Flow types Internal External Relative velocity between fluid & object Auto moving through air Water moving against bridge abutment Wind against building

Drag force Resistance to “forward” motion – push back in direction of fluid flow Depends on Fluid/object velocities Fluid properties Geometry of object Surface roughness

Drag Forces Two types Friction drag: viscous shear effects as flow moves over object surface. Acts parallel to surface Form drag: affected by geometry of object. Acts perpendicular to object

Drag force Theory: integrate pressure & shear forces over object surface. Complex mathematics Empirical approach

Similitude Model simulates prototype Reliance on dimensionless parameters Reynolds Number Relative roughness Drag coefficient - C D

Wind tunnels Experimental drag determinations Buildings Ships Bridge supports/abutments Vehicles

Wind Tunnel DC 3 & B 17: about 100 hours of testing F 15: hours of testing

Drag Coefficient F D = C D A ρ (V 2 /2) V – free stream velocity Characteristic area –e.g. frontal for auto Air density C D – drag coefficient characteristic of geometry

Drag Coefficient Includes both pressure & friction drags: one usually dominates Airfoil – friction; viscous shear drag Auto – pressure; form drag

Drag force Assume for experimentation No adjacent surfaces Free stream velocity uniform & steady No free surface in fluid

Drag force Simplification: power to move vehicle on level ground Rolling friction Drag force

Vehicles Early autos – high C D ; no concern < 30mph Higher speeds concerns increased Advances in metal-forming techniques for improved body designs Control C D Fuel costs Conserve non-renewable resources Pollution

Vehicles Nose of auto Trunk of auto Surface finish Discontinuities Mirrors Door handles Wheel wells Air intakes

Vehicles Reduced drag vs other factors Visibility Passenger accommodation Aesthetics

Fluid Mechanics Lab Simple shapes Disk Hemisphere Sphere Teardrop

Pressure drag Flat disk All pressure; no friction drag Streamline separation → wake; low pressure region. Adverse pressure gradient  P front-to-back

Pressure drag Sphere Streamline separation Wake

Pressure drag Tear drop – streamline Reduce separation – farther along surface yields smaller wake Increase in friction drag; optimum streamline design

Shape and flowForm drag Skin friction 0%100% ~10%~90% ~90%~10% 100%0

Design Process: EWT Models Photo’s of autos SolidWorks design CFD analysis of design: streamlines, C D prediction 3D printer for models using SolidWorks design Preparation of models for EWT: surface & mounting EWT testing: Lab C D vs predicted C D. Agreement within 10%.