Need some physics help!

[mouiw]

Im going over my physics notes on fluids and came across a question that is giving me some trouble... So if you have a horixontal pipe of varying diameters that also has four vertical pipes, and water id allowed to flow through the pipe, how can you tell which vertical pipe will have the lowest and highest water levels. Any help would be greatly appreciated! Thanks!

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[jaxasp]

im not sure what you just asked at all, please clarify(i have no idea what the relationship is between the horizontal/vertical pipes)

 

[mouiw]

I couldnt paste the pic but it looks kinda like the one that i made below.. and the water flow is from the left to the right;; oh and the bottom line is at varying heights


_____I I______I I_________I I________I I______


_______________________________________

 

[0Complications]

I couldnt paste the pic but it looks kinda like the one that i made below.. and the water flow is from the left to the right;; oh and the bottom line is at varying heights


_____I I______I I_________I I________I I______


_______________________________________

My guess is the question is getting at pressure. I think the bottom heights are important, because if an area on the bottom is closer to the top it will have a decreased pressure as a result of the increased velocity.

A1V1 = A2V2

But I'm not sure without seeing the diagram.

So in answer to your question, I believe all 4 would have the same water heights as it stands now, but if you start to narrow the cross sectional area by lifting the bottom, then the tube above the reduced area would have less water in it than a tube above a larger cross sectional area.

 

[Doctor Mayo]

The height that the water rises in the vertical pipes is a function of the pressure in the horizontal pipe (Venturi effect).

From the equation of continuity,

v1A1 = v2A2, the larger the radius (A = pir^2) of the horizontal pipe, the smaller the v is.

Since Bernoulli's equation can be expressed as:

p1 + (1/2)rhov1^2 = p2 + (1/2)rhov2^2

obviously, vertical pipe connected to the portion with highest diameter (with lowest v) will have water rise to the highest because of highest p.

 

[vandyam]

Yep -- I usually can tell just by visualizing it, rather than using an equation, but I believe the one with the smallest diameter fills up with water last.

 

[mouiw]

Thanks everyone! that really, really helped!