Producing a scale to indicate the volume of liquid in a container

Abstract

The present work considers the volume-depth relationship for several container shapes such as cylinders, spheres and cones. The evaluation of the volume corresponding to a given depth is easily carried out on a spreadsheet. A computer program is described for carrying out the inverse process, that is, to output values of depth corresponding to selected volumes, hence producing a depth-gauge. The calculation can take into account the shape of the container and how the divisions (numbered and un-numbered) should be distributed on the scale. If the scale is graduated as a fraction of the total volume and displayed at an arbitrary size on the monitor screen, then “universal” results are obtained, for example for any sphere, or any cylinder, etc., independent of its actual dimensions. In addition, if the volume is specified in litres (or gallons, or any other units) and the length of the depth-scale is specified, then a gauge can be produced that will suit that particular container. It can be displayed on the screen only as a scale drawing, but exact dimensions can be output as a file, which will allow the full-size gauge to be drawn, either using drawing-office equipment or an automatic drawing machine.