Bernoulli's principle states that within a confined system, total energy remains constant, so if the velocity of a fluid increases, the pressure decreases. When air flows over an airfoil, its velocity increases and pressure decreases above the airfoil compared to below it, resulting in higher pressure below pushing the airfoil up. Most but not all of the lift is produced by this differential pressure - the rest is produced by Newton's third law of motion, as the air deflecting downward exerts an equal and opposite force lifting the airfoil upward.
In this presentation, we discussed the different principles explaining the lift generation. Principles such as venturi's principle and time-lapse theory became invalid. The correct theory for the lift generation is explained in this ppt.
FLUID DYNAMICS
Basic terms.
Ideal Fluid.
Equation of Continuity.
Bernoulli's Theorem.
Application of Bernoulli’s Theorem.
FLUID:
A fluid is a substance which can flows.
Such as liquids , gases and plasma.
Example: Water, air etc…
Fluid Dynamics:Study of fluid in motion.
Viscosity:
The frictional effect b/w different layers of a flowing fluid is the viscosity of the fluid.
Drag Force:
An object moving through a fluid experiences a retarding force called a drag force.
Fluid Flow:
Streamline /Laminar Flow:
Every particle of fluid during flow has constant velocity, pressure , density and having regularity.
Turbulent Flow:
The irregular and non-steady fluid flow is called turbulent flow.
Velocity , pressure , and density remain non – uniform.
IDEAL FLUID:
Properties of Ideal Fluid:
Fluid is non-viscous (Internal Friction is neglected).
Fluid is incompressible (i.e. Constant Density).
Flow is Steady (Laminar).
Flow is irrotational (i.e. No angular momentum)
EQUATION OF CONTINUITY:
Statement:“It states that the product of the area and the fluid speed at all points along a pipe is constant for an incompressible fluid.”
Derivation:
𝐦𝐚𝐬𝐬=𝐝𝐞𝐧𝐢𝐬𝐭𝐲×𝐯𝐨𝐥𝐮𝐦𝐞
∆𝑚_1=𝜌𝐴_1 〖∆𝑥〗_1
∵〖∆𝑥〗_1=𝑣_1×∆𝑡
∆𝑚_1=𝜌𝐴_1 𝑣_1×∆𝑡
Similarly
∆𝑚_2=𝜌𝐴_2 〖∆𝑥〗_2
∵〖∆𝑥〗_1=𝑣_1×∆𝑡
∆𝑚_2=𝜌𝐴_2 𝑣_2×∆𝑡
Because the fluid is incompressible and the flow is steady, then
∆𝑚_1=∆𝑚_2
𝜌𝐴_1 𝑣_1×∆𝑡=𝜌𝐴_2 𝑣_2×∆𝑡
𝐴_1 𝑣_1=𝐴_2 𝑣_2
So the product:
𝐴𝑣=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
It has Dimensions:
𝐴×∆𝑥/∆𝑡=𝑉𝑜𝑙𝑢𝑚𝑒/𝑡𝑖𝑚𝑒
It is either called Volume Flux or Flow Rate
The speed of water spraying from the end of a garden hose increases as the size of the opening is decreased with the thumb.
Bernoulli’s Theorem:
It is simply a statement of Law of conservation of energy applied to liquid in motion.
This theorem states that:
“For the steady flow of an ideal fluid, the total energy (i.e., sum of pressure, potential energy & kinetic energy) per unit volume remains constant through the flow.”
𝑃+𝜌𝑔ℎ+1/2 𝜌𝑣^2=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Proof:
The force exerted on lower segment:
𝐹_1=𝑃_1 𝐴_1
The Work Done by force on this segment is:
𝑊_1=𝐹_1 〖∆𝑥〗_1
𝑊_1=𝑃_1 𝐴_1 〖∆𝑥〗_1
Similarly on the upper segment:
𝑊_2=−𝑃_2 𝐴_2 〖∆𝑥〗_2
This work done is negative because the it is against Fluid Fow
The Force 𝐹_1 moves the Liquid a distance 〖∆𝑥〗_1 & the liquid moves a distance 〖∆𝑥〗_2 against the Force 𝐹_2.
Therefore, the net work done on liquid is:
𝑊=𝑃_1 𝐴_1 〖∆𝑥〗_1−𝑃_2 𝐴_2 〖∆𝑥〗_2
𝑊=𝑃_1 (𝐴_1 〖∆𝑥〗_1)−𝑃_2 (𝐴_2 〖∆𝑥〗_2)
∵𝐴_1 〖∆𝑥〗_1=𝐴_2 〖∆𝑥〗_2=m/ρ
𝑊=(𝑃_1−𝑃_2 )V
Part of this Work is utilized by the fluid in changing its Kinetic Energy & a part is used in changing its Gravitational Potential Energy:
∆𝐾.𝐸=1/2 𝑚𝑣_2^2−1/2 𝑚𝑣_1^2
∆𝑃.𝐸=𝑚𝑔ℎ_2−𝑚𝑔ℎ_1
None of the Work Done on the liquid has been used to overcome the internal friction because the liquid is non-viscous.
According to Law of Conservation of Energy:
𝑊=∆𝐾.𝐸+∆𝑃.𝐸
(𝑃_1−𝑃_2 )V=1/2 𝑚𝑣_2^2−1/2 𝑚𝑣
In this presentation, we discussed the different principles explaining the lift generation. Principles such as venturi's principle and time-lapse theory became invalid. The correct theory for the lift generation is explained in this ppt.
FLUID DYNAMICS
Basic terms.
Ideal Fluid.
Equation of Continuity.
Bernoulli's Theorem.
Application of Bernoulli’s Theorem.
FLUID:
A fluid is a substance which can flows.
Such as liquids , gases and plasma.
Example: Water, air etc…
Fluid Dynamics:Study of fluid in motion.
Viscosity:
The frictional effect b/w different layers of a flowing fluid is the viscosity of the fluid.
Drag Force:
An object moving through a fluid experiences a retarding force called a drag force.
Fluid Flow:
Streamline /Laminar Flow:
Every particle of fluid during flow has constant velocity, pressure , density and having regularity.
Turbulent Flow:
The irregular and non-steady fluid flow is called turbulent flow.
Velocity , pressure , and density remain non – uniform.
IDEAL FLUID:
Properties of Ideal Fluid:
Fluid is non-viscous (Internal Friction is neglected).
Fluid is incompressible (i.e. Constant Density).
Flow is Steady (Laminar).
Flow is irrotational (i.e. No angular momentum)
EQUATION OF CONTINUITY:
Statement:“It states that the product of the area and the fluid speed at all points along a pipe is constant for an incompressible fluid.”
Derivation:
𝐦𝐚𝐬𝐬=𝐝𝐞𝐧𝐢𝐬𝐭𝐲×𝐯𝐨𝐥𝐮𝐦𝐞
∆𝑚_1=𝜌𝐴_1 〖∆𝑥〗_1
∵〖∆𝑥〗_1=𝑣_1×∆𝑡
∆𝑚_1=𝜌𝐴_1 𝑣_1×∆𝑡
Similarly
∆𝑚_2=𝜌𝐴_2 〖∆𝑥〗_2
∵〖∆𝑥〗_1=𝑣_1×∆𝑡
∆𝑚_2=𝜌𝐴_2 𝑣_2×∆𝑡
Because the fluid is incompressible and the flow is steady, then
∆𝑚_1=∆𝑚_2
𝜌𝐴_1 𝑣_1×∆𝑡=𝜌𝐴_2 𝑣_2×∆𝑡
𝐴_1 𝑣_1=𝐴_2 𝑣_2
So the product:
𝐴𝑣=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
It has Dimensions:
𝐴×∆𝑥/∆𝑡=𝑉𝑜𝑙𝑢𝑚𝑒/𝑡𝑖𝑚𝑒
It is either called Volume Flux or Flow Rate
The speed of water spraying from the end of a garden hose increases as the size of the opening is decreased with the thumb.
Bernoulli’s Theorem:
It is simply a statement of Law of conservation of energy applied to liquid in motion.
This theorem states that:
“For the steady flow of an ideal fluid, the total energy (i.e., sum of pressure, potential energy & kinetic energy) per unit volume remains constant through the flow.”
𝑃+𝜌𝑔ℎ+1/2 𝜌𝑣^2=𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
Proof:
The force exerted on lower segment:
𝐹_1=𝑃_1 𝐴_1
The Work Done by force on this segment is:
𝑊_1=𝐹_1 〖∆𝑥〗_1
𝑊_1=𝑃_1 𝐴_1 〖∆𝑥〗_1
Similarly on the upper segment:
𝑊_2=−𝑃_2 𝐴_2 〖∆𝑥〗_2
This work done is negative because the it is against Fluid Fow
The Force 𝐹_1 moves the Liquid a distance 〖∆𝑥〗_1 & the liquid moves a distance 〖∆𝑥〗_2 against the Force 𝐹_2.
Therefore, the net work done on liquid is:
𝑊=𝑃_1 𝐴_1 〖∆𝑥〗_1−𝑃_2 𝐴_2 〖∆𝑥〗_2
𝑊=𝑃_1 (𝐴_1 〖∆𝑥〗_1)−𝑃_2 (𝐴_2 〖∆𝑥〗_2)
∵𝐴_1 〖∆𝑥〗_1=𝐴_2 〖∆𝑥〗_2=m/ρ
𝑊=(𝑃_1−𝑃_2 )V
Part of this Work is utilized by the fluid in changing its Kinetic Energy & a part is used in changing its Gravitational Potential Energy:
∆𝐾.𝐸=1/2 𝑚𝑣_2^2−1/2 𝑚𝑣_1^2
∆𝑃.𝐸=𝑚𝑔ℎ_2−𝑚𝑔ℎ_1
None of the Work Done on the liquid has been used to overcome the internal friction because the liquid is non-viscous.
According to Law of Conservation of Energy:
𝑊=∆𝐾.𝐸+∆𝑃.𝐸
(𝑃_1−𝑃_2 )V=1/2 𝑚𝑣_2^2−1/2 𝑚𝑣
1. Bernoulli and his Principal of Airflow
Within any confined system, total energy
remains constant. If one component of energy
increases, there must be a corresponding
decrease in other components.
Total pressure within the confined system is
the summation of static and dynamic pressure
2. Venturi Tube
(subsonic, incompressible flow)
The volume of air passing any given point per unit of
time is equal throughout the tube.
This is known as MASS FLOW RATE
Slow velocity of air with As air velocity increases,
equal static and
equal static and static pressure decreases,
dynamic pressures
dynamic pressures dynamic pressure increases
3. Airfoil
Lets take half of that venturi tube and see what happens
when we move air across the shape
Lets assume there is no upper physical limit of the tube
The flow closest to the airfoil conforms to the shape of the
airfoil while the air farthest from the airfoil remains horizontal
and acts like the upper surface of the venturi
4. How is most of the lift produced?
Since air has a greater distance to travel over the upper surface there is
a greater velocity increase and pressure decrease over the upper
surface than the lower surface. The higher pressure below the airfoil
seeks the lower pressure above causing the airfoil to move up.
Low Pressure Area
Static =1 Static =5
=9 = 10
Dynamic = 8 Dynamic = 5
Static =4
= 10
Dynamic = 6
Static =4
= 11
High Pressure Area Dynamic = 7
High seeks Low
5. Question
If the differential in pressures produces most of
the lift, what is producing the rest of the lift?
The remaining lift is a result of Newton’s third law of motion,
Action and Reaction