ENSC3003 LAB 1 Report PDF

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ENSC3003: FLUID MECHANICS LABORATORY 1 TRANSITION TO TURBULENCE – REYNOLDS EXPERIMENT 8TH MAY 2020 5PM

APOORVA KANTAK 22248072

RAW EXPERIMENTAL RESULTS

Data Point Cylinder hDC1(cm) Cylinder hDC2 (cm) ∆t (s) Manometer Right hMR (cm) Manometer Left hML (cm) Observation Laminar Transitional Turbulent

1 30 40 93.03 90.2 91.5

2 55 58 164.79 90.5 90.75

3 60 70 64.76 90 92

Data Point

6

7

8.1

Cylinder hDC1(cm) Cylinder hDC2 (cm) ∆t (s) Manometer Right hMR (cm) Manometer Left hML (cm) Observation Laminar Transitional Turbulent

50 70 23.36 70.25 112.00

50 70 10.37 12.5 170.5

50 70 11.30 27 155.5

4 50 60 28.53 86.5 95

5 50 70 33.50 79.5 102.5

9

10 (8.3) (4mins later) 50 70 11.94 27 155.5

(8.2) (2min later)

50 70 11.32 27.25 155.75

CALCULATED VALUES

1 2 3 4 5 6 7 8 9 10

Volume Flow Rate Q (m3/s)

Average velocity in the tube 𝑈(m/s)

Reynolds number

Dynamic Head Loss ΔHD (in m of water)

Darcy Friction Factor fD

6.84E-6 1.16E-6 9.82E-6 2.23E-5 3.80E-5 5.45E-5 1.23E-4 1.12E-4 1.12E-4 1.06E-4

0.08535 0.01445 0.1226 0.2783 0.4740 0.6798 1.5314 1.4054 1.4029 1.3300

862.3 145.9 1238 2810 4787 6865 15467 14194 14169 13433

0.00286 0.00055 0.0044 0.0187 0.0506 0.09185 0.3476 0.2827 0.2827 0.2827

0.076 0.522 0.0580 0.0478 0.0446 0.0394 0.0294 0.0284 0.0284 0.0317

METHOD OF CALCULATION Example calculation of Sample 1 0.1

𝑄 = 𝐴 × 𝑉=(0.0452 𝜋 × 93.3) Q =6.84𝐸 − 6 m3/s

Re=

Re=

 𝐷𝑝 𝜌𝑈

𝜇 1000×0.08535×0.0101 0.001

Re=862.3

𝑓𝐷 =

𝑓𝐷 =

𝐻𝐷 (2𝑔)(𝐷𝑝)  𝐿× 𝑈2

0.00286(2 × 9.81)(0.01010) 1(0.08535)2 =0.076

 and ΔHD can be seen in Question 1 and Question 2 Structure and method of working out 𝑈

QUESTIONS 1. Derive the equation that relates the average velocity in the tube (𝑈) to the rate of change of height in the discharge cylinder (∆hdc/∆t).

2. Given that the specific gravity of kerosene is 0.78, derive an expression relating the pressure head loss (ΔHD) between points 1 and 2 to the two-fluid manometer reading (the difference between interface levels ΔhM).

3. Calculate the Reynolds number and Darcy friction factor for each run. Plot your results on the Moody chart (provided below) and use them to obtain an estimate for the roughness of the tube (ε). Describe the method used to estimate the roughness and state the confidence intervals for the estimate. Include the Moody chart with the plotted points in your report. Do your results make sense? If not, what are the possible causes?

LEGEND BLUE = RUN 5 ORANGE = RUN 6 GREEN = RUN 7 RED = RUN 8 PINK = RUN 9 PURPLE = RUN 10 NOTE: HORIZONTAL LINE FOR RUN 8 AND 9 ARE ESSENTIALLY THE SAME THUS DISPLAYED WITH ONLY A SINGLE RED LINE

The interception point of the Reynolds number and the Darcy friction factor was found on a graph that symbolises the relative thickness. The relative thickness axis is seen on the righthand side of the Moody chart.

If certain points (e.g Run 6) didn’t lie on an already existing relative thickness graph then interpolation was used to determine the value.

During the conduction of this laboratory, human error introduced a significant amount of discrepancies. As the time taken for the cylinder to fill up to a certain level was measured and evaluated, human error caused certain errors. This uncertainty caused by the human’s reflex time as well as perception of the value of liquid has led to a measurement of roughness that could be questionable. This time was used to calculate and evaluation the Reynolds number as well as the Darcy friction factor. These values would continue to be graphed, in order to find their intercept; the relative thickness. The relative thickness is then used to find the roughness of the tube. Most calculated values, except date point 5, lie within the upper and lower bound. Thus, data point 5 could be an outlier. This carryover uncertainty has caused a larger margin error; thus, this value of roughness should be deemed an estimated rather than an accurate value.

4. For the repeated run, you should have 3 sets of results for the same experimental conditions. Use this data (and appropriate statistical measures, such as confidence limits) to estimate the uncertainty in your quoted Re and fD values. In this experiment, what are the largest sources of this uncertainty?

Human error due to visual perception and reflex action has caused these uncertainties in the timing value. This time is carried forward to calculate other measurements such as average velocity. This average velocity is used to determine both: Reynold’s number and Darcy friction factor. Thus, this discrepancy largens and introduces margin of error. Another possible cause of uncertainty is welcome when the flow becomes turbulent from transitional; the formation bubbles made it more difficult to precisely get a measurement of a certain centimetre mark.

5. Discuss the relationship between the visual dye indicator observations and your estimated Reynolds numbers. What do your results suggest is the bounding range for the critical Reynolds number for flow in this tube?

Laminar flow is seen when the Reynold’s number is below 2000. An indication of laminar flow was when the visual dye was thin and displayed a clear streamline. As the Reynold’s number increased in value and surpassed 2810, the flow was now looking transitional. The visual dye relatively was still showing a clear streamline but towards the end of the streamline, there was now patches and the visual dye was becoming fainter to see. When the Reynold’s number was between 2000-4000, the flow becomes more unsteady. At data point 5, the dye line is unstable and is barely visible to the naked eye at the end of the streamline. This indicates a sign of turbulent flow. Data points 6 to 10 shows the visual dye becoming more unstable and deformed as soon as it enters. The visual dye can be deemed invisible, as from a reasonable distance its barely seen, but from a much closer and direct view, it’s more visibly prevalent. This is a strong indication of turbulent flow, and this supported by the Reynold’s value. The Reynold’s values for data points 6 to 10 are greater than 4000. The changes and fluctuation of the visual dye support the validity of the Reynold’s number being a predictor of the flow. The Reynold’s numbers that were calculated and valuated through several mathematical equations favour the observations seen in this laboratory. In summary, a Reynold’s number less than 2000 can be regarded as laminar, while a Reynold’s number between 2000 and 4000 can be deemed as an grey area between laminar and turbulent or also now known as transitional. When the Reynold’s number exceeds 4000, it is fully turbulent.

6. Describe the distinguishing features of laminar and turbulent pipe flows. Laminar flow, also known as streamlines or vicious flow, occurs when a fluid flows in parallel layers with no disruptions in between the layers. The distinguishing features of a laminar flow are: 1. Layers of water flowing over one another at different speeds with virtually no mixing between layers 2. Fluid particles move in definite and observable paths or streamlines 3. The flow is characteristic of viscous (thick) fluid or is one in which viscosity of fluid plays a significant part. Turbulent flow is a less orderly flow regime that can be characterized by small eddies or small packets of fluid particles which result in lateral mixing. the irregularity movement of the fluid flow characterized it as a turbulent flow. The Reynold’s numbers that can quantify the two flows; laminar is below 2000, while turbulent is greater than 4000. To simply define laminar and turbulent, it said that laminar flow is smooth and occurs at low velocities while turbulent flow is rough and occurs ate high velocities. The visual dye in this laboratory qualitatively supported these distinguishing features by showing stable and clear streamlines during laminar flow and irregular and barely visible lines during turbulent flow....