Lab 10 - Fluid Dynamics

Alison Whitney December 12, 2023

Group Members: Rook Bergeron

Background: When SCUBA divers enter the water, everything about how their body moves and interacts with the environment around them changes. Instead of walking, running, and jumping like humans do on land, SCUBA divers swim, float, and alter their buoyancy to match the depth they are moving at. This is because forces and how objects or humans interact with those forces is different depending on the medium.

When an object is underwater, an additional force must be accounted for. This is known as the buoyancy force and it is described as the force opposing gravity due to the fluid environment. This force is defined by the density of the fluid, gravity, and the volume of the fluid that is displaced by an object. Density is important as it relates to the consistency of the fluid which can very widely from water to corn syrup or honey. This variable is dependant on the mass of the fluid in a given volume, and for the buoyancy force should be presented as kg per m3. Gravity is the same regardless of the medium, so even underwater it remains 9.8 because gravity is dependant only on the distance from the person/object to the center of the earth. Finally, the displacement volume is represented in m3 and is important as a representation of the objects impact on the fluid itself.

This experiment was constructed in two parts. Part 1 attempted to use the process of submerging an object in a fluid to calculate the density of the fluid. The objects selected were a copper metal weight and an aluminum metal weight. The fluids were vegetable oil, coke, and vinegar. Part 2 attempted to use the same process to calculated the density of the metal weights instead, using the known density of the fluids to minimize the errors. The derived equations for both calculations are presented below.

Methods:

Part 1 -

A graduated cylinder was filled part way with vegetable oil and the initial volume was recorded.
A copper weight of a known mass was attached to the bottom of a scale by a string.
The copper weight was placed in the graduated cylinder so that it was fully submerged in the vegetable oil and freely hanging.
The new volume on the graduated cylinder was recorded.
The mass of the hanging weight was measured and recorded as well (indication of the force of tension)
The copper weight was lifted out of the graduated cylinder and replaced with an aluminum weight.
The same process was repeated for the aluminum weight.
This method was repeated twice more, once with coke as the liquid in the graduated cylinder and once with vinegar as the liquid.
The results were used to calculate the density of the fluid and compared to the known value.

Part 2 -

A pair of calipers was used to measure the height and diameter of the copper and aluminum weights.
These results, as well as the ones from part 1, were used to calculate the density of the weights and compared to the known values.

An image of all of the materials used for the experiment

An image of the experimental set up with the metal attached to the scale and hanging in the graduated cylinder

Equations:

Part 1 -

Ftension + pfluid x g x Vdisplaced = mg

Part 2 -

Ftension + pfluid x g x Vdisplaced = pmetal x vmetal x g

Raw Data:

Ftention copper = 0.622N Ftension aluminum = 0.441 N

Known p vegetable oil = 910 kg/m3 Known p coke = 1000 kg/m3 Known p vinegar = 1015 kg/m3

Vdisplaced copper = 7.8 x 10^-6 m3 Vdisplaced aluminum = 2.25 x 10^-5 m3

m copper = 0.07 kg m aluminum = 0.066 kg

Known p copper = 8940 kg/m3 Known p aluminum = 2710 kg/m3

V copper = 5.67 x 10^-6 m3 V aluminum = 1.77 x 10^-5 m3

Part 1 - Copper in Vegetable Oil

Raw Calculations

Part 1 - Copper in Coke

Raw Calculations

Part 1 - Copper in Vinegar

Raw Calculations

Part 1 - Aluminum in Vegetable Oil

Raw Calculations

Part 1 - Aluminum in Coke

Raw Calculations

Part 1 - Aluminum in Vinegar

Raw Calculations

Part 2 - Copper in Vegetable Oil

Raw Calculations

Part 2 - Copper in Coke

Raw Calculations

Part 2 - Copper in Vinegar

Raw Calculations

Part 2 - Aluminum in Vegetable Oil

Raw Calculations

Part 2 - Aluminum in Coke

Raw Calculations

Part 2 - Aluminum in Vinegar

Raw Calculations

Results:

Part 1 - Density of Fluid Determined by Metals (kg/m3)

FLUIDS COPPER % ERROR ALUMINUM %ERROR

Vegetable Oil 837.3 7.9% 933.3 2.6%

Coke 816.3 18.4% 857.0 14.3%

Vinegar 837.3 17.5% 950.0 6.7%

Part 2 - Density of Metals Determined by Fluids

METAL VEGETABLE OIL %ERROR COKE %ERROR VINEGAR %ERROR

Copper 12446 39.2% 12604 41.2% 12816 43.4%

Aluminum 3699 36.5% 3947 45.6% 3807 40.6%

Discussion: Part 1 of this experiment was somewhat successful in calculating the densities of the three fluids by submerging metal weights in them. Vegetable oil in particular each had percent errors of less that 10%. It was also observed that there was a smaller error in the liquid densities when the aluminum weight was being submerged than the copper weight. This was likely a result of the aluminum weight being physically larger than the copper weight. This meant that there was a larger displacement volume with a little bit more room for error that with the smaller copper displacement volume.

Part 2 of this experiment was less successful in calculating the densities of the two metals by submerging them in various liquids. All of the liquids resulted in a percent error of 35-45%. This meant that the errors were likely not in a misreading or small mistake given that they were consistent across six samples. Instead, it was observed during the calculations that there was a large difference between the volume displaced measured by the graduated cylinder and the calculated volume of the cylinders by a pair of calipers. Therefore, it was likely that the large errors in these measurements arose from one or both of the measuring tools being inaccurate.

Errors: Despite the substantial errors observed in the part 2 measurements in particular, many measures were taken to minimize the room for error. This measures included utilizing the same tools across replicates, ensuring that the mass was hanging directly from the scale and not pressed against the side of the tube, and remeasuring multiple times when errors were observed to prevent potential human errors from impacting the results. To explore the cause of the substantial errors in part 2 of the experiment, all of the measuring tools should be recalibrated before repeating the experiment and comparing the outcome to these results.

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