What is the effect of increased radius on the flow velocity of viscous?

[chaser0]

I am quite confused here, and was wondering if someone could help me.

The radius increases for a pipe where a viscous non-ideal fluid flows. What happens to the flow velocity?


Q=Av
says that the flow velocity should decrease.
I assume this equation cannot be used because it is non-ideal fluid?

v= r^2 x (P1-P2)/ ((viscosity constant)(pipe length))
says that flow velocity should increase.
I assume this equation will be used because it is a viscous fluid?


So, which is the case?
I would assume that an INCREASE in radius would cause the flow velocity to INCREASE, according to the second equation.


I just wanted to confirm with the board.

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[milski]

You don't know unless you explain how the radius was increased.

The first formula tells you that if you keep the flow constant and increase the radius, the flow velocity will decrease. An example of that would be a pipe which widens - the flow is the same in the whole pipe but the flow velocity in the wider areas is lower.

The second forumla tells you that if you keep the same pressure difference between the ends of a pipe the same but make the pipe wider, you'll increase the flow velocity. Since you have also increased the area of the cross-section, the flow itself (Q=Av) will also increase.

 

[chaser0]

oh.... so the distinction has nothing to do with viscosity?


How do you know if a radius is changed while pressure difference on both sides is constant? Does it literally say "pressure is constant on both sides?"

 

[milski]

oh.... so the distinction has nothing to do with viscosity?


How do you know if a radius is changed while pressure difference on both sides is constant? Does it literally say "pressure is constant on both sides?"

Not directly, although if there is no viscosity, the second equation becomes somewhat useless - there is no pressure loss in that case.

It is not going to be necessary called out directly that anything is constant. Normally you would have some description of what's creating the flow and how it's moving. For example you can have a pump which creates certain pressure and moves fluid. What would happen if the radius of the pipe attached to the pump doubles? In this case you have a constant pressure difference, since the pump creates P1, the other pressure is atmospheric - the difference is constant.

Or you can have something that needs to carry 100L/s. What would happen if that pipe is made with larger radius? The velocity will decrease, since you want a constant flow in that case.