Fluid resistance via poiseulle method

[mihkelsoo]

Homework Statement

Why is the friction in the small tube higher than in the big tube.

Homework Equations

F = n * A * dv/dx, where n is internal friction factor, A the area and dv/dx the speed gradient

V= (Pi * p * r^4 * t) / ( 8 l n ), where V is the volume of water, p is the pressure difference, r the radius of the small tube, t elapsed time, l small tube length

The Attempt at a Solution

If i took that each "area" of the fluid that is coaxial to each other and summarized them together, then there would be less friction because there are less layers of water there hence resulting that in the small tube there should be lower friction than in the bigger tube.
Logic however would say that due to the fact that the water is moving at a higher speed in a smaller area should encounter more resistance than when its moving in a big tube slowly.

The last idea i had on this subject was that due to the fact that the area in the bigger tube is so much larger, then the resistance per Area is smaller eg (A / sum F) in the big tube than in the small tube.

n = (Pi * p * r^4 * t) / ( V* 8 * l)

F = (Pi * p * r^4 * t * A * dv/dx) / ( V * 8 *l )

and that doesn't even look close to what the real formula is (http://hyperphysics.phy-astr.gsu.edu/*hbase/pfric.html#tube )

This was part of lab work to determine the validity of the poiseulle law and calculate the internal friction force n. That was the question i was asked to "defend" but i am literally stumped about how the friction works in there.

 

[_coyote_]

I was not able to find any information that would explain why the friction in the small tube is higher than in the big tube.Any help would be appreciated.

 

[kerimek]

As a scientist, it is important to use empirical evidence and established theories to explain phenomena. In this case, the difference in fluid resistance between a small tube and a big tube can be explained by the Poiseuille equation, which takes into account the viscosity of the fluid, the length and radius of the tube, and the pressure difference.

According to the Poiseuille equation, the fluid resistance is directly proportional to the viscosity of the fluid and the length of the tube, and inversely proportional to the radius of the tube. This means that in a smaller tube, the resistance is higher because the radius is smaller, resulting in a higher pressure difference required to maintain the same flow rate.

Additionally, the speed gradient (dv/dx) also plays a role in the fluid resistance. In a smaller tube, the fluid is forced to move at a higher speed due to the smaller area, resulting in a higher speed gradient and therefore higher resistance. This is in line with your logic that a higher speed in a smaller area would result in more resistance.

Your last idea about the resistance per area is also correct. In a bigger tube, the resistance is spread out over a larger area, resulting in a lower resistance per unit area compared to a smaller tube.

In summary, the friction in a small tube is higher than in a big tube due to the combined effects of the tube radius, length, viscosity of the fluid, and speed gradient. The Poiseuille equation provides a mathematical explanation for this phenomenon.