This is another early semester take home lab. When I give this to my students they have already been down to the lab and used a U-tube manometer to measure the specific gravity of oil (See post https://teachingfluids.wordpress.com/2014/01/13/measuring-specific-gravity-of-oil-with-a-u-tube-manometer/). This goes a step further and requires them to find 2 more ways to measure the density of common cooking oil. They have to look at the course material covered so far (typically we just finished hydrostatics when I hand this out) and work out what topics will enable them to measure the density of cooking oil. The two main goals are to (1) have them review the course to find possible measurement techniques and (2) to start doing some error quantification. They are required to give 3 different values of density based on three different measurement tecuniques and explain any possible differences. At this stage in the semester I typically only ask for estimates of their direct measurement uncertainty but not their uncertainty in their final calculated density.

In general the students are able to come up with three different methods for doing the measurement. They also, typically, measure densities that are slightly less than that of water. This puts them in the right ball park for the actual density. However, the students sometimes end up measuring some very small quantities (such as the height differences in the U-tube manometer. This in turn leads to large measurement percentage errors and even larger density percentage errors. The analysis of this error propagation is left to later take home labs though I do discuss error propagation in class around the time when I hand back the graded lab reports.

As with all the take home labs I will not publish methods for conducting the tests as I still use them in class and want my students to figure it out on their own.

Introduction

Fluid density is needed for many fluid mechanics calculations (hydrostatic pressure, forces on submerged structures, buoyancy, conservation of mass calculations). You have already measured the specific gravity of cooking oil in the lab. You are now required to measure its density.

Task

- Use three different methods to measure the density of cooking oil (you can repeat the approach you used in the lab if you like).
- Write a brief report that
- Is 3 pages max including photos of you running your experiments
- Details how you made the measurements
- Details how you used the measurements to calculate the cooking oil density
- Has clear diagrams showing your setup
- Compares the three different measured values of density.
- Quantifies potential sources of error in your measurements including a table of what you measured directly, typical values, and estimated uncertainty.

Rules

- You can use tubing from the fluids lab and a scale from the materials lab if you can get permission and access. Otherwise you are limited to household implements.
- You can take the density of water to be 1,000 kg/m
^{3}. - If you need to go to a store to buy something please come and see me first. I may be able to lend you something or I will buy it and then lend it to you. You will need to explain why you need it and it should be cheap.

Due in 2 weeks

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.