Experiment 2: Fluid Dynamics

9/6/2012

The purpose of the experiment is finding the time to empty a given volume by measurement and calculation from equation.

In this lab, we need a bucket with a small hole drilled in the bottom,bottle with volume marks,ruler, and stop watch.

Fill water into bucket to height h, and use a ruler to measure the height.

h=15cm(In case, to stop water flowing out, we use a piece of tape)

Then we set up the equipment like shown as below.

Second step is that remove the stopper and start the stopwatch. When volume in the small bottle reaches 100ml, stop the stopwatch. Record the time elapsed. Repeat for a total of six tests.

The data is t1=5.83s; t2=6.35s; t3=6.43s; t4=6.23s; t5=6.04s; t6=6.30s

So we take the average of these data which is 6.2s

Follow step is measure the diameter of the hole so that we can figure out the area of drain hole.

We measured the diameter as 5.8mm so the area of drain hole is 0.26cm^2 (A=pi*r^2)

Then we plug in all the data we measured into the equation t show as below

Then t=2.2s(we got this t from theoretical equation)

The theoretical time and actual time are totally different. For the theoretical time, we still used the data we measured like r,v,h. So there must be existing errors. 

Assume the diameter we measured isn't accurate. Then we rearrange the time to drain equation to solve for the diameter of the hole. Then we got the calculated diameter is 3.5mm. 

The given diameter and calculated diameter still need our measurement, so when we calculate the error we only can use the equation show as below.

We plug in x1=5.8; x2=3.5, then we got the error=49.5%

Summary: Theoretically, if we have no error when we measure the data of it h, v, d, we should get the theoretical time as same as the actual time. But error cant be ignored because when we calculated time of empty, we got some trouble from catching the water by the beaker. And when it reaches 100ml, we stop cant stop the stopwatch at time for sure.