TITLE
Drag force in flow over body
OBJECTIVE
To measure the drag coefficient CD, over the range of o f velocities in the test section for hemispherical (open end facing flow and open end facing down stream).
INTRODUCTION
The flow-related force vector acting on an immersed body can be divided into three named components, a drag (drag force), which acts in the flow direction, a lift (lift force) and a side force, all perpendicular perpend icular to each other. The lift usually is in the direction so that it does a useful job, for instance upwards for an airplane in horiontal flight or downwards for inverted wings on race cars. !n many cases the (time-mean) side force is ero, for instance when there is flow symmetry about the plane of lift and drag, as for an airplane flying in still air. "urther, "urther, the components can be divided up with respect to their origin, wall surface pressure and wall friction. The pressure component of the drag, the pressure drag, is often referred to as the form drag since it is is strongly dependent on the body form (shape). The remaining part is the friction friction drag, which is due to shearing viscous forces along the body surface. "low similarity laws are crucial for model testing e#periments. "or instance, the $eynolds similarity law says that for incompressible flow about two geometrically similar bodies, without any effects of free surfaces, the flow itself is similar, if tested at the same $eynolds $e ynolds number.
THEORY
Drag is the component of force on a body acting parallel to the direction of relative motion. The drag force, "D, was written in the functional form " D % f & (d, ', , ). *pplication of the +ucingham i theorem resulted in two dimensionless parameters that written in function form as F D & /
ρ V
/
d /
Vd = f / ρ µ
0ote that d/ is proportional to the cross-sectional area (* % 1d/23) and therefore we could write
= f 4 ρ Vd = f 4 ($e) & µ / ρ V A F D
/
*lthough 56. &.& was obtained for sphere, the form of e6uation is va lid for incompressible flow over any body7 the characteristic length used in the $eynolds 0umber depends on body shape.
The drag coefficient, CD, any body defined as
C D
=
F D & /
ρ V
/
A
APPARATUS
8ind tunnel and accessories
Figure 1 8ind tunnel
Figure 2 9emisphere body
Figure 4 b streamline body (No I!"#u$e$ i! %i& E'eri)e!*
Figure 5 9older2connecting rod
E+PERI,ENTAL PROCEDURES
&. The diameter of hemispherical is measured. This measurement will be use to calculate the $eynolds 0umber and projected area of hemisphere. /. The hemispherical body is fitted to the balance arm, open end facing flow first then open end facing downstream and finally airfoil body. 4. The inclined gage is set to ero, and the reading from drag scale is taen. 3. The blower fan is switch on and set the velocity to :m2s. ;. The reading was taen from the drag scale. <. The velocity is increased to :, &=, &/, &3, &<7 &: and /= m2s, and step ; is repeated. >. Then change the hemispherical body to open end facing downstream. :. Then step 4 to < is repeated and data are taen. ?. "inally change the end facing downstream to streamlined body. $epeat the same step. &=. *fter done the streamlined body e#periment, then placed only the connecting rod into wind tunnel. &&. Then step 4 to < is repeated and data are taen. &/. $eynolds no. and coefficient of drag of streamline object and hemispherical are calculated. &4. The @raph of $eynolds no. vs. drag coefficient is setch for both hemispherical and streamline object.
DATA AND RESULT
-RAPH
@raph & A upstream
@raph / A downstream
SA,PLE OF CALCULATION Temperature in fluids laboratory is /=o C . T % /=o C 4 ρ = &./=3kg 2 m −;
µ = &.:/; × &=
i.
kg m.s
Ne $r/g 0or"e
(u&re/)*
*t reading number / 0et drag force,
(upstream)%Drag force,
$igid rod drag force,
%=.4= B =.=/ %=./: 0 ii.
For $r/g "oe00i"ie! C D (u&re/)* &
*t reading number /, '% &= m2s =./: 0
C D&
=
F D & /
iii.
ρ V
/
D/
Ne $r/g 0or"e
($o3!&re/)*
*t reading number / 0et drag force,
(downstream) % Drag force, % =.=? B =.=/ % =.=> 0
i.
For $r/g "oe00i"ie! C D/ ($o3!&re/)*
*t reading number /,
$igid rod drag force,
'% &= m2s =.=> 0
.
For Ne Dr/g Coe00i"ie! C D
i.
For Re6!o#$& Nu)7er
*t reading number /,
MOHD AMIN B. MAHADZIR DISCUSSION
The drag coefficient values can be calculated after obtaining the drag force. The drag force can be taen by the e#periment. The $eynolds number, $e, also can be obtained using a formula and the data from the e#periment. $e
ρ VD =
µ
"rom the graph drag coefficient, CD
against $eynolds number, $e for hemisphere
0et
object that has been plotted, we can see that the highest drag coefficient C D % &./;4/ occur at $e % . *t this point the velocity of air act to the body is &3 m2s. +ut then the drag coefficient decrease dramatically to =.>:;? when the weight and drag force increase. *fter the drag drop down the value of drag coefficient sometimes is increase and sometimes is decrease."rom the both graph we can conclude that the drag coefficient CD increase when the $eynolds number decreasing from big to small numbers. *fter the drag coefficient CD was increase the $eynolds number also increased. o its mean that the value of drag is depend on their $eynolds number.The average of CD obtained from e#periment is &.<4=> for open end facing upstream =.;< for open end facing downstream and streamline body =./><=. Compare to the theoretical value, the drag coefficient, CD for open end facing upstream is &./ while for open end facing downstream is =.3 and streamline body is =.=3. The percentage of error of CD for the open end facing upstream is /<.3 then open end facing downstream is /:.; and finally for streamline body is :;.;=. "rom the percentage of error calculated, it is not much differ than the theoretical value.The error due to paralla# error occurs in this e#periment while taing the reading and also the error because of apparatus itself such as the air goes out from the hole around the holder that connected to the drag scale. *lso the balancing of the hemisphere body maybe unwell balanced.
MOHD AMIN B. MAHADZIR
CONCLUSION
The objective of the e#periment achieved. The percentage of error between theoretical value and e#perimental value is not much differing. There is no big difference between velocity and $eynolds number and can be concluded similarly same. The paralla# error occur in this e#periment is not constant thatEs mae the reading become difficult. The drag coefficient profile on the graph for open end facing flow and open end facing down stream is differ from each other due to streamlines and bluntness of the air flowing towards the hemisphere. !t is also due to the laminar and turbulent flow that occur during the process that taes place at different $eynolds number"rom the e#periment also it can be concluded that the higher the drag coefficient the higher the drag force involves. "or &=4F$eF4G&=; the drag coefficient is appro#imately constant. !n this range the entire rear of the sphere has a low pressure turbulent wae and most of the drag is caused by the front-rear pressure asymmetry.!n summarie, the drag, which contains portions due to friction (viscous) effects and pressure effects, is written in terms of dimensionless drag coefficients, CD. !t also shown that the drag coefficient, CD, is a function of shape and $eynolds 0umber, $e.
REFERENCES
•
"undamentals of "luid Hechanics, 3th 5dition, 8iley +ruce $. Hunson, Donald ". Ioung, Theodore 9. Jiishi
•
"luid Hechanics 4rd 5dition K." Douglas, K.H @aslore, K.* waffield
•
!ntroduction to "luid Hechanics
