Help for the Lake Simulators

This module includes lake simulators, written in Java, which allow the user to experiment with how changes in quantities such as the lake volume and flow rate affect the level of contaminant in the lake over time. This page is intended to provide more detailed explanation of the simulators. Below is a picture of one of the simulators. Specifically, it is the simulator which is used for an impulse input model. A brief description of each area will appear if you move the cursor over it if your browser is Java enabled. For details about each region, see the table below.

There are also tables summarizing the meanings of the text entry fields and meaning of the displayed info in the information display panel.

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Simulator Picture

Below follows an explanation of the various areas:
Area Explanation
Data Entry Area The text fields in this area allow the user to enter different values for constants such as the lake volume and the flow rate. Different models have different values which can be changed. For example, the sinusoidal input model includes a field for the period of the model, T, while this would not be meaningful for a step input or a impulse input model.

For detailed information, see the table on all available input fields below.

Simulator Area The simulator represents the concentration of contaminant in the inflow and the lake/outflow visually by changing the color on a simple representation. The color bar below the simulator indicates that the colors range from blue (representing pure water) to green (representing the maximum concentration of contaminant). In the simulator, we suppose the inflow enters from the left arm of the diagram and leaves through the right arm. This simulation runs in synchronization with the plotting of the graphs.
Graph Area The graph represents the amount of contaminant in the inflow and in the lake/outflow as two separate graphs. The plotting is done in synchronization with the running of the simulator.
Information Display Area The information area in the bottom left hand corner of the applet provides information about the simulation. For example, the residence time V/Q is calculated and displayed in this area. The constants are not recalculated until the "Start" button is pressed.

For detailed information on the different information displayed in this area, see the chart below.

Buttons There are three buttons available on the panel.

The "Start" button begins the simulation. When it is pressed, the constants in the information display area are recalculated and displayed, and the simulator and graphs begin running. If the "Start button is pressed while a simulation is running, a new simulation begins in its place.

The "Stop" button is used to end a simulation. Use it only if you do not wish to see the rest of the simulation that is running. It is not necessary to press "Stop" before entering new values and pressing "Start" to start a new simulation.

The "Close-up of Graph" button creates a new window which displays a larger version of the graphs for the current values which are entered in the data entry area as well as displaying the information which would normally be found in the information display area. Since there is no simulator and the graphs plot all at once in this window, the "Close-up of Graph" button can be used to get quick answers without running the entire simulation. Simply enter the values you want to use in the text area and press "Close-up of Graph." When you have the information you need, press the "OK" button in the close-up window that appears.

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The table below summarizes all the available text entry fields, including which simulators they are found in.
Field Found in Simulators For Description of Field
Volume (V) All The volume of the lake. Primarily important for calculating the residence time, V/Q.
Flow (Q) All The flow rate. Primarily important for calculating the residence time, V/Q.
Pulse Input Concentration (C0) Impulse The initial concentration in the lake due to the pulse input in the impulse input model.
Final Time (tf) All except steady state models. The time at which the simulation should end. The start time is assumed to be time zero, so the final time should be the duration of the simulation.
Period (T) All sinusoidal models The period of the sinusoidal input function. That is, the function repeats every T units of time.
Step Input Concentration (Cin) Step The concentration at which contaminant enters the lake after time zero in the step input model.
Average Input Concentration (Ci) All sinusoidal models The average concentration in a sinusoidal input model. The actual concentration varies above and below this amount.
(Normalized) Amplitude (a) All sinusoidal models A number between 0 and 1 which determines the amplitude in a sinusoidal input model. The amplitude of the sin function is given by Ci a which is the amount by which the actual concentration varies above and below the average input concentration.
Initial Concentration (C0) All initial value problems The initial concentration of contaminant already in the lake when the simulation starts.
Reaction Rate (k) All constant reaction models The reaction rate determines at what rate the contaminant is being either destroyed (if k is positive) or generated (if k is negative). It comes from the equation tex2html_wrap_inline11 for our simulation. In the lake module simulations we will not consider the case where the contaminant is generated (that is, the negative k case.)

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The following table summarizes all the information that may be calculated and displayed in the information display area. Not all constants are relevant to all models.

Constant Appears In Explanation
Residence Time (V/Q) All models The residence time (sometimes represented as tex2html_wrap_inline13) is the volume of the lake divided by the flow rate in and out of the lake. Intuitively, the residence time represents the amount of time that it would take the lake to be completely flushed. Many of the properties of a lake model will depend on the residence time.
Final Concentration (C(tf)) All except for sinusoidal steady state The final concentration is the concentration of contaminant in the lake at the final time tf.
Attenuation (R) All sinusoidal models The attenuation is given by the formula tex2html_wrap_inline23, where T is the period and tex2html_wrap_inline13 is the residence time. The output concentration in a sinusoidal model can be written using R. Solving the general case, we get:

tex2html_wrap_inline27

Phase angle (tex2html_wrap_inline21) All sinusoidal models The phase angle is subtracted from the argument of the sin function in the output of the sinusoidal modules. It may be thought of as "lag" represented in terms of the argument of the sin function. The phase angle is given by

tex2html_wrap_inline30

Time Lag (tex2html_wrap_inline23) All sinusoidal models The time lag is the time between the change in the input concentration and the corresponding change in the lake concentration in the sinusoidal modules. The time lag is given by

tex2html_wrap_inline34

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John Hoggard <hoggard@math.vt.edu>
Last modified: Mon Aug 25 12:08:44 EDT 1997