Viscosity

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

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

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

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

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.

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

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

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