SPHERIC TANK

• Picture of the frontpanel of the simulator
• What is needed to run the the simulator? Read to get most recent information!
• Tips for using the simulator.
• The simulator: spheric_tank.exe (click to download). The simulator runs immediately after the download by clicking Open in the download window. Alternatively, you can first save a copy of the exe-file on any directory (folder) on your PC and then run the exe-file, which starts the simulator.

Description of the simulated system

A spheric liquid tank with inflow and outflow is simulated, see the front panel of the simulator. You can adjust the inflow and the outflow during the simulation.

A mathematical model of the tank can be derived using mass balance of the liquid:

A(h)*dh/dt = q_in - q_out

where A(h) is the cross sectional area at level h, q_in is the volumetric inflow and q_out is the volumetric outflow.

Taking the Laplace transform of the above differential equation gives the following model:

h(s) = H₁(s)q_in(s) + H₂(s)q_out(s)

where

H₁(s) = 1/(As)

and

H₂(s) = -1/(As)

Aim

The aim of this simulator is to develop an understanding of impact of the cross sectional area on the dynamic properties of a (spheric) liquid tank.

Motivation

Tank of spheric form or any other form (not having straight vertical walls) have a cross sectional area which varies with the liquid level. A consequence of this variation is that the tank has varying dynamic properties. (This may have implications for level control of the tank.)

Tasks

1. (Theory.) Show that the gain of the transfer function from q_in to h and the gain of the transfer function from q_out to h is inversely proportional to the cross sectional area A. Are these gains relatively large or small at high (and low) level?
2. Verify the results from task 1 using simulations.

[KYBSIM] [TechTeach]

Updated August 14, 2004. Developed by Finn Haugen. E-mail: finn@techteach.no.