Experiment 2: Fluid Dynamics

Purpose:
the purpose of this experiment is to analyze the fluid dynamics, figure out what factor will affect the fluid dynamics, and also find the relationsip between time and volume of fluid during fluid dynamics motion.


Equipment used:

Bucket with a small hole drilled in the bottom
tap water
bottle with volume marks
ruler
stopwatch

Data and Calculation:

height from top of the water to the hole: 0.1445+-0.00005 m.

diameter of the hole on the bucket: 0.007+-0.0005 m.

Volume emptied: 200mL = 0.0002 m^3.

acceleration due to gravity (g) : 9.8m/s.

use stopwatch to get the time for 200 mL water drain out of the hole of the bucket:

time 1: 3.82+-0.015.

time 2: 4.75+-0.015.

time 3: 4.35+-0.015.

time 4: 4.35+-0.015.

time 5: 4.38+-0.015.

time 6: 4.52+-0.015.

average of the 6 times: 4.35+-0.31(0.31 is standard deviation of the six data)

four times of the data accord with the range above.

use the calculation way to figure out the time of water flow out of the hole of the bucket.

time (theoretical) = Volume/(Area*sqrt(2gh)) = 3.08 s.

if include the error percent: high: 3.10 middle: 3.08, low: 3.06.

Analyze:

error = 1 - (time of theoretical)/(time of actual) = 1-3.08/4.35 = 29%.

assume the diameter you measured isn't accurate. what is the actual diameter, to sove, rearrange the time -to-drain equation to solve for the diameter of the hole.

t = V/(A*sqrt(2gh)),

A = V/(t*sqrt(2gh)),

pai*r^2 = V/(t*sqrt(2gh)),

r = sqrt(V/(t*sqrt(2gh)*pai)),

d = 2r = 2*sqrt(V/t*sqrt(2gh)*pai)) = 2*sqrt(0.0002/4.35*sqrt(2*9.8*0.1445)*3.14)) = 0.0059 m whicn is the diameter of the hole.

Conclusion:

compare the experimental value and the theoretical value, there have 29% error, and the experimental value overall are larger than the theoretical value. I think there have several reason: 1 during the experiment, when we use stopwatch to catch the time until the beaker reach 200 mL, when we see to tap water reach 200 mL, then press the stopwatch, there have some time delay. 2, in the experiment, we can not get exact 200 mL tap water, after each time, we measure the tap water we received with graduate cylinder, most of them over 200mL, then base on the equation on the lab book, the time we get will larger. 3, in the experiment when we use ruler to measure the height and the diameter of the hole, make some error percent. so for the three types problem, our experimental value is larger than the actual value. and the model is worked, but need have more accurate operation.