### Impulse-Momentum Principle

THIS INTERACTIVE JAVA APPLET WAS DEVELOPED AT UT AUSTIN BY Kyle Douglas AND Lino Geo Lino Bailey, UNDER THE SUPERVISION OF PROFESSOR. Spyros A. Kinnas, 1998.

PERMISSION TO LINK TO THIS JAVA APPLET AND TO DOWNLOAD OR TO USE THE RELATED JAVA SOURCE CODE, MUST BE GRANTED BY PROFESSOR Spyros A. Kinnas ( kinnas@mail.utexas.edu ).

#### Purpose:

This applet calculates and draws the force vector due to the reaction of the pipe on the fluid. The equations used to determine the magnitude and direction of the force are based on the Impulse-Momentum principle and Bernouli's equation.

#### Assumptions:

• The pressure distribution is uniform at any cross-section of the pipe
• The center of pressure for any cross-section is the midpoint of that section
• The velocity distribution is also uniform for any given cross-section

#### Using the applet:

Note: The pipe is not drawn to scale! In order to make the components of the applet a reasonable size, some of the variables (like the diameter and radius of curvature) are scaled in different proportions. However, components which measure similar parameters are scaled equally. For example, the weight is scaled in the same proportion as the force on the fluid, and the entrance diameter is scaled equally to the exit diameter.
• Select the type of pipe to use, horizontal or vertical
• Change the pipe geometry by dragging the yellow, circular handles at the corners of the pipe
• Change the entrance velocity by dragging the yellow, square handle on the velocity vector
• Translate the pipe around the screen by dragging the handle with the black arrows
• Enter values to more accurately change the parameters of the problem. The range for each parameter is:
• Rotation of pipe: 0-180 degrees
• Radius of pipe bend: 30-60 cm
• Exit diameter: 7-13 cm
• Entrance and exit pressure (gage): -30-100 kPa
• Entrance velocity: 1-10 m/s

#### A Note About the Vectors:

To avoid confusion, the vectors and what they describe are given below.
• The Velocity and Weight vectors simply give the magnitude and direction of the velocity and weight
• The Force of Pipe vector gives the magnitude and direction of the force on the fluid due to the pipe
• The Force of Pressure vector shows the force acting on the entrance and exit sections of the pipe due to fluid pressure
• Finally, the Momentum vector shows the magnitude and direction of the term rQV for the entrance and exit sections of the pipe

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Last Revised: August 9, 1998