How can the density, area, and velocity be related in a cyclic fluid flow?

[doctordoom]

[PLAIN]http://img811.imageshack.us/img811/4882/stumped.png

So from the above question I presume that the relation (Density)x(Area1)x(Velocity1)=(Density)x(Area2)x(Velocity2), cannot be applied due to the flow being unsteady and thus the control volume changing with time.

I've read up about steady in the mean flow conditions and since the flow alteration is cyclic (sin wave) that might be applied.

Other than that I'm stumped.

Can anyone out there please give me some advice on this!

-Many thanks in advance.

 

[Phrak]

I think it's nothing but a matter of confusion from the wording of the problem. Use you equations for velocity for both the entrance and exit.

From each velocity equation, take the derivative with respect to time to find the acceleration of each. The accelerations will be different as implied.

 

[doctordoom]

Thank you for your response. I still believe there is a major catch to this question, since it's unsteady flow and hence the control volume boundary fluctuates.

Anyone else with ideas. I've been looking through textbooks and can only find a question with a straight pipe that's similar to this!

Please help!

 

[Redbelly98]

I agree with Phrak.

Since the sound propagation time (roughly 1 ms or less) is a lot less than the period of oscillation (about 20 s), you can use the mass conservation equation for this problem.

 

[doctordoom]

I agree with Phrak.

Since the sound propagation time (roughly 1 ms or less) is a lot less than the period of oscillation (about 20 s), you can use the mass conservation equation for this problem.

Thank you so much for that explanation.

Regards.