Help on Dynamic pressure formula
Thread Starter
Joined: May 2004
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From: Netherlands, the
Help on Dynamic pressure formula
I have a question regarding the dynamic pressure formula:
1/2.ρ.velocity squared
Now the answer you'll find is in hPa. Can somebody tell me how to explain this?
Thanks in advance,
Marcel
1/2.ρ.velocity squared
Now the answer you'll find is in hPa. Can somebody tell me how to explain this?
Thanks in advance,
Marcel
Joined: Jan 2006
Posts: 18
Likes: 0
From: toulouse
Re: Help on Dynamic pressure formula
in formula Rx=1/2 p*S*Vpē*Cx
Cx don't have any dimension so you'll have Rx/S= 1/2pVpē
and Rx is a force divided by an area you 'll have a Pression
and in the SI system N/mē=Pa
I hope I am enough clear marcel
Cx don't have any dimension so you'll have Rx/S= 1/2pVpē
and Rx is a force divided by an area you 'll have a Pression
and in the SI system N/mē=Pa
I hope I am enough clear marcel
Joined: Aug 1999
Posts: 1,050
Likes: 4
From: England
Re: Help on Dynamic pressure formula
Look at the dimensions of Density and Velocity.
(sorry no superscript)
rho = Kg.M-3
V = M.S-1
V2 = M2.S-2
so dynamic pressure units can be stated as
Kg.M-3.M2.S-2
Simplifies to
Kg.M-1.S-2
We are looking to equate the dimensions to Pa, = N.M-2
Can we rearrange the units to make it fit? Use Newtons second law.
F = MA
or better, M = F / A
so Kg = N / (M.S-2)
so Kg = N.M-1.S2
Substitute for mass units in our earlier formula Kg.M-1.S-2
yields N.M-1.S2.M-1.S-2
Seconds cancel out, leaves dymnamic pressure units:
N.M-1.M-1 i.e. N/M2
Hope thats what you wanted. I think its right, though its late.
(c) PB
(sorry no superscript)
rho = Kg.M-3
V = M.S-1
V2 = M2.S-2
so dynamic pressure units can be stated as
Kg.M-3.M2.S-2
Simplifies to
Kg.M-1.S-2
We are looking to equate the dimensions to Pa, = N.M-2
Can we rearrange the units to make it fit? Use Newtons second law.
F = MA
or better, M = F / A
so Kg = N / (M.S-2)
so Kg = N.M-1.S2
Substitute for mass units in our earlier formula Kg.M-1.S-2
yields N.M-1.S2.M-1.S-2
Seconds cancel out, leaves dymnamic pressure units:
N.M-1.M-1 i.e. N/M2
Hope thats what you wanted. I think its right, though its late.
(c) PB
Joined: Jun 2004
Posts: 1,843
Likes: 0
From: Australia
Re: Help on Dynamic pressure formula
Marcel_MPH,
DYNAMIC PRESSURE
I’m not sure of the approach that you’re taking here, but my first thought is that you’re relating the dynamic pressure associated with a given Calibrated Airspeed (CAS). CAS is, of course, the pilot’s practical source of Dynamic Pressure information, as the vital performance characteristics of the aircraft, such as Lift and Drag, depend upon Dynamic Pressure. Pressure may be measured in any number of terms, Pounds per Square Inch, Hectopascals, you name it. The CAS appropriate to a particular dynamic pressure is valid at Sea Level ISA conditions, and the Airspeed Indicator is calibrated for this. The problem is that Dynamic Pressure alone cannot be measured from a Pitot tube, as Impact Pressure is measured instead, the difference being the compression of the air due to Mach Number as Air is compressible.
The simplistic approach for low and slow flight is that air is incompressible. The older airspeed indicators were calibrated for incompressible flow, and used the formula –
V = SQR (2 Q / Rho)
Where Q = Dynamic Pressure, Rho = Air Density, and V = True Airspeed.
Unfortunately for this simplistic formula, compressibility plays an increasingly greater error as speed and altitude are increased, and as Impact Pressure, not Dynamic Pressure is sensed by the Airspeed Indicator, correction for compressibility must be made to yield Dynamic Pressure – the ‘f’ factor.
The calibration formula is as follows –
Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)
Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)
The Left-most portion of the equation is the ‘f’ factor –
F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])
At altitude, the Static Pressure, P, is substituted for Po in the equation.
I’ll leave it to you to convert the various units of measurement to your own requirements.
PS : I don’t care if the U.S. Navy thinks that Sea Level Air Density = .002378 slugs/ft^3, if Douglas thought that it was 0.0023769 slugs/ft^3, that’s good enough for me.
Regards,
Old Smokey
DYNAMIC PRESSURE
I’m not sure of the approach that you’re taking here, but my first thought is that you’re relating the dynamic pressure associated with a given Calibrated Airspeed (CAS). CAS is, of course, the pilot’s practical source of Dynamic Pressure information, as the vital performance characteristics of the aircraft, such as Lift and Drag, depend upon Dynamic Pressure. Pressure may be measured in any number of terms, Pounds per Square Inch, Hectopascals, you name it. The CAS appropriate to a particular dynamic pressure is valid at Sea Level ISA conditions, and the Airspeed Indicator is calibrated for this. The problem is that Dynamic Pressure alone cannot be measured from a Pitot tube, as Impact Pressure is measured instead, the difference being the compression of the air due to Mach Number as Air is compressible.
The simplistic approach for low and slow flight is that air is incompressible. The older airspeed indicators were calibrated for incompressible flow, and used the formula –
V = SQR (2 Q / Rho)
Where Q = Dynamic Pressure, Rho = Air Density, and V = True Airspeed.
Unfortunately for this simplistic formula, compressibility plays an increasingly greater error as speed and altitude are increased, and as Impact Pressure, not Dynamic Pressure is sensed by the Airspeed Indicator, correction for compressibility must be made to yield Dynamic Pressure – the ‘f’ factor.
The calibration formula is as follows –
Vc = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1]) * SQR (2 Qc / Rho0)
Where –
Vc = Calibrated Airspeed in ft/sec,
Qc = Impact Pressure in Lb/ft^2,
Rho0 = Sea Level Air Density = .0023769 slugs/ft^3,
Po = Sea Level Air Pressure = 2116.2 Lb/ft^2,
Y = A constant for air = 1.4, being the ratio of the Specific Heat of Air at constant pressure to that at constant volume (Y = Gamma, I don’t have a Greek key-board)
The Left-most portion of the equation is the ‘f’ factor –
F = SQR ((Y/(Y-1)) * Po/Qc * [(Qc/Po+1) ^ ((Y-1)/Y)-1])
At altitude, the Static Pressure, P, is substituted for Po in the equation.
I’ll leave it to you to convert the various units of measurement to your own requirements.
PS : I don’t care if the U.S. Navy thinks that Sea Level Air Density = .002378 slugs/ft^3, if Douglas thought that it was 0.0023769 slugs/ft^3, that’s good enough for me.
Regards,
Old Smokey
Re: Help on Dynamic pressure formula
Thread Starter
Joined: May 2004
Posts: 60
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From: Netherlands, the
Re: Help on Dynamic pressure formula
Thanks a lot for those answers gentlemen. Although I was looking for the answer from Capt Pitt Bull the information from Old Smokey was very usefull. I have a practical where I have to prove these laws and explain the theory behind the various indicators. Since there's barely a book which explains these formulas I thank you for these wonderfull explanations.
Marcel_MPH
Marcel_MPH
Joined: Jun 2004
Posts: 1,843
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From: Australia
Re: Help on Dynamic pressure formula
Marcel_MPH,
As you say, there's barely a book which explains these formulas, but the one containing a COMPLETE reference to all of the necessary formulae for instrument calibration is -
Air Navigation, H.O. Pub. No. 216, published by the U.S. NAVY HYDROGRAPHIC OFFICE.
It was published for Navigators, not pilots or aerodynamacists, but it was (and still is) my bible during my training for Flight Navigator Licence, and later for Performance Engineering. The much more modern publications I've used don't even come close in many respects. Mind you, there's a lot of cr@p to wade through, like Astro Navigation, which, like me, has outlived it's usefulness.
Last published in 1963, perhaps a little hard to get these days.
Regards,
Old Smokey
As you say, there's barely a book which explains these formulas, but the one containing a COMPLETE reference to all of the necessary formulae for instrument calibration is -
Air Navigation, H.O. Pub. No. 216, published by the U.S. NAVY HYDROGRAPHIC OFFICE.
It was published for Navigators, not pilots or aerodynamacists, but it was (and still is) my bible during my training for Flight Navigator Licence, and later for Performance Engineering. The much more modern publications I've used don't even come close in many respects. Mind you, there's a lot of cr@p to wade through, like Astro Navigation, which, like me, has outlived it's usefulness.
Last published in 1963, perhaps a little hard to get these days.
Regards,
Old Smokey
Joined: Feb 2004
Posts: 4
Likes: 0
From: UK
Re: Help on Dynamic pressure formula
Yes....Still a strong reference book for me...wonderfull diagrams that put the world of spherical trig into so easy diagrams...terrific with even day to day stuff (if one is interested!) re the equation of time, the soltices, equinixes et al...Surely should be a must read for even the remotely curious....
