Transcript Resistance in Fluid Systems

Resistance in Fluid
Systems
4.2
Drag
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The force that opposes the motion when
a solid object moves through a fluid
Occurs only when there is relative
movement between an object and a fluid
Laminar Flow (Streamlined)
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Slow, smooth flow over a surface in which
the paths of individual particles do not cross
Fluid speed at the surface is zero.
Fluid moves in theoretical layers, or
laminates, with increasing speed away from
the surface.
Frictional drag is produced by the friction
between successive layers of fluid.
Turbulent Flow
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irregular flow with eddies and whorls causing fluid to
move in different directions
produced by high speeds, by shapes that are not
streamlined, and by sharp bends in the path of a fluid
produces wakes
Pressure drag is produced because the pressure
difference in the wake is less than the fluid pressure in
the streamlined flow and causes a force to act on the
object in the direction opposite its relative velocity.
Frictional drag and pressure drag both increase as
speed increases.
Frictional drag is directly proportional to the increase
in speed. Pressure drag (and turbulence) increases
as the square of the speed.
Viscosity
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property of a fluid that describes internal
friction
normally how slowly a fluid moves because
of internal bonds
Greek letter η (eta) represents viscosity.
Syrup and ketchup have relatively high
viscosities; water and air have relatively low
viscosities.
Viscosity
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Fdrag = F = η (Av/Δy) (Drag force = viscosity X area ·
velocity divided by the change in the thickness of the fluid
layer)
SI Units—N/m2·s or Pa·s—English Units—lb/ft2·s or psi·s
ηwater = 0.001002 N/m2·s = .01002 poise = 1.002
centipoise
Viscosity for Common Fluids—p. 188
Viscosity of most liquids decreases as temperature
increases—ex: honey
Viscosity of most gases increases as temperature
increases—more collisions per second as temp increases
Stokes Law
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Predicts the drag force on a sphere
moving through a fluid
Low speeds, so only laminar flows—no
turbulence, just frictional drag.
Drag force acts in the direction opposite
the object’s velocity.
Fdrag = 6πrvη-Drag force = 6 X pi X
radius X velocity X viscosity
Terminal Speed
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When drag equals the weight of the
object.
Speed becomes constant.
Terminal speed of baseball—about 40
m/s
Terminal speed of basketball—about 20
m/s
Poiseuille’s Law
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A. gives the volume flow rate of a fluid
flowing through a tube or pipe
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B. V = -(π/8)(r4ΔP/ηL)—Volume flow
rate (change in volume with respect to
time) = (pi divided by 8) X ({radius4 X
change in Pressure} divided by viscosity
X length)
Factors Affecting Flow Through a
Pipe (pp. 193-195)
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radius of pipe
length of the pipe
viscosity of the fluid
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R = -ΔP/V—Fluid Resistance = -change
in pressure divided by the Volume Flow
Rate