Kaplan FL 4 no. 29

[SaintJude]

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An engineer designs an underground tunnel with two ventilation pipes as shown below. Pipe A opens to the air at ground level, while Pipe B extends above ground level and is exposed to air moving at a higher velocity. Which of the following is true? (Assume constant air density, P + (1/2)ρv2 + ρgy = constant)

A. Air will flow from left to right in the tunnel.
B. Air will flow from right to left in the tunnel.

How do I approach this problem?

 

[Buttafuoco]

So this is Bernoulli's principle where the sum of the absolute pressure + "potential energy" (ρgy) + "kinetic energy" ((1/2)ρv2) of fluids in circuit equal each other. (see the equation on top of this image)

The higher the "kinetic" and "potential" aspects of a part, the lower the P (absolute pressure), so with B, it's higher and exposed to faster airflow so the kinetic and potential parts are both higher. Since it has has higher values for both parts, its P value is lower value, so air will flow from A--->B

 

[chiddler]

To simplify what was written above:

High velocity means lower pressure. Low velocity means higher pressure. Air flows from high to low pressure.

 

[Buttafuoco]

Don't forget height too. High height and velocity means lower pressure. Low height and velocity means higher pressure.

 

[SaintJude]

Oh, yeah. O my goodness. I'm pretty sure that we have gone over Bernoulli's soo many times now in this forum since I've joined and I still haven't embedded it. Bernoulli just says: high velocity, low pressure. Low velocity, high pressure.