1. Resistance In Fluid Systems 4.2

2. Define Drag For a solid object moving through a fluid or gas, drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust

3. – The speed of the object (or fluid) –The size and shape of the object –The physical properties of the fluid – The speed of the object (or fluid) –The size and shape of the object –The physical properties of the fluid The drag exerted on an object by a fluid depends on many factors

4. Laminar Flow A slow, smooth flow over a surface, in which the paths of individual particles do not cross. –Each path is called a streamline A slow, smooth flow over a surface, in which the paths of individual particles do not cross. –Each path is called a streamline

5. Turbulent Flow Irregular flow with eddies and whorls causing fluid to move in different directions. –Turbulence is produced by high speeds, shapes that aren’t streamlined and sharp bends in the path of a fluid. Irregular flow with eddies and whorls causing fluid to move in different directions. –Turbulence is produced by high speeds, shapes that aren’t streamlined and sharp bends in the path of a fluid.

6. Pressure Drag Changing direction of fluid into eddies and whorls requires work. When fluid does work – pressure drops.  W = -V  P Changing direction of fluid into eddies and whorls requires work. When fluid does work – pressure drops.  W = -V  P

7. Viscosity The property of a fluid that describes an internal friction between atoms and molecules of a fluid. –These forces create internal friction in the fluid, causing resistance to movement. The property of a fluid that describes an internal friction between atoms and molecules of a fluid. –These forces create internal friction in the fluid, causing resistance to movement.  = viscosity

8. The viscosity of a fluid can be measured by pulling a plate at constant speed across a layer of the fluid.  = F  y Av

9. Stokes’ Law Applies to objects moving at low enough speeds that the flow of fluid around the objects is streamlined. –There is no turbulence and the only drag force on the objects is due to frictional drag. Applies to objects moving at low enough speeds that the flow of fluid around the objects is streamlined. –There is no turbulence and the only drag force on the objects is due to frictional drag. F drag = 6  r 

10. Terminal Speed The terminal speed of a falling object is the constant speed that occurs when the drag force equals the gravitational force.

11. Poiseuille’s Law Gives the volume flow rate of a fluid flowing through a tube or pipe. –Applies to laminar flow Gives the volume flow rate of a fluid flowing through a tube or pipe. –Applies to laminar flow

12. Poiseuille’s Law (cont.) The rate at which fluid flows through a tube increases proportionately to the pressure applied and to the fourth power of the radius of the tube. V  = -  8 r 4  P LL

13. Factors Affecting Flow Poiseuille’s Law shows how resistance of flow through a pipe depends on three factors: –Radius of the pipe –Length of the pipe –Viscosity of the fluid Poiseuille’s Law shows how resistance of flow through a pipe depends on three factors: –Radius of the pipe –Length of the pipe –Viscosity of the fluid R = Pressure drop Volume flow rate = -  P V 

14. Summary Drag is the force that opposes the motion of an object moving through a fluid or the force a moving fluid exerts on a stationary object. Laminar flow is slow, smooth flow over a surface, where particles follow streamlines. Drag is the force that opposes the motion of an object moving through a fluid or the force a moving fluid exerts on a stationary object. Laminar flow is slow, smooth flow over a surface, where particles follow streamlines.

15. Summary (cont.) Turbulent flow is irregular flow with eddies and whorls that mix the fluid. Drag increases with speed. Viscosity is the property of a fluid that describes its internal friction. Stokes’ Law – used to calculate drag force on a sphere moving at constant speed in a viscous fluid. Turbulent flow is irregular flow with eddies and whorls that mix the fluid. Drag increases with speed. Viscosity is the property of a fluid that describes its internal friction. Stokes’ Law – used to calculate drag force on a sphere moving at constant speed in a viscous fluid.

16. Summary (cont.) Terminal speed – when drag equals the gravitational force acting upon a falling body. Poiseuille’s Law – used to calculate the volume flow rate or pressure drop of a viscous fluid flowing through a tube or pipe. Terminal speed – when drag equals the gravitational force acting upon a falling body. Poiseuille’s Law – used to calculate the volume flow rate or pressure drop of a viscous fluid flowing through a tube or pipe.