How can Bernoulli's equation be applied to pitot-static tubes?

[adamlep14]

If anyone can help me, I will be extremely grateful:

i need to make a sample problem for a physics project using Bernoulli's equation:
P+.5pv2+pgy = constant

i don't know how to make a problem using this equation because the physics are a bit advanced for me and i don't know realistic numbers.

thank you to whoever help! -adam

 

[russ_watters]

Well, pick a real-world situation and adapt the generalized equation to it. One I deal with almost every day is using a manometer and pitostatic tube to measure airflow through ductwork. Usually we deal with velocities in the 500 fpm range: can you calculate the velocity pressure?

 

[adamlep14]

my project is on the physics of flight so i would assume anything to do with air pressure for jets in high altitudes would be good. i should have mentioned this before.

all i really need is real life numbers that can be given in the problem so that the students in my class can solve for either P or V.

 

[rcgldr]

Bernoulli's equation ... physics of flight ... P+.5pv2+pgy = constant

This equation needs to be modified to describe the physics of flight. This equation is a mathematical way of stating that the total energy of a volume of air is constant, but when an aircraft passes through the air, the total energy of the air is changed.

An aircraft in flight accelerates air. The amount of work done on the air by the aircraft causes a change in total energy of the air. The equation you've shown needs to be modified to take into account the change in total energy caused by an aircraft.

The acceleration vector of the air is typically split into two components, one perpendicular to the direction of flight, related to lift, and one in the direction of flight related to drag. For an normal aircraft in level flight, most of this acceleration of air is downwards, resulting in a reactive lift force, and some of this acceleration is forwards, resulting in a reactive drag force.

I often see incorrect examples of lift explained with curved top, flat bottom wings, but here is link to a picture of a lifting body glider with a flat top and curved bottom. It glides just fine, and with the top basically horizontal (note the angle of attack of the adjacent chase jet):

lifting body.jpg

 

[russ_watters]

My example works for the physics of flight - it's the method planes use to measure airspeed. You'll want to multiply that speed by about 20 or 40 though, for airplanes...

 

[rcgldr]

Bernoulli's equation as applied to pitot-static tubes is explained in the next link below. Note that the "dynamic" pressure increases with velocity, while static pressure remains constant, so that total pressure increases with velocity. This is how the fact that work is being done on the air is taken into account. This differs from the "classic" Bernoulli situation where total energy is constant, so an increase in dynamic pressure results in a decrease in static pressure (or vice versa). In this (pitot) situation, it's the static pressure that is constant, and the dynamic and total pressures that are increasing as velocity increases.

http://www.grc.nasa.gov/WWW/K-12/airplane/pitot.html

Total pressure as mentioned in the above ariticle increases with velocity and is higher than the actual air presssure at the altitude of the aircraft due to the "ram air" effect mentioned in the Wiki ariticles below and the flash player based simulation of the air speed indicator (also below). Apparently the static ports are setup to minimize "venturi" effect, while the "alternate" ports do experience some "venturi" effect. The static ports have the same (or nearly so) pressure as the actual air pressure, while the alternate ports have slightly less pressure.

Here's a link to an article about airspeed indicators from Wiki.

http://en.wikipedia.org/wiki/Airspeed_indicator

and pitot-static sensors used on aircraft.

http://en.wikipedia.org/wiki/Pitot-static

Flash player simulation of air speed indicator (includes usage of "alternate" static ports):

http://www.luizmonteiro.com/Learning_Pitot_Sim.htm