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Fluid Bluff Body

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1. Develop a calibration curve with the voltages that were taken, in order to determine the velocity at any voltage. You must determine the velocity at each frequency of the stepper motor. If you think of the frequency as being equivalent to some number of cycles per second, then 1 cycle is equal to 1 step. The travel is equivalent to 0.00086’’ per step. Then, use the polyfit and polyval functions in MATLAB to obtain a 5th order polynomial that will fit your data. Polyfit and polyval use the least squares approach to fit the data. Remember, you calibrated the sensor for two directions of flow, so one direction must be considered to be negative velocities and the other direction should be considered positive velocities. Refer to the direction where you only calibrated from 0 to 0.8 kHz as being negative velocity. Display your left, right, and average voltage markers for each known velocity, along with the calibration curve with velocity in meters/second on the x-axis and voltage in volts on the y-axis.
Table 1 – Data for calibration Direction | Frequency (kHz) | Velocity (m/s) | Voltage, left (V) | Voltage, right (V) | Average Voltage (V) | Positive | 0.8 | -0.0175 | 0.1203 | 0.1209 | 0.1206 | | 0.6 | -0.0131 | 0.1323 | 0.1299 | 0.1311 | | 0.4 | -0.00874 | 0.1328 | 0.1365 | 0.1346 | | 0.2 | -0.00437 | 0.1407 | 0.1411 | 0.1409 | | 0 | 0 | 0.1441 | 0.1413 | 0.1427 | Negative | 0 | 0 | 0.1400 | 0.1423 | 0.1411 | | 0.2 | 0.00437 | 0.1413 | 0.1436 | 0.1424 | | 0.4 | 0.00874 | 0.1509 | 0.1510 | 0.1510 | | 0.6 | 0.0131 | 0.1530 | 0.1561 | 0.1546 | | 0.8 | 0.0175 | 0.1576 | 0.1569 | 0.1572 | | 1 | 0.0218 | 0.1659 | 0.1635 | 0.1647 | | 1.2 | 0.0262 | 0.1735 | 0.1744 | 0.1740 | | 1.4 | 0.0306 | 0.1812 | 0.1840 | 0.1826 | | 1.6 | 0.0350 | 0.1960 | 0.1990 | 0.1975 | | 1.8 | 0.0393 | 0.2030 | 0.2044 | 0.2037 | | 2 | 0.0437 | 0.2190 | 0.2222 | 0.2206 | | 2.2 | 0.0481 | 0.2333 | 0.2337 | 0.2335 | | 2.4 | 0.0524 | 0.2469 | 0.2491 | 0.2480 | | 2.6 | 0.0568 | 0.2635 | 0.2643 | 0.2639 |

Data used for calibration is tabulated on Table 1. The velocity is calculated by using Equation 1 below. v=xT=fx (1)
Figure 1 shows calibration curve of left, right and average voltage vs. velocity. The result shows that cubic polynomial fits the average value best.

Figure 1 – Calibration curve 2. What is the difference between the average voltage on the left and right side of the tank for each velocity? What is the percent difference? Create a table showing your results.
Table 2 – Difference between raw data and averaged data Velocity (m/s) | Difference between left and average voltage (V) | % Diff | Difference between right and average voltage (V) | % Diff | -0.0175 | 0.00029 | 0.24 | 0.00029 | 0.24 | -0.0131 | 0.00119 | 0.91 | 0.00119 | 0.91 | -0.00874 | 0.00186 | 1.38 | 0.00186 | 1.38 | -0.00437 | 0.00022 | 0.16 | 0.00022 | 0.16 | 0 | 0.00144 | 1.01 | 0.00144 | 1.01 | 0 | 0.00117 | 0.83 | 0.00117 | 0.83 | -0.00437 | 0.00117 | 0.82 | 0.00117 | 0.82 | -0.00874 | 0.00005 | 0.03 | 0.00005 | 0.03 | -0.0131 | 0.00152 | 0.98 | 0.00152 | 0.98 | -0.0175 | 0.00035 | 0.22 | 0.00035 | 0.22 | -0.0218 | 0.00117 | 0.71 | 0.00117 | 0.71 | -0.0262 | 0.00045 | 0.26 | 0.00045 | 0.26 | -0.0306 | 0.00144 | 0.79 | 0.00144 | 0.79 | -0.0350 | 0.00149 | 0.76 | 0.00149 | 0.76 | -0.0393 | 0.00068 | 0.33 | 0.00068 | 0.33 | -0.0437 | 0.00161 | 0.73 | 0.00161 | 0.73 | -0.0481 | 0.00017 | 0.07 | 0.00017 | 0.07 | -0.0524 | 0.00107 | 0.43 | 0.00107 | 0.43 | -0.0568 | 0.00041 | 0.16 | 0.00041 | 0.16 | 3. Plot the velocity profiles for the data that was acquired both upstream and downstream of the cylinder on the same plot. To do this, take the average value from each data set.
Table 3 – Upstream and downstream voltage and velocity | Upstream | Downstream | Position | Voltage (V) | Velocity (m/s) | Voltage (V) | Velocity (m/s) | 1 | 0.1613 | 1.6825 | 0.1744 | 2.0472 | 2 | 0.1583 | 1.6062 | 0.1733 | 2.0158 | 3 | 0.1556 | 1.5387 | 0.1715 | 1.9628 | 4 | 0.1556 | 1.5389 | 0.1508 | 1.4272 | 5 | 0.1539 | 1.4974 | 0.1223 | 0.8809 | 6 | 0.1506 | 1.4208 | 0.1211 | 0.8622 | 7 | 0.1447 | 1.2912 | 0.1171 | 0.8031 | 8 | 0.1476 | 1.3552 | 0.1180 | 0.8155 | 9 | 0.1520 | 1.4546 | 0.1187 | 0.8265 | 10 | 0.1509 | 1.4295 | 0.1532 | 1.4811 | 11 | 0.1516 | 1.4448 | 0.1671 | 1.8375 | 12 | 0.1545 | 1.5129 | 0.1686 | 1.8809 | 13 | 0.1553 | 1.5322 | 0.1677 | 1.8544 |

Figure 2 – Velocity profile for data acquired

4. Sketch a picture of the set-up you are analyzing. Draw a control volume and clearly indicate the control surface. On your diagram, mark clearly the direction of flow, inlet and outlet velocities and show the direction of the drag force, F you will calculate.

Figure 3 – Sketch of lab set up

5. Using your measured velocity data, calculate a representative Reynolds number based on an average upstream velocity. Compare this number to traditional pipe flow i.e. comment whether the flow for your calculated value of Re would be in laminar, transition, or turbulent regimes for pipe flow.

V_average = 1.485 m/s
D = 25mm = 0.025m ν = 10-6 m2/s
Re=VDv=1.485×0.02510-6=37125<105
Therefore, it is laminar flow.

6. Using Figure 1 and your measured free stream velocity, estimate CD, then calculate the drag from using Equation 3 corresponding to your experimental measurements. Compare this value with the value obtained above in week 2 pre-lab exercise question 2.

FD=12ρV2ACD (2)
According to Figure 1 on lab write up, value of CD approximate to 1. ρ = 1000 kg/m3
V = 1.485 m/s
H = 31 mm=0.031m
A=πDH=π×0.025×0.031=0.0024m2
FD=12ρV2ACD=12×1000×1.4852×0.0024×1=5.37 N
Therefore, the drag is 5.37 N 7. Consider the following values of Re: 0.1, 1, 10, 100, 1000, 10000. Use Figure 1 to determine the drag coefficient vs Re, and then calculate the corresponding drag force by using equation (3) for each Reynolds number. (This will require you to calculate the corresponding characteristic velocity for each value of Re. Use your cylinder submerged height for the characteristic length scale. You may assume that ν = 10-3 N-s/m2). Note that Reynolds number compares the inertial force to the viscous force. Discuss how your drag force compares to relative contribution of viscous and inertial forces. Create a table displaying your results, and a logarithmic plot with the Reynolds numbers on the X axis and the drag forces on the Y axis. Include your experimental data point from question 6 above.

CD could be determined by looking at Figure 1 in lab write up. Since Re=VLν , V=Re νL .
According to equation (3) in text, FD=12ρV2ACD., we can find the drag force.
The result of these values correspond to assigned Re is tabulated on Table 4 as below.
Table 4 – Tabulated corresponding values

Re | CD | V (m/s) | Drag Force (N) | 0.1 | 60 | 3.077E-06 | 7.37E-10 | 1 | 10 | 3.077E-05 | 1.22E-08 | 10 | 2.5 | 3.077E-04 | 3.07E-07 | 100 | 1.8 | 3.077E-03 | 2.20e-05 | 1000 | 0.9 | 3.077E-02 | 0.0011 | 10000 | 1 | 0.3077 | 0.1228 |

According to Table 4, as Reynolds number increases, the drag force increases. Since Reynolds number compares the inertial force to the viscous force, the inertial force increases with Reynolds number. Therefore, large drag force comes with large inertial force and small viscosity force.

Figure 4 – Drag force vs. Re

8. Now using your measured span wise velocity profiles calculate the drag and drag coefficient using the control volume approach of Eq. (1). Hint: You may assume that the span-wise velocity profile is independent of the height above/below the height at which data was taken. In other words you may assume that the total drag is the drag force per unit length of the cylinder multiplied by the submerged height of the cylinder.

Since the control volume does not change over time and the flow is steady, equation (1) can be simplified as:
F=CS VρVdA

9. Comment on the sources of uncertainty in your data. How can these be improved?

The uncertainty might come from system error, such as in accurate sensor transducer, etc. For this of uncertainty, the best way to improve it is to use better sensor and transducer.
The uncertainty might also come from the environment factors, such as the vibration from the equipment, and wind blow through the sensor. For improving this, we could move the lab setup to comparable isolated environment.
The uncertainty might also come from finding the average value of the acquired data. There are many bad data points we want to avoid to use in our raw data. For improving this, we have to be careful.

10. Comment on the differences (and the reasons) between the drag determined in Questions 6, 7, and week two pre-lab question 2.

In the pre-lab, we calculated the drag force as 0, however, the drag force is 5.37 N from the post lab question. This difference is results from the different fluid properties we chose. In pre-lab, we assume the flow is inviscid, however, in our lab, the flow is viscid.

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...original edition)(Revised and reissued 1992)[Version 2.0 by Bbat – august 4 2003][Easy read, easy print][Completely new scan]The Hunter was born to hunt,as his prey was born to bebrought down at his desire . . .Sara Laramie moved through the iron castings in the foundry yard, keeping low so that she was at all times concealed from view. The Hunter Relemar was in pursuit of her. She did not know that he was a Hunter; it was obvious, however, that he was differ-ent from other naoli.Deep scream, lovely scream, wanting out . . . She reached the thousand gallon storage tank in which she now made her home. She pulled open the entry plate (it squeaked; Relemar listened for squeaks) and went inside. Behind her, there was a scraping noise . . . Rats, she thought, lighting the glow lamp. The tank brightened to a warm yellow.“Hello,” said Relemar the Hunter. He was trying to smile.This time, she did not suppress the scream . . . BEASTCHILD IS FORLISA TUTTLEAND DANNY JENNINGSAND JACK CORDESAND FOR THE USPOWHICH INTRODUCED USscience fiction by Dean R. Koontzavailable in Lancer editionsTHE DARK SYMPHONY, 74-621HELL'S GATE, 74-656 BeastchildDean R. KoontzLANCER BOOKS NEW YORK A LANCER BOOKBEASTCHILDThe characters in this book are entirely imaginary and have no relation to any living person.Copyright © 1970 by Dean R. KoontzA substantially shorter version of this novel appeared in Venture Science Fiction Copyright © 1970 by Mercury Press, Inc.LANCER BOOKS, INC. • 1560......

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