANTAGE AND DISADVANTAGE

Less road spray (i.e. better visibility for other road users)

Reduced dirt deposition on the tractor and semi-trailer

Reduced sensitivity to crosswinds, hence better steering


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Stability, less tyre wear and tear and improved driving comfort

Better safety (additional crumple zones, better protection against blind spot accidents)

Lower noise

MODELLING OF AERODYNAMIC

The drag coefficient (Cd) of a car tells you how well it cuts through the air. In other words, how

aerodynamically efficient it is. A low Cd figure brings three main benefits higher top speed,

better fuel consumption and quieter cruising.

A Lexus car spends thousands of hours in the wind tunnel during its aerodynamic development.

Yet achieving the optimum body shape is only the first of the refinements that ensure the car

slips through the air with the minimum of effort.

The precise and narrow gaps in Lexus bodywork also contribute significantly. So do flush-fittingwindows and trim, tyre spoilers behind the front wheels and ahead of the rear wheels, under-

body panels that streamline chassis components, and rear spoilers that reduce turbulence as

the airflow leaves the car.


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REFERENCES

D. M. Smiadak.2008. ,Fluid Mechanic: Drag Coefficient of a Sphere.

G. Bruschi, T. Nishioka, K.Tsang and R. Wang.,2003. A Comparison Of Analytical Methods.

Drag Coefficient Of A Cylinder.

A.W. Preukschat, 1962. Measurements of Drag Coefficients for Falling And Rising Spheres In

Free Motion. California Institute of Technology Pasadena, California

Joe, 2002. Determination of the Drag Coefficient of a Sphere.College of Engenieering and

Sciences,Louisiana Tech University.

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Drag Coefficient Report