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FINAL LECTURE of NEW MATERIAL!!!

In this final lecture on new material, we explore the key principles of modeling in fluid dynamics, including the lift, drag, and pressure forces. The concepts of similitude and dimensional analysis are crucial for predicting the performance of prototypes based on model data. We emphasize the importance of maintaining the same dimensionless numbers in both models and prototypes, discussing geometric and dynamic similitudes. Key dimensionless numbers such as Reynolds, Mach, and Froude are examined, along with how forces interact when objects are submerged in flowing fluids.

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FINAL LECTURE of NEW MATERIAL!!!

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  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 ) = ( LM / WM ) • Sometimes a “model scale” is specified • Scale of 1:10 usually means LM / L = 1 / 10 (for any length) • Dynamic • Involves dimensionless variables of force scales • E.g. Inertial and viscous scales are both important: (Finertial / Fviscous) = (Finertial, M / Fviscous, 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:

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