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Old 11-01-2009, 08:28 PM   #1
Arrowstar
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Default Flow across a screen/radiator/etc

Hello,

I have a quick question in fluid mechanics I've been considering. Consider a pipe that has a screen, radiator, or some other flow impeding device contained within. Assume that the pipe is connecting two large tanks of constant pressures and that the radiator/screen is of negligible length in the direction of flow. Additionally, assume no major (frictional) losses in the pipe and that the flow is steady.

Assuming the flow is incompressible, is there a velocity drop across the screen? I know there is a pressure drop, but should I expect to find that my fluid has physically slowed? My current reasoning suggests not:

Conservation of mass must apply across the screen. If the area directly before the screen is identical to the area directly after the screen, and the fluid density is constant (incompressible assumption, above), then the velocity must be equal by the reduced form of conservation of mass:

v_1A_1\rho_1 = v_2A_2\rho_2

Where A is the cross section area of the pipe, v is the fluid velocity, and rho is the fluid density. If A and rho are constant, then the velocity at 1 (before the screen) must be equal to the velocity after the screen, 2.

Does this reasoning fit with reality, or is there something I'm missing?

Additionally, if there was a finite thickness screen (say it was an extended grille on a car), would you see an non-negligible velocity drop?

Last edited by Arrowstar; 11-01-2009 at 08:47 PM.
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Old 11-01-2009, 09:00 PM   #2
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Well, if you put something inside the pipe, you're gonna reduce the surface area at that point...
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Old 11-01-2009, 09:01 PM   #3
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You're exactly right. Assuming the inlet and outlet piping have the same area, the velocity thru both will be the same.
The velocity thru the restriction will be higher since the area is smaller.

I don't understand your question at the end. Can you restate it?
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Old 11-01-2009, 09:07 PM   #4
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The question I was asking at the end was for a restriction which has a non-negligible length in the direction of the flow. So, say I have a pipe which immediately contracts to some smaller diameter, uses that smaller diameter for 10 meters, and then expands again immediately to the original diameter. You'll obviously have a loss at the inlets and exits, but, neglecting major losses, should the velocity of the fluid directly before the inlet be the same as the velocity of the fluid directly after the exit of the constriction?
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Old 11-01-2009, 09:16 PM   #5
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Nope same phenomenon.
if Af = Ai then Vf = Vi
the reduced diameter section will increase the overall flow resistance .
One way this sort of system is frequently analyzed is with the "equivalent length method"
each pipe fitting is treated as a certain length of open pipe, for example an elbow might offer the same flow resistance as 3 feet of open pipe whereas a globe valve might be 100ft. To determine the flow thru the system, you add up the equivelant length of all of the fittings and piping in the system.
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Old 11-02-2009, 04:31 AM   #6
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One trick used in in-line catalytic converters for mitigating the flow loss from an obstruction is to expand the diameter of the flow just before the screen and then reducing the diameter shortly afterwards. The expansion slows the velocity of the gas and reduces the turbulence of passing thru the larger surface area of the obstruction, and then necking down the tube accellerates the flow back to its previous velocity (mostly, you are still going to have loss no matter what).

That is in exhaust systems where the pressure waves and flow are very dynamic. Induction (intake) systems are simpler but can be tricky too. Many sport motorcycles use a complicated ram-air system of ducts and surge tanks to get intake air from the high pressure area at the nose of the bike around the fairing, thru the air filter, and into the carbs/throttle bodies with a minimum of disturbance or loss of pressure.

Last edited by JamesG; 11-02-2009 at 10:50 AM.
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Old 11-03-2009, 04:52 AM   #7
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Flow of gasses, in witch rho (density) is not constant is very much more difficult to analyze than liquids.
OP was about constant density.
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Old 11-03-2009, 05:53 AM   #8
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It works the same for both. Its actually more straight forward for steadstate flows. You just don't get to take advantage of some of the tricks of pressure dynamics (ie; 2 stroke expansion chambers).
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