Subject: Project 3, Terminal Velocity

Subject: Project 3, Terminal Velocity

In this project you are asked to prepare a spreadsheet to calculate terminal velocity for objects of various sizes and materials falling through different fluids. The purpose is to help a high school science teacher explain the concept of terminal velocity to a class of 11th grade students. In addition to the concept, you should provide an example of how this concept can be used for industrial applications. Investigate the application using your model to generate appropriate data. Plots and tables should be included in the memo with your discussion. Printed and electronic file copies are due at the time of the final exam. Remember to write for your audience, follow the guidelines for memos, document your work and pay attention to your visual display of data (tables and plots – follow the guidelines).

When an object falls in a fluid its downward motion is opposed by a buoyancy force and a drag force. The buoyancy force is equal to the weight of fluid displaced by the object. The drag force is proportional to the square of the velocity and depends on properties of the fluid and the object. If the distance travelled is long enough, the object will reach a constant velocity, called the terminal velocity. The equations below show this concept applied to a spherical object:

The drag coefficient ( CD ) is a function of the Reynold's number, with the latter calculated from the expression Re = (fluid density * velocity * diameter)/ (fluid viscosity). Note that the fluid properties are used here along with the velocity and diameter of the particle. Equations and symbol definitions are provided in a spreadsheet posted with this assignment sheet.

The Spreadsheet Model

Design your spreadsheet to solve for the terminal velocity of a sphere using iteration. Solver may be used to implement the iteration, however, you will need to set up the sequence of calculations. You will need at least 3 VBA routines to help in this model:

·  a function to calculate and return the drag coefficient as a function of the Reynold's Number (why should this be a function and not a sub?)

·  A sub attached to a button to run Solver

·  A sub to record key results to a location near the active cell.

The recording sub can be used to create data tables by running the calculations for a set of cases. Thus you can generate a table to show how velocity varies with diameter for a particular particle material, the effect of changing the material and the effect of changing the fluid. Such tables can be used to make plots that will help in your explanation of the concept of terminal velocity.

The following features should be included in your spreadsheet:

·  List boxes to select the material for the falling object and the fluid

·  Automatic retrieval of relevant properties when choices are made from the list boxes

·  Set of option buttons to select the units for the particle diameter (mm, cm or m)

·  Scroll bar to set the particle diameter

·  The above scroll bar should work with the option buttons to set the diameter

·  Show the diameter in meters for use in calculations and in the selected units for display

·  Check boxes to select which results are to be copied by your sub in creating results tables

·  A button to automate the running of Solver – you may want to name the cells used by Solver

The Memo

To help the teacher with this lesson, provide a brief explanation of the concept, including the relevant equations in the form of a technical memo. The memo should include brief tables and plots that illustrate the points you are making in the discussion. Include both liquid and gas fluids to show how the effect of buoyancy differs depending on the fluid density. You should prepare plots that show the effect of the size of the object and the density of the object on the terminal velocity. Likewise, the effect of fluid choice should be explored. Discuss how the concept of terminal velocity can be applied to separate particles by size or by density or for removal of liquid droplets from a gas stream.

For example, small aluminum particles can be separated from plastic particles by difference in the settling rate in a fluid. A table or plot of the terminal velocity vs size for particles of different density (eg, aluminum and plastic) will show that the particles would settle at different rates if placed in a container of fluid. If the fluid is flowing up the container, particles which move downward faster than the fluid will reach the bottom, while slower moving particles will be carried out of the container with the flowing fluid. Thus aluminum particles above a certain size should settle, while smaller ones do not. A similar effect will occur for the plastic particles. A careful choice of velocity should allow for the desired separation. Select a fluid velocity to achieve your design and be sure to report it in your memo.

A similar application is used to remove condensed water from a gas stream. When the water vapor condenses, it will form droplets of various sizes. By creating a vertical flow of the gas in a vessel, the droplets moving downward at a velocity above the fluid velocity can collect in the vessel, while slower droplets will be entrained by the gas and carried out. Again, report your chosen velocity.