The Mandelbrot Set

Nozzle Flow

Background Theory

The purpose of this program is to demonstrate the one-dimensional flow of an incompressible, frictionless fluid through a simple nozzle.  The behavior of this flow is governed by the law of conservation of mass which states that mass is neither created nor destroyed.  When applied to flow through a nozzle with circular cross-section, the following equation results:

Program Operation

For this demonstration, the inlet area, outlet area and inlet velocity will be the independent variables.  The outlet velocity will depend on the values of these three independent variables which may be changed by dragging the blue anchors (it may take a second the first time).

Program Design

The program was written in Java and compiled using the Java Development Kit (JDK 1.3).  The JavaBeans component architecture and event model were used.

The program uses the following classes:

State - This is the heart of the program.  It contains all the flow variables and the methods to update them in response to changes in the inlet or outlet conditions.

Display - This is an abstract base class that contains the generic machinery for displaying variables and for capturing mouse events (specifically, actions involving the anchors).

RadiusDisplay - This class displays the value of the radius of the nozzle along the axis of the nozzle.  It inherits from the Display class.

VelocityDisplay - This class displays the value of the velocity along the axis of the nozzle.  It also inherits from the Display classs.

WaterTunnel - This is the applet class where the objects are instantiated.