Resistance In Fluid Systems

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```					Resistance In
Fluid Systems

4.2
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
The drag exerted on an object by a
fluid depends on many factors

– The speed of the
object (or fluid)
– The size and shape of
the object
– The physical properties
of the fluid
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
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.
Pressure Drag

• Changing direction
of fluid into eddies
and whorls requires
work. When fluid
does work –
pressure drops.
 W = -V P
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               = viscosity
movement.
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’ 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.

F = 6 r
drag
Terminal Speed

• The terminal speed
of a falling object is
the constant speed
that occurs when
the drag force
equals the
gravitational force.
Poiseuille’s Law
• Gives the volume
flow rate of a fluid
flowing through a
tube or pipe.
– Applies to laminar
flow
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.

          4
V =- r P
8 L
Factors Affecting Flow
• Poiseuille’s Law shows how resistance
of flow through a pipe depends on three
factors:
– Length of the pipe
– Viscosity of the fluid

Pressure drop = - P
R=     Volume flow rate   
V
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.
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.
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.

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