Analyzing the Pneumatic Reservoir Building a Mathematical Model of The Interior Volume of the Reservoir.

Analyzing the Pneumatic Reservoir

Building a Mathematical Model of The Interior Volume of the Reservoir

Steps to Determine the Interior Volume of the Pneumatic Cylinder

•Measure and Record Reservoir Component Dimensions

•Calculate The Component Volumes

•Research The Component Material Density

•Calculate the Weight of Each Component

•Calculate The Interior Volume of the Reservoir

•Verify the Answer

Download and Complete the Work Sheet Supplied With This Lesson.

The Pneumatic Reservoir Analysis Work Sheet

Can be Found in the Learning Tools Section of this Lesson

Maintain a Notebook That Documents All Your Work

1.) A, BEnd Cap

2.) C, DThreaded

Boss

3.) A, ESS Tube

Step 1Measure and Record

Component Dimensions

Component DiameterLength Volume Weight

SS Tube

End Cap

Threaded Boss

Pneumatic Reservoir

Interior Cyl.

Record Your Work

Exterior cyl.

Water Volume

Material Density

Aluminum Density

Stainless Steel Density

Zero the Calipers Before Each Measurement

Step 2Calculate the Component Volumes

The Aluminum End Caps (2)

The Threaded Boss (2)

The Stainless Steel TubeThese Are Cylindrical Shapes

LengthRVolume 2Record Your Answers

Density = Weight / Volume

Equal Volumes

Different Weights

Less Dense

More Dense

The Concept of DensityMore Matter Contained in an Equal Volume

Step 3Research and Record the Density of

Aluminum and Stainless Steel

Aluminum AluminumStainless Steel____________

Find and Record the Density of:

Aluminum____________

Stainless Steel

Note: There are many alloys of Aluminum and Stainless Steel. Use an Average Density

Click Here for an online list of material densities

Step 4 Calculate the Weight

of the Aluminum Components

VolumeDensityWeight Weight of Aluminum End Cap x 2 = ____________

Weight of Threaded Boss x 2 = ____________

Total Weight Aluminum Components = ____________

Record Your Answers

Step 5Calculate the Weight

of the Stainless Steel Tube

Weight of Pneumatic Reservoir

Total Weight Aluminum Components

Weight of Stainless Steel Tube

Record Your Answer

Stainless Steel Exterior Cylinder

Imaginary Stainless Steel Interior Cylinder

Imagine Two Solid SS CylindersThe Exterior Cylinder Dimensions are Known

The Interior Cylinder Dimensions Are Calculated From Known Values and the Density Equation

Step 6Calculate The Exterior Cylinder Weight

Begin by assuming the Stainless Steel Tube is a Solid Stainless Steel Cylinder

Calculate the Weight of This Imaginary Cylinder: Use Outside Dimensions

Weight = Density x Volume

Record Your Answer

Step 7 Calculate the Interior Cylinder Weight

Weight of Exterior Stainless Steel Cylinder(From Previous Slide)

Weight of Stainless Steel Tube

Weight of the Interior Stainless Steel Cylinder

Record Your Answer

Step 8 Calculate the Interior Volume the

Pneumatic ReservoirUse the Density Equation and the Weight of the Interior

Stainless Steel cylinder to Calculate the Volume

D (Density SS) = W (Weight) / Vi (Interior Cylinder Volume)

Vi (Interior Cylinder Volume) = W (Weight) / D (Density SS)

Rewrite the Equation to Solve for Vi

Record Your Answer

Step 9 Verify the Answer

Two Possible Methods

1. Consult the Manufacturers Specification

1. Measure the Fluid Volume of the Reservoir

This is the easiest and most efficient method. Learn to use specifications.

This process is explained in the next slide

Measure the Fluid Volume of the Reservoir

1. Unscrew and remove the Schrader valve.2. Unscrew and remove the one touch tubing

connector.3. Holding the reservoir level, slowly fill it with

water.4. When the reservoir is full, empty the reservoir into

a graduated cylinder.5. Read the volume of water in the graduated

cylinder.

Caution: Remove ALL the Water before pressurizing the reservoir

How Closely Does Your Mathematical Model Agree With The Measured Fluid

Volume?