## Chemical Engineering:Dimensionless quantity

2013.4.17

Lecture note of Dr. Hiroshi Yamamoto

The dimensionless quantity (Wiki ) is a quantity without an associated physical dimension (unit). It is thus a "pure" number. Dimensionless quantities are widely used in chemical engineering area.

By contrast, non-dimensionless quantities are measured in units of length, area, time, etc.

Dimensionless quantities are often defined as ratios of quantities that are not dimensionless, but whose dimensions cancel out when their powers are multiplied. This is the case, for instance, with the engineering strain, a measure of deformation. It is defined as change in length over initial length but, since these quantities both have dimensions L (length), the result is a dimensionless quantity.

The most important dimensionless quantity in Chemical Engineering is Reynols number. It is Ratio of fluid inertial and viscous forces.

Prandtl number (Wikipedia): ratio of viscous diffusion rate over thermal diffusion rate

Nusselt number (Wikipedia): heat transfer with forced convection

Marangoni number (Wikipedia): Marangoni flow due to thermal surface tension deviations

it is becoming very important to estimate Marangoni number for the Ink Jet printing industrial aera. I made HTML5 base software to estimate Marangoni number from solvent structure. If you are using HTML5 enable browser such as Chrome, FireFox or Safari, please try this software.

The marangoni number play very important role on solubility in Supercritical Carbon dioxide.