How would the length affect flow rate?

[random1234]

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? not the radius but would the length affect it

 

[MCATMountain]

The formula for the force slowing a liquid down in a vessel is F = 4(pi)👎(L)(v). This means that the force slowing down the liquid is directly proportional to the length of the vessel. The longer the vessel length, the slower the speed.

If the velocity is slower, theoretically, the flow rate should be slower. The reason being that flow rate depends on volume, and volume indirectly depends on velocity. The length of ground covered in order to measure the volume of output is velocity*time.

Hopefully a picture helps

=========== <--- that's a pipe
===========| x | < ---- thats the output end of the pipe. The gap with the x is the output volume. If you notice, there is a displacement x. If you were to calculate the volume output, you'd have to multiply the area of the cylinder times the x value to get the volume. But that x value depends on velocity, and therefore, so does flow rate.


If anyone sees errors, please correct.

 

[mehc012]

The formula for the force slowing a liquid down in a vessel is F = 4(pi)👎(L)(v). This means that the force slowing down the liquid is directly proportional to the length of the vessel. The longer the vessel length, the slower the speed.

If the velocity is slower, theoretically, the flow rate should be slower. The reason being that flow rate depends on volume, and volume indirectly depends on velocity. The length of ground covered in order to measure the volume of output is velocity*time.

Hopefully a picture helps

=========== <--- that's a pipe
===========| x | < ---- thats the output end of the pipe. The gap with the x is the output volume. If you notice, there is a displacement x. If you were to calculate the volume output, you'd have to multiply the area of the cylinder times the x value to get the volume. But that x value depends on velocity, and therefore, so does flow rate.


If anyone sees errors, please correct.

Alternatively, you could look at Poiseuille's Law, where

Flow rate (dV/t) = piR⁴dP / 8Leta

if you don't want to do the thinking parts...it's all the same, really.

 

[random1234]

Thank you so much, MCATMountain and mehc012! I appreciated both approaches, but especially the non-formulaic approach as that formula was not given so I think they expected you to reason it out, since I think most test takers do not have Poiseuille's Law memorized 😳

 

[Vurday]

Another way of looking at it is to consider friction: If you increase the length of a pipe, you are adding more surface area that a liquid flowing through the pipe can contact. An increase in contact area is an increase in friction, which would oppose flow.

==> An increase in length --> More friction --> decrease flow rate

Hope that helps!

 

[mehc012]

Thank you so much, MCATMountain and mehc012! I appreciated both approaches, but especially the non-formulaic approach as that formula was not given so I think they expected you to reason it out, since I think most test takers do not have Poiseuille's Law memorized 😳

They're both formulaic...I believe the other one is Stokes' (correct me if I'm wrong)...and both concepts are on the AAMC list.

If you want a truly non-formulaic approach, think of the drag force as the force resisting movement between a layer of fluid and either the pipe wall or another layer of fluid.

The larger the interface between the two layers, the larger the drag force will be...so longer pipes have a larger drag force.

HOWEVER, the drag force between two layers of fluid is smaller than that between the fluid and the pipe wall, so pipes of a larger radius, where more layers of fluid are far from the wall, have less overall drag force.

 

[mehc012]

Another way of looking at it is to consider friction: If you increase the length of a pipe, you are adding more surface area that a liquid flowing through the pipe can contact. An increase in contact area is an increase in friction, which would oppose flow.

==> An increase in length --> More friction --> decrease flow rate

Hope that helps!

This is how I think of it, but I'm always careful about explaining it that way because a friction force is not dependent on the size of the interface between the objects...fluids are weird because there is no defined unit of mass or anything.

 

[MCATMountain]

Thank you so much, MCATMountain and mehc012! I appreciated both approaches, but especially the non-formulaic approach as that formula was not given so I think they expected you to reason it out, since I think most test takers do not have Poiseuille's Law memorized 😳

Glad I could help.