Understanding Fluid Viscosity: Resistance and Drag Forces Maximize Efficiency

1. Viscosity

2. Fluid Resistance • An object moving through or on a fluid meets resistance. • Force causes the fluid to move. • The velocity is proportional to the force. F vx

3. Velocity Gradient • The resistance tends to keep the fluid in place. • Law of inertia • The fluid moves most near the object and least farther away. • This is a velocity gradient. F vx y

4. Law of Viscosity • Newton combined these two proportionalities. • This is the law of viscosity. • A is the area of the solid sliding on the fluid • The constant h is the dynamic viscosity and depends on the type of fluid. F vx y

5. Flow in a tube is affected by sides in all directions. The relationship between velocity and distance is The total volume flow rate is Poiseuille’s Law r P1 vx P2 L

6. Drag • Kinetic friction is a constant force. • If there is a net force an object would accelerate forever • Air resistance causes a friction called drag. • At low velocity drag is proportional to velocity, Fd = bv • At higher velocity drag goes as velocity squared, Fd = cv2 • The direction of drag force is opposite to the velocity.

7. Falling Leaves • The drag coefficient depends on the surface area. • Large surfaces – high drag • Leaves • Feathers • Papers • Small surfaces – low drag • Stones • Balls • Bullets

8. Drag Force • Objects falling through a fluid reach terminal velocity. • For low speeds this is due to viscocity. • Stokes’s Law describes the drag force. Fd Fb Fg

9. Terminal Velocity • An object may fall through the air at constant velocity. • By the law of inertia the net force is zero. • The force of drag must balance the force of gravity. • This velocity is called the terminal velocity. Fg = -mg