1. FINAL LECTURE of NEW MATERIAL!!! (1) How to build a better model (2) Lift, Drag, Pressure forces considered together

2. Simulitude, dimensional analysis, modelling Similitude –The theory and art of predicting prototype performance from model observations Part of this art and theory involves building a good model Tip: –It helps if the important dimensionless #’s are the same for the models and the prototype

3. Some types of simultude Geometric –Involves dimensionless variables created using length scales –e.g. ( L / W ) = ( L M / W M ) –Sometimes a “model scale” is specified Scale of 1:10 usually means L M / L = 1 / 10 (for any length) Dynamic –Involves dimensionless variables of force scales –E.g. Inertial and viscous scales are both important: (F inertial / F viscous ) = (F inertial, M / F viscous, M ) How do you find the appropriate dimensionless numbers –Intuition What seems to be important? Use associated dimensionless numbers –Dimensional analysis provides important dimensionless numbers

4. Common dimensionless numbers (in fluid dynamics. See section 8.5) Reynolds number –Inertial / viscous force Mach number –Inertial / compressibility force Weber number –Inertial / surface tension force Froude number –Inertial / gravitational force Pressure coefficient (Euler number) –Pressure / inertial force Strouhal number –Local / convective force (unsteadiness importanat)

5. Lift / drag When an object is submerged in a flowing fluid, the fluid is forced to move around it. As a result, the object is (usually) subjected to forces perpendicular and parallel to free stream velocity Drag: –forces parallel to free stream velocity Lift: –forces perpendicular to free stream velocity These take the form: