Iconic Diagrams And Dimensional Analysis For Bond Graphs

This paper consists of two parts. Firstly, we consider icons instead of BG symbols, which are better accepted by some people. Secondly, we take dimensional analysis for any physical quantities that are built from fundamental and derived quantities. The main thing is that they have a special mathematical structure and only quantities of the same dimension can be equated, added or subtracted. By multiplication, on the other hand, physical quantities can be combined, i.e. area is the product of two lengths and velocity is the quotient of a length and atime. We develop this algebra where nondimensional combinations are important such as for instance the Reynolds number. This leads to Buchingham’s π theorem. Also, physical quantities are built from fundamental units such as length, time and mass. However it is clearer to use length, time and force or even length, time and energy instead. INTRODUCTION BGs (bondgraphs) are an universal graphical means to represent dynamic systems that we have used for many years: components of systems are represented by letters, that is an alphanumeric code which represents a certain abstraction. Some people prefer a iconic code, which is more suitable for their intuition. So one purpose of this paper is to develop an iconic or picture code to complement BGs. The other purpose of the paper is dimensional analysis, a very old technique that has spawned a large literature including some papers by Thoma [THOMA 1968]. If done properly, dimensional analysis is a very powerful tool for modelling, especially to set up practical formulae. Let us note also that on all graphical representations the dimensions of the quantities should be given, for instance volt per meter V/m for electric field strength. Another example is the product of voltage and current VA, which is power, expressed in Watt, the time derivative of transported energy. In mechanics we have the newton N and the velocity in meters per second m/s, whose product is again the transported power or time derivative of energy. ICONS FOR HOT GAS SYSTEMS According to the general philosophy of hot gas systems, which is developed in [THOMA 2006], thermofluid machines are built quite naturally as a sequence of RECO, HEXA and TEFMA.