Transcript AE 301 Aerodynamics I - Embry–Riddle Aeronautical University

Fluid Properties
• Density, r
– The measure of the mass per unit volume
 M 
r

Lim

V 0 
– Mathematically:
– Units:
slugs/ft3 (British)
 V 
kg/m3 (SI)
• Specific volume, u
– The term “specific” implies “per unit mass”.
– Thus, “specific volume” = “volume per unit mass”
– u = 1/r
– Specific volume is primarily used when dealing with
thermodynamics - density is preferred in most
aerodynamics!
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Fluid Properties (continued)
• Pressure, p
– The measure of the average momentum exchanged per unit
area between a gas and a solid surface.
– Closely related to the average momentum due to the
random motion in a gas or liquid.
– The force due to pressure always acts normal to the
surface.
F
A
 F 
p

Lim

A0 
– Mathematically:
 A 
– Units:
lbf/ft2 (British)
N/m2=Pascal
– Alternate units:
AE 301 Aerodynamics I
(SI)
lbf/in2, atm, bar, mmhg, mmH20, inH20, ...
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Fluid Properties (continued)
• Temperature, T
– The measure of the average random kinetic energy per unit
mass in a gas or liquid
– Units:
oR
– Alternate units:
(British)
oK
(SI)
oF, oC
• Learn conversions!
0oF=460oR
0oC=273oK
• Equation of State
– Equation expressing the relationship between r, p, and T
– For a perfect gas: p = rRT
– R is the specific gas constant. For air at standard
conditions:
•
R = 1716 ft2/sec2/oR = 287 m2/sec2/oK
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Fluid Properties (continued)
• Velocity, V
– A vector describing the direction and magnitude (speed) of
motion
– In Cartesean coordinates:
V  ui  vj  wk
• Viscosity, m
– A measure of the resistance a fluid offers to a shearing
velocity gradient.
– On surfaces, a shearing gradient is created by the no slip
condition
– The resulting shearing stress, t, due to viscosity always acts
tangent to the surface
– Units:
slug/ft/sec (British)
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kg/m/sec (SI)
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Flowfields
• Dependencies of Properties
– When dealing with large volumes (like the atmosphere) or
flowing fluids, the fluid properties are different at different
locations in the fluid. I.e.:
• Air temperature, density, and pressure vary with altitude
• Sitting in the bed of a truck is much more pleasant then sitting
on the hood at 60 mph.
– Fluid properties may also vary with time. I.e.:
• Air temperature heat up during the day, cools at night.
• A wind sock fills up and drops back in a gusting wind
– Thus:
r(x,y,z,t)
p(x,y,z,t)
V(x,y,z,t)
m(x,y,z,t)
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T(x,y,z,t)
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Flowfields (continued)
• Streaklines
– The path a fluid packet makes as it moves through a
flowfield is called a streakline
– Streaklines can be visualized with smoke, bubbles, ink (in
liquids)
– Mathematically, streaklines can be found by integrating the
velocity or tracing the velocity vector
• Streamlines
– In many situations of interest, the fluid properties are not
changing with time and is called steady
– If a flowfield is steady streaklines are repeatable from one
instance to another.
– These repeatable streaklines are called streamlines
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Aerodynamic Forces
• There are only two sources of aerodynamic forces:
– Pressure forces which act normal and into the surface.
p
– Viscous forces which act tangent and in the direction of local
fluid flow
t
– The total force is found by finding and then integrating these
forces, p and t, over the surface area.
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