ENGG 2230 Lecture Notes - Lecture 10: Dimensional Analysis, Reynolds Number, Mach Number

• School: University of Guelph
• Department: Engineering
• Course: ENGG 2230
• Professor: Bill Van Heyst

Document Summary

A method that is used to reduce the complexity of an equation by reducing the number of terms with non-dimensional groupings. Based on experiments since many fluids problems are too complicated to solve analytically. An equation will have all of its additive terms contain the same dimensions if it: all three of the additive terms are in metres represents a proper relationship between variables. Reynolds number: (cid:3034)+(cid:3023)22(cid:3034)+=(cid:1867)(cid:1866)(cid:1871)(cid:1872)(cid:1866)(cid:1872, =(cid:3022) = (cid:3041)(cid:3032)(cid:3045)(cid:3047) (cid:3049)(cid:3046)(cid:3030)(cid:3042)(cid:3046)(cid:3047, (cid:1870)=(cid:3022)2(cid:3034)=(cid:3041)(cid:3032)(cid:3045)(cid:3047) (cid:3034)(cid:3045)(cid:3049)(cid:3047, =(cid:3022)= (cid:3033)(cid:3042)(cid:3050) (cid:3046)(cid:3043)(cid:3032)(cid:3032)(cid:3031) (cid:3043)(cid:3045)(cid:3032)(cid:3046)(cid:3046)(cid:3048)(cid:3045)(cid:3032) (cid:3050)(cid:3049)(cid:3032) (cid:3046)(cid:3043)(cid:3032)(cid:3032)(cid:3031) Geometric similarity: the dimensions of a prototype are accurately scaled down into a model. Kinematic similarity: the model and the prototype have the same length scale and time scale ratios. Dynamic similarity: the model and the prototype have the same length scale, time scale, and force scale ratios.