AERO40001 Aerodynamics I Section 1-3
__________________________________________________________________________
Outline
• Last lecture discussed how shear stress is proportional to the rate of deformation and
that a fluid needs to be in motion to produce shear forces on a body.
• We will continue our introduction by
• Discussing how pressure plays an equally important role
• Introduce the ideas of conservation of mass
• Finally discuss the concept of frame of reference.
Velocity and Pressure
To describe a fluid flow we must consider both velocity
velocity and pressure
pressure.
Pressure
Typically of great practical importance are the changes in pressure that occur as air flows past
an aircraft. e.g. for a wing we need to know the differences in pressure generated on the upper
and lower surfaces.
p
high
N
Drug
un
remote
low
pressure
}
I
-
- -
from
-
-
i
-
-
-
- -
-
-
Relative
.
↳
.
.
.
aerofoil
-
↳
.
top .
high pressure
Lift µ Pressure Distribution
• N/m2
In SI units the pressure is measured in N/m Pascals
2 or Pascals.
• In English or Imperial Units lbs/sqm psi
lbslsqimh -
psi
pressure drags
The changes in pressure also cause a force in the flow direction known as Drag u .We have
already seen that shear stress contributes to Drag through skin friction but an equally important
contribution (particularly if the body is not steamlined) comes from pressure drag.
Note that the lift and drag act perpendicular and parallel to the direction of motion.
Formal definition from Anderson p13:
Pressure is the normal force per unit area exerted on a surface due to the time rate of
change of momentum of the gas molecules impacting on (or crossing) the surface.
1
, AERO40001 Aerodynamics I Section 1-3
__________________________________________________________________________
• Normally consider pressure at a point in the fluid or on a surface.
• In this case the pressure P is the limiting form of the force per unit area, where the area of
interest has shrunk to zero, i.e
As Al → 0 we have
pressure
at a
foil
Pressure is sealer -
no
torque
can consider Deca size
of problem
only
our
a
large enough
but real
DL gasggeits
U
>
< DL
• The pressure at a point is equal in all directions and is a scalar value.
Flow Velocity
air , w
Velocity is a vector with 3 components in each of the co-ordinate directions
2- w z
,
V 280km
y,
-
JC u
, x
The velocity of an aircraft might be 280 knots on a bearing 270° at a fixed altitude.
The knot is an international unit used by ships and aircrafts.
\nautical
1 knot = 1 nautical mile
mile/hour
Ihr
A nautical mile is a length corresponding to:
1 nautical mile = 1 minute of Earth's circumference at the equator.
• 1 knot = 1.853 km/hr l . 853 4 1000/3600
• 1 knot = O S IS .
Velocity can also be measured in mile/hr, ft/min as well as in SI units km/hr, m/s.
(In the USA they use Imperial units (i.e. ft, lb) but still manage to make good aeroplanes!).
2
__________________________________________________________________________
Outline
• Last lecture discussed how shear stress is proportional to the rate of deformation and
that a fluid needs to be in motion to produce shear forces on a body.
• We will continue our introduction by
• Discussing how pressure plays an equally important role
• Introduce the ideas of conservation of mass
• Finally discuss the concept of frame of reference.
Velocity and Pressure
To describe a fluid flow we must consider both velocity
velocity and pressure
pressure.
Pressure
Typically of great practical importance are the changes in pressure that occur as air flows past
an aircraft. e.g. for a wing we need to know the differences in pressure generated on the upper
and lower surfaces.
p
high
N
Drug
un
remote
low
pressure
}
I
-
- -
from
-
-
i
-
-
-
- -
-
-
Relative
.
↳
.
.
.
aerofoil
-
↳
.
top .
high pressure
Lift µ Pressure Distribution
• N/m2
In SI units the pressure is measured in N/m Pascals
2 or Pascals.
• In English or Imperial Units lbs/sqm psi
lbslsqimh -
psi
pressure drags
The changes in pressure also cause a force in the flow direction known as Drag u .We have
already seen that shear stress contributes to Drag through skin friction but an equally important
contribution (particularly if the body is not steamlined) comes from pressure drag.
Note that the lift and drag act perpendicular and parallel to the direction of motion.
Formal definition from Anderson p13:
Pressure is the normal force per unit area exerted on a surface due to the time rate of
change of momentum of the gas molecules impacting on (or crossing) the surface.
1
, AERO40001 Aerodynamics I Section 1-3
__________________________________________________________________________
• Normally consider pressure at a point in the fluid or on a surface.
• In this case the pressure P is the limiting form of the force per unit area, where the area of
interest has shrunk to zero, i.e
As Al → 0 we have
pressure
at a
foil
Pressure is sealer -
no
torque
can consider Deca size
of problem
only
our
a
large enough
but real
DL gasggeits
U
>
< DL
• The pressure at a point is equal in all directions and is a scalar value.
Flow Velocity
air , w
Velocity is a vector with 3 components in each of the co-ordinate directions
2- w z
,
V 280km
y,
-
JC u
, x
The velocity of an aircraft might be 280 knots on a bearing 270° at a fixed altitude.
The knot is an international unit used by ships and aircrafts.
\nautical
1 knot = 1 nautical mile
mile/hour
Ihr
A nautical mile is a length corresponding to:
1 nautical mile = 1 minute of Earth's circumference at the equator.
• 1 knot = 1.853 km/hr l . 853 4 1000/3600
• 1 knot = O S IS .
Velocity can also be measured in mile/hr, ft/min as well as in SI units km/hr, m/s.
(In the USA they use Imperial units (i.e. ft, lb) but still manage to make good aeroplanes!).
2
