Please help. I have a question thats been on my mind:

Static pressure is the pressure when moving with the fluid. Total pressure is the pressure when the fluid comes to a stop (i.e. V=0)

My question is what is the difference between the freestream static pressure measured in the wind tunnel and the one measured in real flight? What I mean is that in real flight the static probe (on a Pitot-static tube) measures the static pressure which is the same as the atmospheric pressure and does not vary with airspeed?...but in the wind tunnel the freestream static pressure (also from a Pitot static tube) would vary with airspeed?..am I right to say this?

Please help. Its driving me crazy.

Thanks in advance.

No, you're not right. The static pressure is not a constant atmospheric pressure - it is simply the local pressure, which in the case of a compressible flow is the thermodynamic pressure. The total pressure is the pressure (ideally at the same point in the flow) if you decelerate the flow and convert the kinetic energy into an additional pressure. Doesn't matter whether you are in a wind tunnel or on a flight vehicle. The local pressure will in all likelihood not be equal to the freestream atmospheric pressure, but will vary with local velocity (like around an airfoil).

Yes I know which is why the pressures measured around the airfoil would change (and for incompressible flow would satisfy the Bernoulli equation). BUT I am talking about freestream static pressure, i.e. if the probe is far ahead in the stream unaffected by the airfoil boundary layer. Then what?...would it be equal (or approx.) to atmospheric?

In other words 2 airplanes flying at the same altitude but different speeds....would the ''freestream'' static pressure be the same in both cases?...

If the probe is "far ahead" then what difference does it make how fast the airplane is going? The effect of the airplane speed will be felt in the boundary layer. Far away from the plane the air is not moving in the atmosphere (barring gusts) so the static pressure would depend only on altitude, and in the case you are describing then the answer is that the static pressures would be the same. But the case you are describing is trivial, because you have removed the only thing that could affect the static pressure. If you consider the wind tunnel as a Gallilean transformation of a non-accelerating aircraft, the same argument holds. The static pressure is just the local thermodynamic pressure. If you remove any disturbances, then it will be equal to the so-called free-stream pressure, which in the case of an aircraft in free flight would be atmospheric. For a tunnel, it would be whatever pressure the tunnel can generate.

Okay so in CFD and wind tunnel tests because we assume the air is flowing past a fixed body then the static pressure measured ''far ahead'' of the airfoil is different than in the case of real flight were the body is moving and the air is at rest. PLUS in all cases regardless of the different pressures measured,.. the same velocity would be calculated using Bernoulli equation (assuming invisid, incompressible).

No.

Think of it like this - you stand next to an airplane on the ground and the wind is blowing over it. What is the static pressure at the control tower? Once the plane takes off, has the static pressure at the control tower changed?

The static pressure in a fluid is not dependent on whether we do CFD or run a wind tunnel test or fly an airplane. It is just a function of the thermodynamic state of the fluid at a point. The pitot probe measures this regardless of where the probe is or what is going on around it. The Gallilean transformation will have no effect on the static pressure. If I fly my plane at 10000 ft altitude in still air and the static pressure is some value "far" from the aircraft, I can replicate that exact same static pressure (in theory) in a wind tunnel by fixing the plane to a support and blowing air over it at the same velocity.

I get your point but if as you said:

"I fly my plane at 10000 ft altitude in still air and the static pressure is some value "far" from the aircraft, I can replicate that exact same static pressure (in theory) in a wind tunnel by fixing the plane to a support and blowing air over it at the same velocity. "

..then in flight (still considering youre example) if I increase my aircraft speed then the static pressure measured doesnt change (as we have agreed)...BUT in the wind tunnel if we increase the fan (blower) speed then the static pressure would change...do you get me?

No, if you increase the wind tunnel speed, you increase the total pressure but not the static pressure. If you use a Pitot tube to measure the wind speed, both in air or wind tunnel, you consider the difference between total and static pressure so to calculate dynamic pressure.

Yes using Bernouilli we calculate dynamic pressure (0.5pV^2) and get the speed. But are you sure that the static pressure measured from a Pitot-static tube (placed far ahead of the airfoil) in a wind tunnel is constant regardless of air (blowing fan) speed?

SORRY for the confusion. Its just that I did wind tunnel tests and CFD tests in Fluent and in both cases, the static pressure (far ahead of the wing) was changing with airspeed and wanted to verify this....

The static pressure in the tunnel is going to depend on the thermodynamic state of the fluid at the point you put the probe. How do you reach a particular thermodynamic state? In the case of the wind tunnel, if you crank the fan up you will be doing more work on the air moving through the fan, which will result in a different thermodynamic state, unless you add some conditioning to the airstream (which could be done. Was this done in your case? I don't know, because you've given no details. Could the static pressure change in the way you describe - yes, for the reason mentioned above. What I said originally was that you could simply match the free-stream behavior in a tunnel at a given velocity. Now you're talking about changing the fan speed - what else are you going to change?

Yes, you are right. Changing the speed of a flying aircraft does not change the static pressure of the atmosphere at "upstream infinity". Only the relative velocity is (and thus the dynamic and stagnation pressures are) changed.

Whereas, in any particular wind-tunnel installation, if you do not change out any equipment, or modify the test section, the "freestream" static pressure (indicated by a Pitot static probe upstream of the model) will change along with fluid velocity relative to the model, when you change the tunnel-fan speed. On a single plot, you can draw the fan characteristic (pressure ratio versus mass flow rate curves, parametrized by fan speed) and the characteristic of the tunnel (approximated as a nozzle), and then the operating point of the tunnel will be at the intersection of the two characteristics (you have to account for source and exhaust pressure differences in your plot, and also stagnation versus static). If you increase the fan speed (and power), not only will the mass flow rate increase (and thus velocity) but so will the static pressure. Basically, running the fan at two different speeds is like flying the aircraft at two conditions differing in both speed AND altitude.

However, keep in mind that in incompressible flow, the static pressure is of no account (as long as it stays positive). It is the dynamic pressure that matters. In your experiments and simulations, with incompressible or low-speed flow, subtract out the "freestream" pressure from all pressures. For significantly compressible flow, rescale using dimensional analysis. The freestream Mach number will then enter as a parameter that should be matched between experiment and numerics.

Thanks Ananda. You see I thought that the reason freestream static presssure increased is a misalignment in the Pitot-static tube, i.e. the static pressure port is not correctly aligned in parallel with the flow + the fact that the air is not flowing in a straight line anyways.

It is confusing because if you read any book, they say that static pressure measured from a Pitot-static probe far upstream is invariant with fluid motion,..i.e. its like hopping on one of the particles and moving with it at the same speed therefore you would feel the molecular bombardements but no effects due to airspeed.

You are welcome. Yes, I understand the cause of the confusion. The books are really talking about the changing the speed of the aircraft, which does not disturb the thermodynamic state of the air far upstream. Some books may portray this as a magical (and entirely hypothetical) change in the fluid motion which does not disturb the thermodynamic state. In the wind tunnel, the change in fan speed changes the enthalpy being imparted by the blades to each unit mass of fluid. If the test section area is not changed, this energy shows up as a change in both static pressure and speed of the air. As I said, you can remove the static pressure from consideration by subtracting it out (incompressible) or matching Mach numbers (ideal gas) between experiment and numerics.