Posted: September 13th, 2017

Fluid Flow

Fluid Flow

Web Site:

http://lectureonline.cl.msu.edu/~mmp/labs/labflow/lab.htm

Introduction:

We want to know what law applies for water draining from a cylindrical container. We can imagine two different scenarios:

1.    Flow of an ideal fluid:  Here the rate of change in the height of the liquid in the container will be proportional to the square root of the height, and we arrive at the time dependence of the height:

h(t) = ho – a • t + b • t2

where a and b are two constants to be determined by the experiment, and ho is
the beginning height. (This derivation uses Bernoulli’s Law.)

2. Flow of a viscous fluid:   Here the rate of change in the height of the liquid in the
container will be proportional to the height, and we arrive at the time dependence
of  the height:

h(t) = ho • exp(- t / ?)

where ? is a constant to be determined by the experiment. (This derivation uses
Poiseuille’s Law and the pressure-depth relation.)

It is the purpose of this experiment to find out which of the two scenarios describes this particular physical reality better.

If you want to preview a condensed version of what is going to happen in this experiment, you can load either of these video clips, the larger size, (280 kB, Sorenson compression) or smaller size (176 kB, cinepak compression) versions are available. The are recorded in time-lapse, with 3 seconds between frames. Since they will play at 8 frames per second, the roughly two minutes that it took to drain this container are compressed to less than 5 seconds.  (I didn’t have much luck trying to load either clip, so I hope that if you want to look at the preview, that you are more fortunate!)

Instructions:

1.    Load up the Java Lab from the web site shown above.

2.    Run the Java applet by clicking “JavaLab” button. (It will open in a separate window).

3.    Digitize the height of the liquid column by clicking on the upper limit of it. After each click, the mouse position is recorded and the movie is advanced one frame. You should try to devise a consistent strategy on where you click (left, right, center, …). If you make a mistake, click on the “Undo Pt.” button in the applet, and the last point will be erased.
Please Note: If you are using a phone line to perform this experiment, then please keep in mind that it can take a couple of seconds between two successive frames of the video you are digitizing. Please do not get impatient. You can see when the next frame is ready for you from observing the text area: as soon as the result of your previous click is displayed, the next video frame is ready for processing.

4.    You can display the points that you have already digitized before by clicking on the “Plot y(x)” button. It will turn red and show the points overlaid on the video. Clicking the same button again will turn this feature off.

5.    You can also plot the trajectory as a function of time directly within the applet by clicking on the “Plot h(t)” button. Clicking on the “Digitize” button will bring you back to the data input mode.

6.    The numerical data you have collected are displayed in the text area on the right side of the applet. After you are done digitizing all frames, please copy your data into your clipboard and export them into your favorite spreadsheet or graphing program. There, you can fit the above two functional dependencies to your data and decide which one fits better.

7.    Now produce a plot with your graphing program or by screen-capture of the applet.

8.    Finally, write the report with your favorite word processor or text editor and submit is to the instructor.

Use the “Sample Laboratory Report” as a guide in preparing your lab report.

Any problems – please e-mail me.  Also if you have any complaints, comments, suggestions, or kudos concerning this experiment, please e-mail me.  It won’t help your class, but I will take them into consideration for the next time this course is offered.  You will be remembered and given complementary Rolling Stones concert tickets by subsequent generations of Physics students.

Prof. Shah ?