Dynamic pressure problems

[hinhin]

Hey guys,


I have a confusing thought regarding the dynmaic pressure....
I am wondering if the dynamic pressure experiencing by the a/c would change in different altitude


Given dynamic pressure: 1/2 p V^2

At a higher altitude, P drops
but flying at a constant IAS, TAS increases.
Since V is with a square(the increase in V should be larger than P) , can i say that the dynamic pressure increases at higher altitude?!

By then it contradicts that flying at a constant IAS, dynamic pressure experienced by the a/c at different altitudes should be the same.....


Can someone spot out what went wrong in the above statments...?

Big thanks in advance!

[oggers]

can i say that the dynamic pressure increases at higher altitude?!

Dynamic pressure does not increase as you climb.

Since rho drops as you climb the dynamic pressure drops if V (TAS) remains constant. Therefore V must increase to maintain constant dynamic pressure (and IAS). So what happens is that by maintaining the IAS as you climb you are actually accelerating.

[pattern_is_full]

The formula you use for dynamic pressure only applies to incompressible fluids (e.g. water)

The formula for dynamic pressure in a compressible fluid (e.g. air, up to a point, and specifically for aeronautics, where it is called impact pressure - qc) is different:

https://wikimedia.org/api/rest_v1/media/math/render/svg/89f40de2bde8d4bc9104ec3b5456a2ef01b3d69b

P = static pressure

Note that Mach number (M) is the factor for "speed" (not V), and at any speed below Mach 1.0, the square of M will be less than M.

e.g. M = 0.8, Mˆ2 = 0.64

https://en.wikipedia.org/wiki/Impact_pressure

[keith williams]

The first point which you need to understand is the fact that an airspeed Indicator (ASI) is essentially a pressure measuring instrument. It measures the dynamic pressure and gives an airspeed indication that is determined by the magnitude of that dynamic pressure. This means that every time an ASI sees a given value of dynamic pressure it gives out the same indicated airspeed. This in turn means that for two indentical ASIs to give the same indicated airspeed, they must be sensing the same magnitude of dynamic pressure.

Dynamic pressure = ½ Rho V squared

Where Rho is the air density and V is the TAS.

To answer your questions let us start by imagining that we have two identical aircraft with two identical ASIs, one at mean sea level and the other at 40000 feet. The two aircraft are flying at the same indicated airspeed (IAS) so their airspeed indicators must be sensing the same magnitude of dynamic pressure.

Let us imagine that the magnitude of the dynamic pressure in both cases is 1 unit (for the purposes of this explanation we do not need to concern ourselves with what those units are)

At mean sea level we have:

Dynamic pressure = 1 unit = ½ (mean sea level Rho) x (mean sea level TAS squared).

And at 40000 feet we have:

Dynamic pressure = 1 unit = ½ (40000 feet Rho) x (40000 feet TAS squared)

At 40000 feet the value of Rho is about ¼ of its mean sea level value, so to maintain the same dynamic pressure our TAS squared at 40000 feet must be 4 times its mean sea level value. This means that the TAS at 40000 feet must be about 2 times the means sea level value.

So at mean sea level we have:

Dynamic pressure = 1 = ½ (mean sea level rho) x (mean sea level TAS squared).

And at 40000 feet we have:

Dynamic pressure = 1 = ½ (1/4 x mean sea level Rho) x (2 x mean sea level Rho)

Looking at the above figures we can see that for both aircraft to be flying at the same Indicated Airspeed the TAS at 40000 feet must be twice that at mean seal level.

In reality the whole subject is made more complex by factors such as the compressibility of the air, but for the purposes of your question, it is better to keep the matter simple by ignoring these complications.

[underfire]

https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/Images/pitot.gif

https://www.grc.nasa.gov/www/k-12/airplane/Images/pitot.jpg

[flyburg]

I can't figure this out myself, so for any of your whiz kids, roughly, what is the dynamic pressure in psi at say 37.000 flying .79?

Thanks

Reason I'm asking, had a discussion the other day with a college, at cruise altitude, is the cabin pressure more or less than the outside dynamic pressure in case of a window failure? We couldn't figure it out!

[Goldenrivett]

what is the dynamic pressure in psi at say 37.000 flying .79?


Ans = 1.3769 psi.

Atmospheric pressure at 37,000 ft = 3.1518 psi
so the dynamic pressure at 0.79M is less than half of the static pressure.

If the front window blows out at 37,000 alt, the dynamic pressure + static pressure = 4.5 psi which is equivalent to an ALT of about 29,000 feet.

Aerospaceweb.org | Atmospheric Properties Calculator (http://www.aerospaceweb.org/design/scripts/atmosphere/)

[flyburg]

Thanks!!👍🏻