How Does Air Pressure Affect Wing Velocity in Aerodynamics?

[Hobbledehoy53]

Not sure how to approach this problem. Seems simple. Here it is...

An airplane is moving through still air at 60m/s. At some point on the wing, the air pressure is -1200N/m^2 gauge. If the density of air is 0.8kg/m^3, find the velocity of the flow at this point. Carefully list the assumptions you have made in your analysis. Express your answer in terms of nondimensional pressure coefficient Cp.

I can tell you that Cp=(p-pinf)/qinf, where pinf is the free stream pressure and qinf=0.5*freestremdensity*freestreamvelociy^2.

Any help would be much appreciated...

 

[Jhero]

Thank you for your question. I can understand how this problem may seem simple at first, but it requires careful analysis and consideration of various factors. I will guide you through the steps to solve this problem and also list the assumptions made in the analysis.

Firstly, let's define the variables given in the problem:
- Airplane velocity (V) = 60m/s
- Pressure at a point on the wing (P) = -1200N/m^2 gauge
- Air density (ρ) = 0.8kg/m^3

To find the velocity of the flow at this point, we need to use the formula for pressure coefficient (Cp) given in the problem: Cp = (P-Pinf)/qinf, where Pinf is the free stream pressure and qinf = 0.5*ρ*V^2.

Now, let's list the assumptions made in our analysis:
1. The air flow is considered to be incompressible, which means the air density remains constant throughout the flow.
2. The flow is assumed to be steady, which means the velocity and pressure do not change with time.
3. The air flow is assumed to be inviscid, which means there is no friction between the air and the surface of the wing.
4. The air flow is assumed to be two-dimensional, which means the flow is happening in a single plane.
5. The air flow is assumed to be irrotational, which means there is no rotation of air particles.
6. The air flow is assumed to be in a state of equilibrium, which means the forces acting on the air particles are balanced.

Now, let's plug in the values in the formula for Cp:
Cp = (-1200N/m^2 - Pinf)/(0.5*0.8kg/m^3*60m/s)^2

To solve for Pinf, we need to rearrange the formula:
Pinf = (-1200N/m^2 - Cp*0.5*0.8kg/m^3*60m/s^2)

Plugging in the value of Cp = -1 (as given in the problem, the pressure is negative), we get:
Pinf = (-1200N/m^2 - (-1)*0.5*0.8kg/m^3*60m/s^2)
Pinf = -1140N/m