How to calculate change in pressure of air through a funnel

[fergusonc]

i am looking for a formula or text containing information on how to calculate the change in pressure when air is funneled, in a closed system, where the air is being forced through the system initially with no motion then forced through a pipe that has the same diameter for a relatively long distance then is suddenly funneled down to a much smaller diameter. any help is much appreciated. i can't seem to find anything related to this topic. most formulas i have found deal only with incompressible fluids where i am interested in air which, of course, can be compressed. thanks for any help.

 

[russ_watters]

Welcome to PF.

I'm having trouble visualizing what you are talking about. How is the air forced to move? A fan? A diagram would help a lot.

Yes, air can be compressed, but that doesn't necessarily mean that it is compressed in yoru scenario. Unless you are dealing with compressed air (above, say, half a psi), the incompressible flow assumptions will work fine. It sort of sounds like you need Bernoulli's equation applied to a Venturi tube, but I'm not certain.

 

[cjl]

Unless the airspeed is very high (V > mach 0.2-0.3 or so, depending on the required accuracy), or there is significant pressure variation within your system, you can treat the flow as incompressible.

 

[rcgldr]

If you're trying to model a real world situation, note that the pipe does work against air flow by reducing it's pressure over distance. The rate of mass flow is the same everywhere in the pipe, but pressure is reduced due to friction with the pipe itself and viscosity within the air, with the pressure energy being converted into heat.

 

[fergusonc]

i am dealing with compressed air and it's forced out of an air tank or air compressor through the pipe toward the funnel section where the diameter is reduced. i was just wondering what the relationship would be in the pressures at each end of the funneled section.

 

[cjl]

If the velocity is not extremely high, then the pressure will remain roughly constant throughout the funnel, with the velocity increasing in inverse proportion to cross sectional area.

 

[russ_watters]

Yes, I phrased that poorly: it's when the velocity pressure pressurizes the air (which happens at high velocity) that the incompressible flow equations start to break down.