Role of Pipe Length in Poiseuille's Law

[Willis92]

I can't figure out why the length the a pipe (L) increases the change in driving pressure with respect to this law:

Delta P = (8*mu*L*Q)/(pi*(r^4))

I would think that delta P wouldn't change because the fluid is incompressible.

Does anyone have a conceptual explanation for the simple fact I can't seem to find?

Thanks in advance.

 

[Chestermiller]

I can't figure out why the length the a pipe (L) increases the change in driving pressure with respect to this law:

Delta P = (8*mu*L*Q)/(pi*(r^4))

I would think that delta P wouldn't change because the fluid is incompressible.

Does anyone have a conceptual explanation for the simple fact I can't seem to find?

Thanks in advance.

If you want to hold the volumetric throughput rate Q constant while you increase the length of the pipe, you have to increase the pressure drop. Why do you think that the pressure drop from one end of the pipe to the other end of the pipe wouldn't change if the fluid is incompressible? The incompressibility of the fluid means that its density doesn't change when you change the pressure. That doesn't have any bearing on the pressure drop/flow rate behavior of the fluid.

Chet

 

[Philip Wood]

The longer the pipe the more drag on the fluid from the pipe wall.

 

[Willis92]

Ok, so it's just the drag from the pipe wall then? That makes sense.

I got hung up thinking about if you have a certain force pushing an amount of fluid through at a time, the same comes out at the other end, regardless of how far away that end is.

But it makes sense if drag is the only thing preventing that.

 

[Philip Wood]

Yes; when the fluid is flowing at a steady rate, the difference in pressures at either end of the pipe times the cross-sectional area must balance the drag forces from the pipe walls.