Fluid Mechanics Lab 2 Copy

8/3/2019 Fluid Mechanics Lab 2 Copy

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LaboratoryReportFM2

WakeInterferenceandDragReduction

DipeshRana

11/1/11

TA:ParvezSukheswalla

ABSTRACT

Through the utilization of interference plates, a reduction of drag force on a bluff body can be

achieved. The reduction of drag can be applied to vehicles to improve efficiency. Potential flow

theory is explored in this experiment. Two modes of wake interference, cavity mode and wake-

impingement mode, are observed in the experiment. Cavity mode relies on driven, counter-

rotating vortices resulting in a decrease in the pressure experienced by the frontal face of the

cylinder. Wake-impingement mode relies on free vortices and results in more drag compared to

cavity mode. During wake-impingement mode, a Karman street is formed causing the excessivedrag. The experiment was benchmarked with a bare cylinder case and was compared with

different plate size and distance from the bar. Based on size and distance, optimum values of the

coefficient of drag were calculated to be 0.556 at a g/h value of 1.5 and a p/h value of 25%. In

some cases negative drag resulted in a thrust force. The bluff cylinder and plate were considered

as one unit and the optimum geometry was found.


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TableofContents

1. Summary .................................................................................................................................... 3

2. Experimental Methods ............................................................................................................. 5

2.1 Overall Layout................................................................................................................................... 5

2.2 Pitot-Static Tube ............................................................................................................................... 5

2.3 Test Components ............................................................................................................................... 6

2.4 Coefficients of Pressure and Drag ................................................................................................... 7

3. Wake Interference and Drag Reduction ................................................................................. 8

3.1 Drag coefficient and pressure distribution for bare cylinder ....................................................... 8

3.2 Mechanism for drag reduction by wake interference .................................................................. 10

3.3 Optimum Drag Reduction .............................................................................................................. 13

4. Concluding Remarks .............................................................................................................. 16

Appendix ...................................................................................................................................... 17

Appendix A: Post Script ....................................................................................................................... 17

Appendix B: Graphs ............................................................................................................................. 18

Appendix C: Tables .............................................................................................................................. 27

Appendix D: Additional Figures .......................................................................................................... 29

Appendix E: Bibliography.................................................................................................................... 29

TableofFigures

Figure 1: Windtunnel Layout .......................................................................................................... 5Figure 2: Pitot-Static Tube Layout ................................................................................................. 5

Figure 3: Test Components ............................................................................................................. 6

Figure 4: Cavity Mode Flow ......................................................................................................... 11

Figure 5: Wake Impingement Mode ............................................................................................. 12Figure 6: Cp vs y/h for Bare Cylinder Case .................................................................................. 18

Figure 7: Cp vs y/h for 37% Splitter Plate with g/h=1.5 ............................................................... 19Figure 8:Cp vs y/h for 37% Splitter Plate with g/h=4.0 ............................................................... 20Figure 9: Cd/CdBare vs g/h for 13% Splitter Plate ....................................................................... 21

Figure 10: Cd/CdBare vs g/h for 37% Splitter Plate ..................................................................... 22

Figure 11: CD/CDBare vs P/h ........................................................................................................... 23

Figure 12:CDSystem/CDBare vs P/h ................................................................................................... 24Figure 13: Evidence of Bistable Flow .......................................................................................... 25Figure 14: Plate Drag vs. Normalized Plate Height [1] ................................................................ 26

Figure 14: Free Vortex .................................................................................................................. 29Figure 15: Driven Vortex .............................................................................................................. 29


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1.Summary

The reduction of drag on a bluff body through the use of interference plates was

investigated in this experiment. Pressure sensors controlled by a Scanivalve pressure instrument

along with a Pitot-static tube allowed for the calculation of pressure coefficient distribution. A

Scanivalve has 24 locations and has pressure taps at each location; location 12 in this experiment

was the point of stagnation. The coefficient of drag for the bare cylinder case was calculated

using manual readings from the Scanivalve and voltmeter. The addition of interference plates

was introduced in the experimental setup causing a drastic reduction in the drag force on the

bluff cylinder body. The drag coefficient was measured based on the size of interference plates

and the how far in front of the bluff body they were placed. Interference plates of 13% and 37%

of the bars height were used in this experiment. A LabView program was utilized in order to

automate the acquisition of pressure values from the Scanivalve configuration. This allowed for

the experimentation of multiple distances from the bar with a particular interference plate. The

last portion of the experiment defines the system to include both the interference plate and the

bluff body as opposed to just the bluff body itself. This is a better overall representation of

system drag reduction because it takes into account the drag experienced by the plate. All in all,

multiple plots were generated and can be found in the Appendices.

When these plots were generated a strange effect was noted. In the plots for both the 13%

and 37% interference plates, there seemed to be a hazy, unstable region (see Figures 9 and 10).

At first glance, it seems as if the spontaneous variation of the drag coefficient was caused by

hysteresis. However, this is not a characterization of hysteresis. In fact, it is an intermittent mode

characteristic of the flow, where the flow erratically changes from wake-impingement mode to

cavity mode. The bi-stable flow region, occupied by the cavity mode and wake-impingement

mode, has characteristics of lower and higher drag, respectively (Figure 13). The oscillation of

the flow between the two regions is the source for the hazy region.

Moreover, there are two modes of wake interference experienced in this experimental

laboratory. The first is cavity mode, which relies on driven vortices (Figure 4). Cavity mode is

when the pressure on the front end of the cylinder decreases which in turn decreases the drag; the

velocity of the fluid is fastest outside the vortices. The other wake interference mode, wake-

impingement mode, has vortices that hit the front face of the bar resulting in higher frontal


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pressure. In this mode, free vortices dictate flow and have a maximum velocity at the center. The

vortices are essentially bashing against the frontal face of the square cylinder. Compared to the

cavity mode case, the coefficient of drag increases as a result of free vortices. Both cases

however reduce the drag considerably compared to a bare cylinder case.

Additionally, other objectives of this experiment were to find the optimal drag

coefficients of the overall systems including the bar alone and the bar with the interference plates

as a whole. For the case when the bar is an isolated system, measurements were taken for the

13% and 37% plates and other predetermined values were presented in Table 4. With a g/h value

of 1.5, the 50% plate had a negative drag coefficient value. This translates to a force thrust on the

plate rather than drag. Therefore, the 50% plate was actually more effective at reducing, or rather

eliminating the drag experienced by the square cylinder.

The optimal reduction of the drag coefficient for the entire system including the

interference plates was also found. The optimal plate was 25% of the bar height and a g/h ratio of

1.5. This optimal combination yielded the lowest drag on the overall system. Practical

applications of this experiment can be applied in numerous ways. A truck following a car (25%

the truck height) with a g/h ratio of 1.5, will experience drastically reduced drag while traveling

down a freeway as opposed to a truck traveling with no leading vehicle.


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2.ExperimentalMethods

2.1OverallLayout

The wind tunnel is comprised of three main sections: intake, test, and pumping section.

The intake section is comprised of a smooth intake nozzle, a settling chamber and then a

contraction section. The settling chamber is comprised of honeycombs and screens of decreasing

cross sectional area as shown in the figure. The honeycombs and screens are used to filter out

large-scale vortices and eddy currents. As the air then flows through the contraction area of the

wind tunnel, small-scale vortices are compressed and taken out of the flow as well. The airflow

goes through the test section, which will be discussed in greater detail later. As the air flows

through the diffuser it slows down. The 25 horsepower centrifugal blower pulls the air through

the entire system, and then outputs it to the acoustic diffuser, which damps out noise pollution.

Figure 1: Windtunnel Layout

2.2Pitot-StaticTube

The test section is made of Lucite

plastic in order to enable viewing of the

test piece. A door on the top of the test

section allows for access to the test

components. A pitot static tube is

located at the start of the test section. The

Air fromlaboratory

Settling Chamber:Honeycombs and screens

Smooth IntakeContraction

Diffuser

25 hp Centrifugal Blower

Acoustic Diffuser

Air FlowAir Flow

Test Section

Pitot - Static Tube

Test Components

PT

PS

PS

PT

Figure 2: Pitot-Static Tube Layout


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Pitot Static tube has a hole at the very tip, which measures the pressure at the stagnation point

or total pressure; the holes around the tube which measures the free stream pressure or static

pressure. Using Bernoullis principle:

! +1

2!

!= ! +

1

2!

!

Because the stagnation pressure occurs where the velocity is 0 the equation simplifies to the

following:

! = ! +1

2

!

where ! is the total pressure, !is the static pressure, and U is the velocity. From this we canderive the dynamic pressure as a function of the pressure difference.

=1

2

!= ! !

2.3TestComponents

The actual testing apparatus is comprised of a rack and pinion system, which is used to

control the spacing, g. A splitter plate can be placed in front of the square cylinder, which is

used to create turbulent flow. The splitter plate can be removed in order to measure the flow

around the bare cylinder. The flow is

measured through nineteen pressure

taps on the front and rear face of the

square cylinder. The pressure taps are

positioned along the vertical axis of

the front and rear face. A tap was place

at every .05 y/h, which resulted in a total number of 38 pressure taps. However, due to symmetry

about the y=0 plane, measurements are only recorded from taps at y/h=0 to y/h = 0.45.

The tubes from the pressure tap feed into a scanivalve. The scanivalve can automatically

cycle through the taps to take measurements. A computer using LabView gathers the data from a

pressure transducer that measures the pressure and outputs a voltage, which is used to populate

SquareCylinder

h

g

p

Rack and pinionSplitter Plate

y

Figure 3: Test Components


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data tables. When taking data manually, an averaging device is used over a time span of five

seconds to find a proper value due to the variation in pressure due to turbulent flow.

2.4CoefficientsofPressureandDrag

The surface pressures are normalized into a pressure coefficient Cp. This is done using

the following equation:

! = !

1/2!=

!

! !

Using this we can determine the Cp at every pressure tap location. Cp can vary between 0 and 1

for the front face of the bare case. While for the rear, vortices can create a slight vacuum and

therefore values of Cp can become negative. Values are usually around -1.6 for the rear face of

the bear case.

Ideally the drag coefficient CD is computed using integration. However due to the non-

continuous nature of data, numerical integration is used instead.

! = !!

Where Wn is a weighting function to take into account the area of the surface for which each Cp

is valid. Derivations for this can be found in section 2 of the lab manual [3].


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3.WakeInterferenceandDragReduction

3.1Dragcoefficientandpressuredistributionforbarecylinder

A starting point for the analysis of any fluid system is the Reynolds number. As always

the Reynolds number is the ratio of inertial forces to viscous forces. This can be expressed as:

!=

=

The velocity can be computed by the supplied formula in the lab handout, the kinematic

viscosity is given to be 1.5 10-5

m2/s and the height is that of the cylinder. In the experiment

the Reynolds number was 39053. This value is in the range anticipated for the formation of a

Karman vortex street.

The Reynolds number is important in this experiment because it is a key difference

between the experimental results and theoretical potential flow. Potential flow, also known as

inviscid flow is a method of simplifying the Navier-Stokes equations by neglecting all terms with

viscosity, assuming that the viscous effects are negligible. While in some cases this may be valid

it leads to several interesting results in the experiment which demonstrate its inappropriateness.

The primary flaw with potential flow in our experiment is dAlemberts Paradox, which is that

an object moving through a volume of a fluid at rest does not feel drag. The existence of a drag

force shows that the theory is inaccurate in the experiment providing an explanation for the

difference in pressure distribution. Potential flow also lacks a mechanism to account for

boundary layers. The Karman street is caused by the separation of boundary layers from the

bluff body and is responsible for the drag on the body, with no boundary layer basic potential

flow cannot capture this interaction. Techniques such as the use Riabouchinsky bodies can

approximate these effects but they are beyond the scope of this experiment and class.

Potential flow with the experimental conditions predicts a smooth pressure distributionover the front of the cylinder, equal and opposite to the one on the back of the cylinder leading to

a zero net force. The experimental results diverge substantially for the reasons outline above.

The actual pressure distribution on the rear face of the cylinder is almost uniform, (see Figure 6)

Using the coefficient of pressure allows for the coefficient of drag to be found, 2.318, a much

more reasonable result than potential flows zero. On the front face the actual pressure


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distribution is far closer to the predicted distribution, again in Figure 6, the difference between

the two is largest at the edges of the cylinder due to the existence of the boundary layer and its

effects on the flow. The similarity in the central region is due to the formation of the stagnation

point in the middle of the block as predicted in potential flow theory. The velocity at the

stagnation point is by definition zero and the pressure is solely a function of the upstream

conditions as in set in Bernoullis equation. Further away from the center of the cylinders face

the pressures diverge as the viscous effects neglected in potential flow manifest in the creation of

the boundary layer.

Another important factor in analysis is how the test set up matches to the assumptions

made in theory. In this experiment, conducted in a wind tunnel blockage is a concern. Blockage

is when the flow around the body in the wind tunnel is influenced by the presence of the walls.

Most fluid dynamics equations treat an infinite expanse of fluid, in reality the walls only a few

characteristic lengths away from the body. To correct to coefficient of pressure for blockage

several empirical equations have been developed, in this experiment the one by Maskell was

used.

!!"##$%&$' = !!"#$%&"' 1 1.5 + 1.5

Maskells formula is the above where B is the blockage ratio, the width of the body over the

width of the wind tunnel section. In the experiment B was 11%. A corrected list of the

coefficient of pressures can be seen in Table 1. With the corrected values a new coefficient of

drag can also be found, again in the same table. The corrected drag was 1.936, lower than the

uncorrected coefficient. This reduction can be explained by the walls forcing the flow to

accelerate as it passes around the body. By Bernoullis equation this leads to a lower pressure

past the body, causing a greater drag. By correcting for the flow acceleration the solution is

more in line with the infinite fluid solution.

A more direct method to correct for the blockage is to use the initial coefficient of drag

and conservation of mass. In the wind tunnel there is a constant volume transfer rate the velocity

of the flow multiplied by the area of the tunnel. The blockage ratio of the can be seen as the

reduction of area of the tunnel leading to an increase of velocity, this can be stated

mathematically as:


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!! = !! = ! 1 ! !"#$%& ! = !1

Cd is a function of the velocity, by using the corrected velocity a more accurate drag coefficient

can be found. In the uncorrected formula the drag coefficient is described as follows:

! =2

!

!!

!

!

Replacing the velocity with the average of the velocities gives:

!!"##$%&$' =8 1

!

2 !!

!!

!

!

=

!4 1 !

2 !

This equation gives a drag coefficient of 2.056, higher than that predicted by Maskell by 6.1%.

This is a fairly simplistic approach to the problem and it is likely a more sophisticated equation

with more information is needed to fully capture the effects of the blockage.

3.2Mechanismfordragreductionbywakeinterference

The experiment was concerned with drag reduction; a critical first step is to check if the

drag forces were actually reduced. As explained in the Experimental Methods section the

independent variables were the plate size and its distance from the cylinder. By changing thesevalues the coefficient of drag for the cylinder was affected. The coefficient of drag is the area

integral of the coefficient of pressure; by comparing the coefficients of the cases with plates

interfering with the bare cylinder case the efficiency of the plates on reducing the cylinders drag

can be seen.

In the bare cylinder case the coefficient of drag was 2.318. In both the 37% plate and the

13% plate cases the plate reduced the drag on the cylinder. When the plate was at g/h= 1.5 the

coefficient dropped to .104 for 37% and .693 for 13%. When the plate was located at g/h=4 thecoefficient of drag was .762 for the 37% case and no value was recorded for 13%. However

examining other points it can be seen that both plates reduce drag on the cylinder and there is a

minimum drag coefficient of the cylinder between g/h=0 and g/h=4. These values are tabulated

in Tables 2 and 3.They were calculated by integrating the areas between the front and back


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pressure coefficients plotted against the height of the block. Examples of this can be seen in the

appendix in Figures 7 and 8.

The reduction in the drag coefficient by moving the plate can best be seen by plotting it

as a function of g/h normalized by dividing by the coefficient of drag for the bare plate. The

plots showing this for the two cases, 13% and 37% plate heights can be seen in Figure 9 and

Figure 10 respectively. The coefficient of drag decreases on the cylinder but there is a

discontinuity that exists as g/h increases past a certain point. Other experiments have shown that

despite the hysteresis like appearance inside this discontinuity is actually a region of chaotic

mode switching. A time history of the mode switching can be seen Figure 13, as provided in

recitation. The discontinuous region is shaded in the figures. In the initial mode, at low g/h

values the coefficient of drag appears to asymptotically approach some value while after the

discontinuity it appears to be a linear increase. In all data points measured in both cases the plate

lowered the cylinders coefficient of drag. The two modes are known as cavity mode and wake

impingement mode respectively. The modes rely on driven vortices and free vortices for drag

reduction respectively. Driven vortices have the velocity profile shown in Figure 16, with the

fastest fluid at the outside. Free vortices are the opposite with the maximum velocity at the

center of the vortex as shown in Figure 15.

Figure 4: Cavity Mode Flow

Cavity mode occurs when two counter rotating driven vortices form in the region

between the plate and the cylinder. A drawing of this phenomenon can be seen at above in

Figure 4. The vortices effect can best be understood through a potential flow framework. In

potential flow fluid cannot cross streamlines; streamlines can thus be seen as solid boundaries.


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from the shear layer separation but with lower kinetic energy than in the bare case. This leads to

a higher but still negative pressure behind the cylinder as shown in Figure 8. The reduced drag is

caused by the kinetic energy of the flow being reduced around the cylinder leading to lower

velocity vortices. By Bernoullis this implies the vortices have lower pressure leading to the

results seen in the Figure. In addition the plate in front causes the flow to have a lower normal

velocity than in the bare case when it hits the front of the cylinder, leading to a lower pressure at

the stagnation point.

3.3OptimumDragReduction

In the initial parts of this experiment the drag reduction isolated the square cylinder as an

independent system and the optimal drag was found. That information is not of particular interest

in a practical setting, but finding the optimum drag reduction on the overall system containing

the plate is noteworthy. For specific values of!

!, such as0.37for the 37% case, an optimum

!

!

value was found in order to achieve optimal drag reduction of the overall system. Using values

graphed for!

!= 13%and

!

!= 37%,the optimal

!

!value is 1.5 giving the smallest coefficient of

drag ratio. The table found in Appendix C, Table 4, presents the data collected from the 13% and

37% experimental cases along with given values for other!

!cases. In order to determine the

optimal plate selection, the corresponding values of!!

!!!"#$

and!

!are plotted and presented in

Figure 11.

After careful observation of the plot in Figure 11, there is a region of interest where the

minimum!!

!!!"#$

falls below the horizontal resulting in a negative drag value. The negative drag

occurs after the optimal!!

!!!"#$

value and is a result of thrust on the square cylinder. There is a

thrust force on the bluff body because cavity vortices in the front of the body cause a lower

pressure on the front face than the pressure caused by rear vortices on the rear face (See Figure4).


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The last column of the table in Table 4, presents the numerical values for!!!"!

!!!"#$

,which is

calculated through rudimentary derivations shown below.

The drag on the system is defined as the summation of the drag on the cylinder and plate:

!"!#$% = !"#$%&'( + !"#$%

The ratio of!!"!#$%

!!"#$

can be presented through the following expression and presented using non-

dimensional quantities through the use of the coefficient of drag:

!"!#$%

!"#$

=

!"# +!"#$%

!"#$

=

!"#

1

2!

+!"#$%

1

2!

!"#$

1

2!

Since all quantities take on a non-dimensional form, the following reduction can take place:

!!"!#$%

!!"#$

=

! + !!"#$%

!!"#$

The coefficient of drag on the plate is based on plate width. For this experiment the following

equation calculates the value of!!"#$% as a function of!

!:

!!"#$%= 1.369

+ 0.862

The origin of the equation above was the result of a linear regression line measured by Purdy &

Sheridan. The linear regression line verifies the linear correlation between!!"#$% and

!

!values

and is presented in Figure 14.

The final ratio for!!!"!#$%

!!!"#$

incorporates the derivations from above resulting in the following

expression:


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!!"!#$%

!!"#$

=

!

!!"#$

+

!!"#$%

!!"#$

The overall system drag increases when then drag on the plate is included and represented by the

second half of the equation presented above. The overall system drag compared to the bare

cylinder is graphically presented in Figure 12. The plot has a U shape where extreme values of

!

!result in a

!!!"!#$%

!!!"#$

ratio of near 1. Otherwise, the ratio is fairly constant fluctuating within the

0.2 to 0.4 range. From the data presented, the optimal coefficient of drag for the system is equal

to 0.556, and occurs at a plate size of!!

=0.25. The coefficient of drag on the system was foundby multiplying the coefficient of drag on the bare plate, 2.318, with the ratio!!!"!#$%

!!!"#$

, which is

equal to 0.239. At this value of!

!,the coefficient of drag on the plate is equal to 1.204 (Table 4).

The optimum coefficient of drag reduction equals -0.23 at!

!=0.75;since the value of the

coefficient of drag is negative there is a resulting thrust on the system. This does not make for a

realistic setup; therefore choosing the optimal ratio of!!!"!#$%

!!!"#$

makes the system performance

most efficient in a practical setting. The optimal ratio occurred at a!

!value of 0.25 and a drag

minimum of 0.239. By looking Figures 9 and 10, a conclusion can be drawn that the minimum!

!value occurs at 1.5. Therefore a summary of the practical values includes a !

!value of 0.25 and

a!

!value of 1.5 in order to achieve minimum overall system drag.


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4.ConcludingRemarks

As seen in this experiment, putting a small splitter plate in front of a larger bluff body can

significantly reduce the overall drag of the system. The main cause for this is due to the concept

of aerodynamic shapes. The small plate acts like the tip of a bullet and begins the flow

separation, reducing the drag on the bluff body. When the wake interference pattern is in the

cavity mode, which is when counter-rotating vortices are between the plate and the cylinder, the

overall system assumes a shape similar to that of a bullet, an incredibly aerodynamic shape.

Also, the swirling vortices lower the pressure in front of the cylinder so significantly it can

sometimes experience a forward force. This is the reason that the drag of the entire system is at

its lowest when counter-rotating vortices are formed. This occurs at about a g/h of 1.5. When the

g/h is larger, between two and five, a mode known as wake impingement occurs. In this case, the

wake behind the plate forms free vortices known as a Karman street. This also lowers the

pressure in front of the cylinder, as well as makes the flow turbulent, which has lower kinetic

energy impacting the front face. For these reasons the drag is reduced.

This concept has many applications in the real world. There are many current

technologies that already use the concept of splitter plate drag reduction. Many racing bicycles

come with handlebars that place the riders hands together, at the centerline of the bike, and far

forward. Downhill skiers duck and push their hands forward to create a splitter plate out of their

hands. In vehicles, putting such a plate about six to eight feet in front of cars and ten to fifteen

feet for SUVs and trucks would greatly increase fuel efficiency. A technology to extend and

retract such a system from the front bumper of a car would be incredibly helpful for developing

this technology.


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Appendix

AppendixA:PostScript

We are given that the power is constant. Knowing that we have the following two equations:

= !

!!"#$!"#$ = !!"#$!"#$

where FD is the drag force and U is the velocity. Knowing the force of drag is described by the

following equation:

! =1

2

!!

we get that

!!"#!!"#$! = !!"#$!"#$!

from this we can solve for!!"#$

!!"#$

!"#$

!"#$

= !!"#$!!"#$

!

!"#$

!"#$

= 2.3180.104

!

= 2.814

Therefore, the truck is moving at 182.9 mph if it is the second truck in a convoy. However, this

is making many assumptions, mainly that the CD values do not scale with velocity, which is not

true.

Fluid Mechanics Lab 2 Copy

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