Fluid Flow-3

pdf

School

Northeastern University *

*We aren’t endorsed by this school

Course

1146

Subject

Chemistry

Date

Apr 3, 2024

Type

pdf

Pages

Uploaded by GeneralElectronGull33

Report of Experiment #7 Fluid Flow TA: Yasamin Masoumi Sefidkhani 11/18/2022 Abstract: In this experiment, we looked at fluid flow and Poseuille's law. There were two inquiries in it. We employed one capillary in the initial investigation, and three distinct capillaries in the subsequent investigation. We measured the duration of the water's passage through the capillaries. The fluid's flow rate was then determined using the data. This fluid's flow rate can be influenced by size and pressure. This pace can be affected by pressure and size. In experiment 1, the apparatus' reservoir's height was modified to vary the pressure, and in experiment 2, the capillaries' diameter was varied to change the pressure. Introduction:

To acquaint and validate Poiseuille's Law, this experiment is being conducted. We investigated how fluid flow rates and several types of flow relate to one another. Using capillaries of varied sizes and a flow rate monitor as characteristics. We timed how long each capillary took to fill a graduated cylinder to a specified mark to calculate the flow rate. Next, we calculated the results’ average. We did this several times with different pressures and capillary sizes to understand the link between the flow rate and each. Investigation 1: Using a capillary with a 1.25 mm (about 0.05 in) diameter, we first assembled the equipment as seen in Figure 1 to start this experiment. The capillary’s height was modified so that the graduated cylinder rests directly beneath it. Once the capillary was attached to the system and water could flow to remove air bubbles, the plastic bottle's height was adjusted. We timed how long it took the device to fill the graduated cylinder to the 50-cc mark after it was positioned beneath the capillary. We refreshed the water in the bottle so that its level stayed at our predetermined baseline to maintain a constant pressure. To obtain two sets of time data, we later calculated the average flow rate and its error at the current pressure. The pressure was then raised three millimeters each time, and we timed how long it took the graduated cylinder to fill to the 50-cc mark three more times. To understand the correlation between pressure and flow rate vs. pressure, we make use of this data. By displaying the data’s best fit line, the relationship between pressure and flow rate was made clear. By including additional data points where the source of the pressure is ambiguous. The more meticulously we measured, the closer our line is to the origin. This is accurate because our measurements of the two heights completely determined the pressure readings. Our findings support a section of Poiseuille’s Law, which states that flow rate is (at least somewhat) influenced by pressure. Since flow rate and pressure and proportional flow rate increase so does the pressure. Figure 1- Experiment Apparatus Table 1- Heights 1&2, Time 1&2, Diameter of Capillary, Average Time, Average Flow Rate Trail h1 h2 ∆𝑝 t1 t2 t avg. avg. δ time δ𝑎𝑣𝑔. ?𝑖𝑚𝑒 𝑎𝑣𝑔. ?𝑖𝑚𝑒 avg Q ( ) 𝑐𝑚 3 ? δ𝑄 𝑄 δ𝑣 (𝑐𝑚 3 ) ∆ 𝑄 Trail 1 32. 75 43. 8 11 98. 9 97. 3 98. 12 0. 005 0. 6886 0. 510 0. 6886 0. 05 0. 351 Trail 2 32. 75 46. 8 14 88. 4 83. 3 85. 86 0. 005 0. 6886 0. 582 0. 6886 0. 05 0. 401 Trail 3 32. 75 49. 8 17 73. 5 73. 5 73. 50 0. 005 0. 6886 0. 680 0. 6886 0. 05 0. 468 Trail 4 32. 75 52. 8 20 57. 5 66. 3 61. 88 0. 005 0. 6886 0. 808 0. 6886 0. 05 0. 556

Graph 1- Average Flow Rate vs. Pressure Investigation 2: We compared the flow rates via four capillaries of various diameters for this portion of the experiment. We timed how long it took the capillary to fill the graduated cylinder to the 50-cc mark three times without altering the height of the capillary or reservoir. We repeated this process using capillaries of various diameters. Since the flow rate would be incredibly sluggish for the capillary with the smallest diameter (0.5 mm), we adjusted the pressure and utilized a 10-cc graduated cylinder. However, none of the capillaries our group tried to use to collect data worked properly. Since the pressure, in this case, was changed we needed to calculate the correct flow rate so we can compare it to the other capillaries. This was done by dividing our flow rate (Q) by 2.5. We then obtained the logarithms of d and Q by deriving an equation from Poiseuille’s Law . Then, since neither of these variables has units, we generated a 𝐶 = ∆𝑝 128δη𝐿 graph of lnQ vs lnd. After plotting the best fit line, we used the IPL Calculator to determine its slope and slope error: 2.63658±1.521759. Our values were within the allowable error limits, the slope should have been in the 4 range which in still case with margin of error it was roughly 4. This graph demonstrates the relationship between flow rate and diameter. Table 2- Data for Investigation 2 Capillary diameter (d) h1 h2 ∆𝑝 t1 t2 t3 t avg. avg. δ time δ𝑎𝑣𝑔. ?𝑖𝑚𝑒 𝑎𝑣𝑔. ?𝑖𝑚𝑒 avg Q ( ) 𝑐𝑚 3 ? δ𝑄 𝑄 δ𝑣 (𝑐𝑚 3 ) 1. 5𝑚𝑚 32. 75 52. 8 20 31. 4 31. 0 31. 47 31. 28 0. 005 0. 6886 1. 598 0. 689 0. 5

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

1. 0𝑚𝑚 32. 75 52. 8 20 69. 3 72. 7 69. 8 70. 61 0. 005 0. 6886 0. 708 0. 689 0. 5 0. 5𝑚𝑚 32. 75 82. 8 50 334. 0 336. 3 335. 4 335. 2 0. 005 0. 6886 0. 149 0. 689 0. 05 1. 25𝑚𝑚 32. 75 52. 8 20 57. 5 66. 3 61. 88 0. 005 0. 6886 0. 808 0. 689 0. 5 Graph 2- lnQ vs. lnd, Slope, Intercept and Errors Conclusion: This lab’s purpose was to familiarize the experimenter with and support Poiseuille’s Law. We looked at the relationship between flow rate and pressure in the first half. Our graph of Average Flow Rate vs. Pressure revealed a linear relationship between the two, with flow rate increasing as pressure grows. In the lab’s second half, we looked at how diameter affects flow rate. Our graph of lnQ versus lnd demonstrated their proportional relationship: doubling the diameter yields a flow rate that is sixteen times higher, etc. Compared to the known value of n for laminar flow, 4 our value of 2.63658±1.521759 was within an acceptable error tolerance. Questions: 1.) If both hoses have identical pressure, the water will flow from the hose with a diameter of ⅝ inch more quickly than the one with a diameter of ½ inch. 2.) A fluid's flow rate will decrease by 50% if its viscosity doubles. The flow rate would be lessened by a doubling of the density. 3.) There is a 3:9 ratio. One can get the conclusion that as the diameter rises, the resistance falls. 4.) The resistance ratio and the ptube/pcap ratio are identical.

5.) If a fluid is horizontal, the force of gravity does not increase it; rather, it just increases the pressure difference.