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Laboratory Report 4 Wind Tunnel

Prepared by: Group 4

Cooper Auge John Bergum Alex Franke Ryan Kunz Gage Wavra

Prepared for:

Dr. Vida Atashi

University of North Dakota Civil Engineering Department CE 423 Civil Engineering Hydraulic Engineering Laboratory – Spring 2024

Lab Completed: 02/06/2024

Date Submitted: 02/13/2024

Rectangle

Table of Contents

1. Introduction........................................................................................................................................1

2. Objectives...........................................................................................................................................2

3. Experimental Design...........................................................................................................................2

4. Relevant Equations.............................................................................................................................3

5. Equipment and Materials....................................................................................................................5

6. Procedures..........................................................................................................................................5

7. Results................................................................................................................................................5

8. Discussion and Conclusions..............................................................................................................13

9. References........................................................................................................................................13

10. Appendices...................................................................................................................................14

10.1 Appendix A....................................................................................................................................14

10.2 Appendix B.....................................................................................................................................16

iii

List of Tables

Table 1 Test Data for 113 ft/s Flow.............................................................................................................7

Table 2 Test Data for 102 ft/s Flow.............................................................................................................9

Table 3 Test Data for 98 ft/s Flow.............................................................................................................11

Table 4 Experimental Results Summary for Each Tested Flow Velocity..................................................13

List of Figures

Figure 1 Experimental Design Diagram........................................................................................................3

Figure 2 Static Pressure vs Angular Position for 113 ft/s Flow...................................................................8

Figure 3 Static Pressure vs Angular Position for 102 ft/s Flow.................................................................10

Figure 4 Static Pressure vs Angular Position for 98 ft/s Flow...................................................................12

Figure 5 Schematic for Angular Positions on Cylinder...............................................................................16

Figure 6 Published Values for the Drag Coefficient....................................................................................16

1. Introduction

Air flow with varying Reynolds numbers (Re) around a circular cylinder in a wind tunnel

produces distinct effects on the calculation of their corresponding drag coefficients (Cd).

Reynolds number represents the ratio of inertial forces to viscous forces and is crucial in

determining flow state characteristics. “…the drag force on the static cylinder increases, reaches

a maximum value, decreases, and stabilizes” (P.V.S. Souza, 2017). At low Reynolds numbers,

the flow around the cylinder is laminar, characterized by smooth and orderly layers of air. In this

state, the drag coefficient tends to be relatively low and stable. However, as Reynolds number

increases, the flow transitions into a turbulent state, marked by chaotic and irregular motion of

air particles. In the turbulent state, the drag coefficient typically increases due to the intensified

mixing and separation of airflow around the cylinder.

In wind tunnel experiments, observing the effects of Reynolds numbers on drag coefficients

helps engineers and researchers understand aerodynamic behavior under different flow

conditions. “The drag coefficient expresses the ratio of the drag force to the force produced by

the dynamic pressure times the area. In a controlled environment (wind tunnel) the velocity,

density, and area can be set so the drag force can be measured. Through division we arrive at a

value for the drag coefficient” (Wind Tunnel- Force, 2015). Low Reynolds numbers often result

in predictable and steady flow patterns, enabling accurate predictions of drag coefficients. As

Reynolds numbers increase, the transition to turbulent flow introduces complexities such as

increased drag, vortex shedding, and separation regions, leading to higher drag coefficients. By

systematically varying Reynolds numbers in wind tunnel experiments, scientists can map out the

aerodynamic characteristics of the cylinder across different flow regimes, providing valuable

insights for designing efficient structures and vehicles.

Additionally, the point of highest pressure is located at the stagnation point. Generally, the

leading edge of the shape where flow velocity is zero is the point at which the stagnation point

occurs (Dockter, 2024). Velocity head is minimized to zero. The net pressure can be added up to

calculate the net pressure change on the object in the cylinder.

2. Objectives

The objective of this lab was to examine the effects of air flow with different Reynolds

numbers (Re) around a circular cylinder in a wind tunnel with the intention of calculating

their corresponding drag coefficient (C ¿¿d)¿. To do so, the experiment will be performed at

three different air flow rates (v0), and 19 different pressure head (h in inches of H 2O) values

that are measured from tubes connected to the cylinder. The data was captured and computed

into this report, and sample calculations are shown.

3. Experimental Design

The experimental set up consists of a wind tunnel with a test cylinder of known height

and diameter set within the tunnel. A series of 19 manometers is connected to one side of the

cylinder to measure the pressure head (hi) for various points covering 180 ° of the cylinder’s

circumference. At its rear end, the wind tunnel has a series of stacked tubes to attempt to

stimulate laminar flow into the test area. The front (exit) end of the tunnel consists of a large

fan to bring the air up to a certain air flow speed (v0). Having measured the different pressure

head values, the data can be compiled into a table and static pressure (P-Static), incremental

drag force ¿, and total drag force ¿ can be calculated.

4. Relevant Equations

The static pressure (P or ) can be found by taking the difference of the maximum pressure

head (hmax) and the pressure head (hi∨hx) at various points on the cylinder, and multiplying

it by a conversion factor to convert inches H 2O to lbs

ft2 .

Pi( lbs ft2 )=(hmax−hx)(5.20

lbs

ft3

inches H 2O )

The incremental drag force (∆ Fd) at a selected point can be calculated using the static

pressure at that point (Pi), known height of the cylinder (H=0.875 ft ), known diameter of

the cylinder (D=0.292 ft ), and the angular position (θ) at the selected point.

∆ Fd , i ( lbs )=2π (Pi)(HD)( ∆θ 360 °

)(cos (θ ))

The incremental drag force for each of the 19 points can be added together ¿ to find the total

drag force for half of the cylinder. This value only accounts for half of the total drag force

Figure 1 Experimental Design Diagram

value because the 19 points of measurement are only located on one side of the cylinder.

Therefore, the total drag force (Fd) can be calculated as such.

Fd ( lbs )=2(∑ ∆ Fd ,i)

Next, the air flow velocity (vo) can be calculated from the max static pressure value (Pmax),

and the density of air (ρair). The air flow velocity will be determined for each of the three

tests to calculate the succeeding values needed for this experiment. Also, the density of air is

found with an equation that includes barometric pressure, a given gas constant for air (R),

and the ambient temperature (T). The calculated density of air is shown in the laboratory

manual for this experiment (ρair=0.00229 slugs

ft3 ¿ .

v0( ft s )=√ 2(Pmax)

ρair

The Reynolds Number (Re) for a selected air flow can be calculated by using the calculated

stream velocity (vo¿, given cylinder diameter (D), calculated density of air (ρair), and the

dynamic viscosity of air (μ) which can be found in the Table of Mechanical Properties of air

at T ambient, the value of which is equal to 3.85 x10−7( lbs × s

ft2 ). The equation is given as

follows.

ℜ= vo D ρair

μair

To calculate the drag coefficient for a certain air flow around the test cylinder, the projected

area ( Ap) must first be calculated. The equation for which is shown below and is based on

the given values of height (H) and diameter (D) of the cylinder.

Ap ( ft2 )=HD

The drag coefficient (Cd ) equation comes from combining the calculated values of total drag

force (Fd), projected area ( Ap), air flow velocity (vo¿ for each of the three different air speeds.

This calculated value can be compared to the published drag coefficient which can be found by

inspecting the published Wind Tunnel Drag Coefficients chart for a rough cylinder.

Cd= Fd

ρair vo 2

5. Equipment and Materials

 Wind tunnel.

 Circular cylinder.

 Series of nineteen manometers connected to the test cylinder.

6. Procedures

First place the circular cylinder into the wind tunnel before turning it on. You are then to

set a speed at which the fan will run. Then, read the different manometer readings which will

be used to calculate the force on the cylinder. Repeat this with two more additional fan

speeds to complete the data collection portion of this lab.

7. Results

In the following discussions the published drag coefficient is referred to. These published

drag coefficients are the drag coefficients determined by the graph in Appendix B for a rough

cylinder. These are compared with the calculated drag coefficient throughout this report.

Appendix B also shows a picture explaining the angular positions used throughout the

experiment. The point at which θ=0 is the far-left side of the picture. The first manometer is at

the 5˚ position and increased by 10˚ from there to get the position of the next manometer.

Tables 1, 2, and 3 show the data collected at each of the 19 manometers for the 113 ft/s, 102

ft/s, and 98 ft/s air flows, respectively. Each manometer’s angular position is given for the point

of the cylinder that it represents. The density of air, dynamic viscosity, and Reynolds number for

the flows are shown at the bottom of each table. From these values, the static pressure, drag

force, and cumulative drag force were calculated values and are displayed in each table. This

value is two times the cumulative drag force found because we only analyzed one side of the

cylinder. These were calculated using the equations in part 4 of this report. Finally, the drag

coefficient was determined, this is shown at the bottom of each table.

Figures 1, 2, and 3 show the relationship between static pressure and angular position.

As one can see, the static pressure is 0 where the maximum manometer reading occurred. The

static pressure and the manometer readings are inversely related. When the readings are high on

the manometers, the calculated static pressures are lower. In all the figures the stagnation point

occurs at the smallest angular position (θ=0), this is where the static pressure is maximized.

Table 1 displays the data for the 113 ft/s flow. The highest static pressure found in this trial

was 43.2 and it occurred at cumulative 75˚. The minimum reading, 43.2 occurred at the point

closest to the stagnation point (θ=5˚). This was the highest pressure seen between all the trials

since this flow was the fastest. After all the calculations had been completed, the cumulative

drag force was found to be 1.094lbs. From this, the drag coefficient for the 113 ft/s flow was

determined to be 0.29. This was considerably lower than the published drag coefficient of 0.91.

Table 1 Test Data for 113 ft/s Flow

Velocit y

(ft/sec)

Pressur e

Sensor

Static Pressur

e (in, H2O)

P-Static (lb/ft2)

Δ Ө (degrees

)

∑Ө (degrees

) Cos ∑Ө Δ Fd (lb) Cumulative

∑Fd (lb)

112.77 hmin 40.4 0 hmax 43.2 14.56 h1 40.4 14.56 5 5 0.9962 0.3234 0.3234 h2 40.5 14.04 10 15 0.9659 0.6048 0.9282 h3 40.8 12.48 10 25 0.9063 0.5044 1.4325 h4 41.2 10.4 10 35 0.8192 0.3799 1.8124 h5 41.6 8.32 10 45 0.7071 0.2623 2.0748 h6 42.3 4.68 10 55 0.5736 0.1197 2.1945 h7 42.9 1.56 10 65 0.4226 0.0294 2.2239 h8 43.2 0 10 75 0.2588 0.0000 2.2239 h9 43.1 0.52 10 85 0.0872 0.0020 2.2259 h10 43.1 0.52 10 95 -0.0872 -0.0020 2.2239 h11 43.1 0.52 10 105 -0.2588 -0.0060 2.2179 h12 42.7 2.6 10 115 -0.4226 -0.0490 2.1689 h13 41.2 10.4 10 125 -0.5736 -0.2660 1.9029 h14 42.3 4.68 10 135 -0.7071 -0.1476 1.7553 h15 42.2 5.2 10 145 -0.8192 -0.1899 1.5654 h16 40.8 12.48 10 155 -0.9063 -0.5044 1.0610 h17 42.3 4.68 10 165 -0.9659 -0.2016 0.8594 h18 42.3 4.68 10 175 -0.9962 -0.2079 0.6515 h19 42.3 4.68 5 180 -1.0000 -0.1043 0.5471

Fd = 1.0943

*ρair = 0.0023 slugs/ft3

*μ = 3.85*10-7 ft2/sec

*Re = (vDρair)/μ *= (112.77*0.292*0.00229)/(3.85*10-7) = 195855 *Cd = Fd/(v2Apρair/2)

= 1.0943/(0.292*0.875*0.00229*112.772/2) 0.29

In Figure 1, the relationship between static pressure and angular position is shown for the

113 ft/s flow. From the figure, it is seen that the minimum static pressure occurred at angular

position 75˚. As one follows the perimeter of the cylinder, static pressure starts high, lowers to

zero, then experiences two surges in pressures before falling back down again. These peaks seem

absurd, but they also occurred in Figure 2 and Figure 3.

0 20 40 60 80 100 120 140 160 180 0

Velocity = 112.77 ft/s

Angular Position ( ∑Ө )

Pr es

su re

(l b/

ft^ 2)

Figure 2 Static Pressure vs Angular Position for 113 ft/s Flow

Table 2 displays the data for the 102 ft/s flow. In this trial, the maximum manometer

reading was 42.6 and occurred at angular position 75˚. The minimum reading, 40.9 occurred at

the point closest to the stagnation point (θ=5˚). The cumulative drag force was calculated to be

0.577lbs. From this the value of 0.19 was obtained for the drag coefficient. The slower flow

analyzed in Table 2 resulted in a lower drag coefficient than the one found in the faster flow

analyzed in Table 1. Although the drag coefficient was supposed to be slightly lower for this

lower flow than the 113 ft/s flow, it still was significantly lower than the published value of 0.89.

Table 2 Test Data for 102 ft/s Flow

Velocit y

(ft/sec)

Pressur e

Sensor

Static Pressur

e (in, H2O)

P-Static (lb/ft2)

Δ Ө (degrees

)

∑Ө (degrees

) Cos ∑Ө Δ Fd (lb) Cumulative

∑Fd (lb)

102.20 hmin 40.9 3.12 hmax 42.6 11.96 h1 40.9 11.96 5 5 0.9962 0.2657 0.2657 h2 41 11.44 10 15 0.9659 0.4928 0.7584 h3 41.1 10.92 10 25 0.9063 0.4413 1.1997 h4 41.4 9.36 10 35 0.8192 0.3419 1.5417 h5 41.6 8.32 10 45 0.7071 0.2623 1.8040 h6 42.1 5.72 10 55 0.5736 0.1463 1.9503 h7 42.4 4.16 10 65 0.4226 0.0784 2.0287 h8 42.6 3.12 10 75 0.2588 0.0360 2.0647 h9 42.5 3.64 10 85 0.0872 0.0141 2.0789 h10 42.5 3.64 10 95 -0.0872 -0.0141 2.0647 h11 42.5 3.64 10 105 -0.2588 -0.0420 2.0227 h12 42.3 4.68 10 115 -0.4226 -0.0882 1.9345 h13 41.9 6.76 10 125 -0.5736 -0.1729 1.7616 h14 42 6.24 10 135 -0.7071 -0.1968 1.5648 h15 42 6.24 10 145 -0.8192 -0.2279 1.3369 h16 41.2 10.4 10 155 -0.9063 -0.4203 0.9166 h17 42.1 5.72 10 165 -0.9659 -0.2464 0.6702 h18 42.1 5.72 10 175 -0.9962 -0.2541 0.4161 h19 42.1 5.72 5 180 -1.0000 -0.1275 0.2886

Fd = 0.5771

*ρair = 0.0023 slugs/ft3

*μ = 3.85*10-7 ft2/sec

*Re = (vDρair)/μ *= (102.2*0.292*0.00229)/(3.85*10-7) = 177504 *Cd = Fd/(v2Apρair/2)

= 0.5771/(0.292*0.875*0.00229*102.22/2) 0.19

Figure 2 shows the relationship between static pressure and angular position for the 102

ft/s flow. This figure looks very similar to Figures 1 and 3 as it should, but there is only 1

distinct peak. The first peak after the static pressure goes to zero is not as clear as it is in Figures

1 and 3.

0 20 40 60 80 100 120 140 160 180 0

Velocity = 102.2 ft/s

Angular Position ( ∑Ө )

Pr es

su re

(l b/

ft^ 2)

Figure 3 Static Pressure vs Angular Position for 102 ft/s Flow

Table 3 shows the data for the 98 ft/s flow. In this trial the maximum manometer reading

was 42.4 and occurred at the angular position 75˚. The minimum reading, 41.4 occurred at the

point closest to the stagnation point (θ=5˚). The cumulative drag force was calculated to be

0.1345. Due to this, the drag coefficient was 0.05, which was much lower than the 113 ft/s and

102 ft/s trials. In all three trials, the drag coefficient was much lower than the published value.

For the 98 ft/s flow this value was supposed to be around 0.80.

Table 3 Test Data for 98 ft/s Flow

Velocit y

(ft/sec)

Pressur e

Sensor

Static Pressur

e (in, H2O)

P-Static (lb/ft2)

Δ Ө (degrees

)

∑Ө (degrees

) Cos ∑Ө Δ Fd (lb) Cumulative

∑Fd (lb)

97.658 hmin 41.1 4.16 hmax 42.4 10.92 h1 41.1 10.92 5 5 0.9962 0.2426 0.2426 h2 41.2 10.4 10 15 0.9659 0.4480 0.6905 h3 41.3 9.88 10 25 0.9063 0.3993 1.0898 h4 41.5 8.84 10 35 0.8192 0.3229 1.4127 h5 41.7 7.8 10 45 0.7071 0.2460 1.6587 h6 42 6.24 10 55 0.5736 0.1596 1.8183 h7 42.3 4.68 10 65 0.4226 0.0882 1.9065 h8 42.4 4.16 10 75 0.2588 0.0480 1.9545 h9 42.3 4.68 10 85 0.0872 0.0182 1.9727 h10 42.3 4.68 10 95 -0.0872 -0.0182 1.9545 h11 42.3 4.68 10 105 -0.2588 -0.0540 1.9005 h12 42.2 5.2 10 115 -0.4226 -0.0980 1.8025 h13 41.5 8.84 10 125 -0.5736 -0.2261 1.5764 h14 42 6.24 10 135 -0.7071 -0.1968 1.3796 h15 42 6.24 10 145 -0.8192 -0.2279 1.1517 h16 41.3 9.88 10 155 -0.9063 -0.3993 0.7524 h17 42 6.24 10 165 -0.9659 -0.2688 0.4836 h18 42 6.24 10 175 -0.9962 -0.2772 0.2064 h19 42 6.24 5 180 -1.0000 -0.1391 0.0673

Fd = 0.1345

*ρair = 0.0023 slugs/ft3

*μ = 3.85*10-7 ft2/sec

*Re = (vDρair)/μ *= (97.658*0.292*0.00229)/(3.85*10-7) = 169615 *Cd =

Fd/(v2Apρair/2) = 0.1345/

(0.292*0.875*0.00229*97.6582/2) 0.05

Figure 3 shows the relationship between static pressure and angular position for the 98

ft/s flow. This figure looks like Figures 1 and 2, but with lower maximum values and higher

minimum values. The two peaks after static pressure was minimized are distinct, unlike Figure

2. The minimum pressure in Figure 3 was significantly higher than the minimum values in

Figures 1 and 2.

0 20 40 60 80 100 120 140 160 180 0

Velocity = 97.658 ft/s

Angular Position ( ∑Ө )

Pr es

su re

(l b/

ft^ 2)

Figure 4 Static Pressure vs Angular Position for 98 ft/s Flow

Table 4 compares the calculated drag coefficients with the published drag coefficients

found by the graph in Appendix B. By looking at the table, one can see that with slower flows,

the difference between the calculated and published drag coefficients got much higher. Even

though the published drag coefficients got smaller with slower flows, the calculated drag

coefficients dropped faster so the differences increased. The trend of the calculated values being

significantly lower than the published values must have been due to the head loss through the

tubes making up the manometers.

Table 4 Experimental Results Summary for Each Tested Flow Velocity

Trial # Velocity

(ft/s) Reynold's Number

Calculated Drag

Coefficien t

Published Drag

Coefficien t

Difference in Drag

Coefficient s

1 112.8 1.959*105 0.29 0.91 68.13%

2 102.2 1.775*105 0.19 0.89 78.65%

3 97.66 1.696*105 0.05 0.80 93.75%

8. Discussion and Conclusions

The objective of this lab was to examine the effects of air flow with different Reynolds

numbers (Re) around a circular cylinder in a wind tunnel with the intention of calculating their

corresponding drag coefficient (C ¿¿d)¿. For the velocity of 113 ft/s the found drag coefficient

was found to be 0.29. This is much less than the expected value of 0.91, leading to a difference

of 68.13%. For a velocity of 102 ft/s the calculated drag coefficient was found to be 0.19. The

expected value is determined to be 0.89. This leads to an error of 78.65%. For the last velocity

of 98 ft/s, the drag coefficient was calculated to be 0.05. This calculation has the most

calculated error, with the expected value to 0.80, the difference between the two is 93.75%. In

conclusion, there seemed to be a lot of error within this lab. Our group compared data with

other groups and their findings were similar, this leads to a conclusion of the experiment having

some reoccurring unknown flaw or head-loss within the manometer tubing.

9. References

Dockter, B. (2024). Laboratory #4.

P.V.S. Souza, D. G. (2017). Drag force in wind tunnels: A new method. Physica A: Statistical Mechanics and its Applications, 120-128.

Wind Tunnel- Force. (2015). Wind Tunnel Fundamentals.

10. Appendices

10.1 Appendix A.

Sample calculations will be based on Tube # h10 for the first air flow velocity of 112.77 ft/s.

Equation I

P10=( hmax−hx ) (5.20 )= lbs

ft 2

P10=(43.2inches H 2O−43.1inches H 2O )(5.20 lbs

ft2

inches H 2O )=0.52 lbs ft2

Equation II

∆ Fd , 10=2π (P i)(HD )( ∆ θ 360 °

)(cos (θ ))=lbs

∆ Fd10=2 π (0.52 lbs

ft2 )(0.875 ft)(0.292 ft)( 10 ° 360 ° ) (0.08756 )=0.00203 lbs

Equation III

Fd=2 (∑ ∆ Fd ,1−19 )=lbs

Fd=2 (0.54714 lbs )=1.0943 lbs

Equation IV

v0=√ 2 ( Pmax ) ρair

= ft s

vo=√ 2(14.56 lbs ft 2

)

0.00229 slug

ft3

=112.7659 ft s

Equation V

ℜ= vo D ρair

μair

=¿

ℜ= (112.7659 ft

s )(0.292 ft )(0.00229 slug

ft3 )

(3.85 x10−7 lbs× s ft2

) =1.9586 x105

Equation VI

Ap ( ft2 )=HD=ft2

Ap=(0.875 ft ) (0.292 ft )=0.2555 ft2

Equation VII

Cd= Fd

ρair vo 2

=¿

Cd= 1.0943lbs

(0.2555 ft2) (0.00229 slug

ft3 )(112.7659 ft s )

=0.29

10.2 Appendix B.

Figure 5 Schematic for Angular Positions on Cylinder

Figure 6 Published Values for the Drag Coefficient