Fluid Dynamics Lab

The goal for this experiment is to analyze the behavior of fluid dynamics and come up with relevant experimental data when compared with calculations.
The principle used for this experiment is Bernoulli Equation:

P₁ + ρgh₁ + ½ ρv₁² = P₂ + ρgh₂ + ½ ρv₂²

^{Under laboratory environment and for simplicity purposes, we can assume the pressures to be the same, and the velocity of the fluid at the top to be zero.} 

^{Since the fluid is water, the density will cancel out yielding a resemblance of the conservation of energy formula:} 

Incorporating the continuity and rate formulas we obtain,

and finally to get the time, we arrive at this expression;

First we measured the diameter of a hole in the bottom of the bucket from which the water came out. We used a caliper in order to obtain a more precise reading. We found it to be 0.5±0.025cm. 

We then took another container in which the 16 ounces of water would be poured. Having the container weighed, we came up with the mass based on the density of water that would cover 16 ounces (or 453.6 ml). We put a mark on the container so that we would know where to stop the timer.

We came up with most of the times being consistent with one another except for one that threw off our data.







 

	1st Run	2nd Run	3rd Run	4th Run	5th Run	6th Run
Time to empty (t actual)	21.05	21.30	21.46	22.87	20.96	20.95

Calculations:

Volume emptied (V): 16 ounces * 1ft³/998.83ounces = 0.0160187 cubic feet

^{Area of the drain hole (A): pi*r^2 = 0.000233012 ± 0.0000427 sq.ft.} 

^{Acceleration due to gravity (g) = 32.2 ft/s}

^{Height of water : 3in. = 0.25ft}

 

Having a theoretical time and times based on experimentation, we proceeded to calculate the percent error for each trial using the following formula:

	1st Run	2nd Run	3rd Run	4th Run	5th Run	6th Run
% error	20.53	21.7	22.44	28.70	20.11	20.06

The formula of the time required to empty the container can be manipulated to obtain the diameter of the hole, by just solving for the Area having a time t. 

 Solving for d using the theoretical time of 17.13 s and a height of 4.5 in, yields a calculated diameter of 0.015565 ft.  When calculated with the measured diameter of 0.01722 ft, the percent error is equal to 10.10%. 

At the end of the experiment, we were given the diameter of the drill bit used for perforating the whole in the bucket to be 1/4 in (0.0208333ft). When calculating the percent error between the given and calculated diameters, the percent error comes up to be 28.95%.

Summary:

The percent errors in this experiment came up to be quite acceptable and very close to one another considering the level of precision in the tools used throughout. Proper technique while delivering the water to the container matters when determining the volume. Another source of error could have been the use of imperial units when measuring the height the water dropped in the bucket.