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Aerodynamics - Fundamental Equations

17 important questions on Aerodynamics - Fundamental Equations

What is the velocity and how can we decribe it?

The velocity in point B is the velocity of an infinitesimally small fluid element as it sweeps through B.

Where is the stagnation point located and what is it?

The point at the front of the airfoil where the velocity is zero V=0.

Which two aerodynamic forces are there?

Shear stress or friction force
Pressure distribution

Consider a flow with velocity V penetrating a plane through area A in a time interval dt

(gas density: ρ)

What is the mass flow that passes A in time dt?

Mass flow per second: m = m / dt

m = ρAVdt / dt
m = ρ AV

What does it mean that in the continuity equation for steady flow, the ρ and V are mean values?

ρ and V are uniformly distributed over A. This is a assumption.

Example 4: Consider a converging duct with an inlet area A1= 5 [m2].
Air enters this duct with a velocity V1=10 [m/s] and leaves the duct exit with a velocity V2= 30 [m/s].

What is the area of the duct exit?

We consider incompressible flow:
AV = constant
A1V1 = A2V2

5 * 10 = A2 * 30
A2 = 50/30
A2 = 1.67 [m2]

Which three forces do we consider to act on a certain element and what forces do we neglect in the derivation?

Pressure force
Friction force
Gravity force

We neglect:
4. Neglect the gravity force (small)
5. Neglect the viscosity --> No friction forces

How do we derive the left part of newton's second law for Euler equation?

F = m*a
We have an element dx dy dz
For equation of F = p*A
Two sides of the element in the X direction
F = p*A - P2 *A

F = pdy dz - (p + dp) dydz
Etc.

How do we derive the right part of newton's second law for Euler equation?

F = m * a
Mass m of the fluid element is m = ρ*V = ρdx dy dz
Acceleration a of the fluid element is a = dV/dt = dV/dx * dx/dt = dV/dx *V

etc.

What is the Euler equation?

.dp = -ρVdV
It is a differential equation

It is the relation between force and momentum
Also called the momentum equation

Gravity forces are neglected
Viscosity is neglected (inviscid flow)
Steady flow
Flow may be compressible.

How do we use the Euler equation along a stream line between point 1 and 2.

Integrate the Euler equation dp + ρVdV = 0

Then we get
p1 + 1/2 ρ V2 = p2 + 1/2 ρ V2

p + 1/2 ρ V2 = pt

Static pressure + dynamic pressure = total pressure

What is bernoulli's principle?

Inviscid flow; viscosity = 0
Incompressible flow
Gravity forces neglected

What does the application of Bernoulli's principle show and what can we calculate?

This is the pressure distribution over an airfoil (static pressure). With this, we can caluclate the change in velocity over the airfoil.

How can we define the pressure coefficient.

Let op de plek van po en deeld door de dynamic pressure of the incoming flow.

Why is the maximum Cp, 1?

Lowest velocity is at the stagnation point where V=0 [m/s]

How can you measure the velocity in a pitot-static tube?

Total pressure is constant along a streamline if M<0.3 (incompressible flow).
So:
pto = pt1 = pt2 = pt

We actually measure pt - po
Bernoulli gives: pt -po = 1/2 ρ V2(0)

Example 5: Consider the same convergent duct as in the previous example. If the air pressure and temperature at the inlet are p1= 1.2 x 10^5 [N/m2] and T1=330 [K] respectively, calculate the pressure at the exit.

Example 4: Consider a converging duct with an inlet area A1= 5 [m2].
Air enters this duct with a velocity V1=10 [m/s] and leaves the duct exit with a velocity V2= 30 [m/s].

.p - 1/2ρ V2 = constant
p1 - 1/2ρ V^2,1 = p2- 1/2ρ V^2,2

ρ = p/RT
ρ1 =

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Aerodynamics

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Aerodynamics - Fundamental Equations

17 important questions on Aerodynamics - Fundamental Equations

What is the velocity and how can we decribe it?

Where is the stagnation point located and what is it?

Which two aerodynamic forces are there?

Consider a flow with velocity V penetrating a plane through area A in a time interval dt(gas density: ρ)What is the mass flow that passes A in time dt?

What does it mean that in the continuity equation for steady flow, the ρ and V are mean values?

Example 4: Consider a converging duct with an inlet area A1= 5 [m2].Air enters this duct with a velocity V1=10 [m/s] and leaves the duct exit with a velocity V2= 30 [m/s].What is the area of the duct exit?

Which three forces do we consider to act on a certain element and what forces do we neglect in the derivation?

How do we derive the left part of newton's second law for Euler equation?

How do we derive the right part of newton's second law for Euler equation?

What is the Euler equation?

How do we use the Euler equation along a stream line between point 1 and 2.

What is bernoulli's principle?

What does the application of Bernoulli's principle show and what can we calculate?

How can we define the pressure coefficient.

Why is the maximum Cp, 1?

How can you measure the velocity in a pitot-static tube?

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Consider a flow with velocity V penetrating a plane through area A in a time interval dt

(gas density: ρ)

What is the mass flow that passes A in time dt?

Example 4: Consider a converging duct with an inlet area A1= 5 [m2].
Air enters this duct with a velocity V1=10 [m/s] and leaves the duct exit with a velocity V2= 30 [m/s].

What is the area of the duct exit?