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CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Fastest Flowing Liquid

Suppose I have a liquid, which is flowing through a pipe in this direction:

Considering the following factors:

1. Surface Tension
2. Cohesive - Adhesive force
3. Pressure on the bottom layers exerted by the upper layers

Which layer of the liquid will move the fastest?

Last edited by CurlyBracket (2022-04-30 18:03:55)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Fastest Flowing Liquid

hi CurlyBracket

My understanding is that the fastest flow is in the centre of the pipe, with the slowest where the liquid is next to the pipe edges.

Assume the pipe is circular. Divide the liquid into a series of concentric circles; the outermost is next to the pipe edge; each circle after that is adjacent to a circle 'outside it' and a circle 'inside it, until we reach the centre.

The pipe edge is stationary so the drag is maximum there.  Each concentric circle of liquid gets drag from the next circle outwards, so each circle is able to go a little faster, as you work inwards towards the centre of the pipe.

This would cover adhesion and surface tension.  Not sure if layers above and below make a difference. It probably depends on the weight of liquid and the pressure at the end to make a flow happen at all.

I expect you can google for a formula.

Bob

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Sometimes I deliberately make mistakes, just to test you!  …………….Bob

CurlyBracket

Member

From: Your Maths Textbook

Registered: 2022-01-03

Posts: 155

Re: Fastest Flowing Liquid

Hi Bob,

I came to the same conclusion, but in a slightly difference way. Making a list of the force which can stop the layer from increasing its speed:

1st Layer - Adhesion with pipe     Surface Tension     Cohesion

3rd Layer -                                                            Cohesion

5th Layer - Adhesion with pipe                                Cohesion    Pressure from upper layers

Since the 3rd layer is the least bothered, I conclude it moves the quickest.

Is this reasoning correct?

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Filling the unforgiving minute with sixty seconds’ worth of distance run!