Resistance In Fluid SystemsResistance In Fluid Systems

4.24.2

Define DragDefine 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

• 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

– 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

Laminar FlowLaminar 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

Turbulent FlowTurbulent 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.

Pressure DragPressure 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

ViscosityViscosity

• 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

The viscosity of a fluid can be measured by pulling a plate at

constant speed across a layer of the fluid.

The viscosity of a fluid can be measured by pulling a plate at

constant speed across a layer of the fluid.

= F y

Av

Stokes’ LawStokes’ 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.

Fdrag= 6 r

Terminal SpeedTerminal Speed

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

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

Poiseuille’s LawPoiseuille’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

Poiseuille’s Law (cont.)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.

• 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

= - 8r

4 PL

Factors Affecting FlowFactors 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 dropVolume flow rate

= - P

V

SummarySummary• 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.

Summary (cont.)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.

Summary (cont.)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.