Analyzing the Pneumatic Reservoir Building a Mathematical Model

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

Step 1 Measure and Record Component Dimensions 1. ) A, B End Cap 2. ) C, D Threaded Boss 3. ) A, E SS Tube

Component Length Diameter Volume Weight SS Tube End Cap Threaded Boss Pneumatic Reservoir Exterior cyl. Interior Cyl. Water Volume Record Your Work Material Density Aluminum Density Stainless Steel Density

Zero the Calipers Before Each Measurement

Step 2 Calculate the Component Volumes The Threaded Boss (2) These Are Cylindrical Shapes The Stainless Steel Tube The Aluminum End Caps (2) Record Your Answers

The Concept of Density More Matter Contained in an Equal Volume Density = Weight / Volume Less Dense Equal Volumes More Dense Different Weights

Step 3 Research and Record the Density of Aluminum and Stainless Steel Find and Record the Density of: Aluminum ______ Stainless Steel ______ 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 Aluminum

Step 4 Calculate the Weight of the Aluminum Components Weight of Aluminum End Cap x 2 = ______ Weight of Threaded Boss x 2 = ______ Total Weight Aluminum Components = ______ Record Your Answers

Step 5 Calculate the Weight of the Stainless Steel Tube Weight of Pneumatic Reservoir Total Weight Aluminum Components Weight of Stainless Steel Tube Record Your Answer

Imagine Two Solid SS Cylinders The Exterior Cylinder Dimensions are Known The Interior Cylinder Dimensions Are Calculated From Known Values and the Density Equation Imaginary Stainless Steel Interior Cylinder Stainless Steel Exterior Cylinder

Step 6 Calculate The Exterior Cylinder Weight = Density x Volume Begin by assuming the Stainless Steel Tube is a Solid Stainless Steel Cylinder Calculate the Weight of This Imaginary Cylinder: Use Outside Dimensions Record Your Answer

Step 7 Calculate the Interior Cylinder 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 Reservoir Use 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) Rewrite the Equation to Solve for Vi Vi (Interior Cylinder Volume) = W (Weight) / D (Density SS) Record Your Answer

Step 9 Verify the Answer Two Possible Methods 1. Consult the Manufacturers Specification This is the easiest and most efficient method. Learn to use specifications. 1. Measure the Fluid Volume of the Reservoir 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?