Fluid flow rates in straight vs coiled tubes

[mahdis]

Homework Statement

If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?

Relevant Equations

not sure which equation to use

If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?

 

[berkeman]

Homework Statement: If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?
Relevant Equations: not sure which equation to use

If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?

Can you say more about the two setups? Is the straight pipe vertical, and the coiled pipe wound around a vertical cylinder? Or are the setups different from that?

And why do you say that the coiled tube is "theoretically shorter"?

 

[erobz]

Homework Statement: If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?
Relevant Equations: not sure which equation to use

If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?

The coiled pipe should have higher head loss per unit length than the straight section of pipe ( in any orientation ), but if you are looking at a vertical pipe where the elevation head becomes a factor in each configuration (depending on how tightly you coil it) , its probably not entirely clear what the overall effect on the flowrate would be.

I'm with @berkeman, the more information the better.

 

[Rusty123]

Homework Statement: If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?
Relevant Equations: not sure which equation to use

If you have 2 pipes of the same cross sectional area, same volume of fluid, and same length, the only difference is one pipe is coiled several times over a cylindrical object theoretically shortening the length of the pipe, while the other is a straight pipe. Will the flow rate be same in both pipes?

No, the coiled pipe will have more friction loss due to a greater surface area.

 

[erobz]

No, the coiled pipe will have more friction loss due to a greater surface area.

I don't think that's theoretically a problem if we are saying the arc length of the coiled pipe is equivalent to the straight length of pipe.

In reality bending a pipe is a plastic deformation so its length wouldn't be preserved. Even still, I don't believe the slight change in length is going to be a dominant form of head loss. I believe the dominant form of head loss comes from the increased turbulence associated with changing the flow direction. That is usually a function of radius and angle of turn.

 

[mahdis]

Can you say more about the two setups? Is the straight pipe vertical, and the coiled pipe wound around a vertical cylinder? Or are the setups different from that?

And why do you say that the coiled tube is "theoretically shorter"?

the straight and coiled pipe are vertical with the coiled pipe wound around a vertical cylinder. the 2 pipes when straight are of equal length but the coiled pipe appears shorter due to being wound around the vertical cylinder

 

[mahdis]

I don't think that's theoretically a problem if we are saying the arc length of the coiled pipe is equivalent to the straight length of pipe.

In reality bending a pipe is a plastic deformation so its length wouldn't be preserved. Even still, I don't believe the slight change in length is going to be a dominant form of head loss. I believe the dominant form of head loss comes from the increased turbulence associated with changing the flow direction. That is usually a function of radius and angle of turn.

so in this case coiling it would result in higher head loss and slower velocity at the same exerted pressures?

 

[mahdis]

The coiled pipe should have higher head loss per unit length than the straight section of pipe ( in any orientation ), but if you are looking at a vertical pipe where the elevation head becomes a factor in each configuration (depending on how tightly you coil it) , its probably not entirely clear what the overall effect on the flowrate would be.

I'm with @berkeman, the more information the better.

the straight and coiled pipe are vertical with the coiled pipe wound around a vertical cylinder

 

[erobz]

the straight and coiled pipe are vertical with the coiled pipe wound around a vertical cylinder

Well look at some extreme's. You could have a small radius helix with a steep helical angle, in which the elevation of the discharge is not greatly affected. I would guess the straight vertical pipe to do better in terms of flowrate. Conversely, a large radius shallow helical angle where the elevation of the discharge is greatly affected to do better in terms of flowrate than the straight vertical pipe. On its surface it isn't appearing to be a straightforward "its always this way or always that way" result.

It's an interesting problem. Probably quite advanced analysis would be required unless I'm missing something...which I often do.

 

[erobz]

so in this case coiling it would result in higher head loss and slower velocity at the same exerted pressures?

If you take elevation of the discharge out of the equation by turning everything horizontal, it's a more forward result. The coil will have a higher head loss per unit length. Meaning the same flow in each, requires higher differential pressure across the coil...Again. If you eliminate the discharge elevation variable.

 

[erobz]

Its such a vague problem statement, is this really a homework problem? For what course?

 

[mahdis]

Its such a vague problem statement, is this really a homework problem? For what course?

there is an experiment I have to design to test the difference in flow rate in a tube of 3mm internal diameter of 100cm length where initial pressure is 300mmHg
the second pipe I would coil over a 10cm diameter cylinder shortening the initial length from 100cm to 30cm. all other properties kept the same

 

[erobz]

there is an experiment I have to design to test the difference in flow rate in a tube of 3mm internal diameter of 100cm length where initial pressure is 300mmHg
the second pipe I would coil over a 10cm diameter cylinder shortening the initial length from 100cm to 30cm. all other properties kept the same

So you are just trying to get some ideas for a hypotheses? What level coursework, what discipline?

 

[mahdis]

So you are just trying to get some ideas for a hypotheses? What level coursework, what discipline?

I'm studying fluid dynamics. do you believe coiling would lead to slower flow rate

 

[berkeman]

I'm studying fluid dynamics. do you believe coiling would lead to slower flow rate

This article may be of help:

https://www.thermopedia.com/content/577/

Single-Phase Flow​

The main feature of flow through a bend is the presence of a radial pressure gradient created by the centrifugal force acting on the fluid. Because of this, the fluid at the center of the pipe moves towards the outer side and comes back along the wall towards the inner side. This creates a double spiral flow field shown schematically in Figure 1. If the bend curvature is strong enough, the adverse pressure gradient near the outer wall in the bend and near the inner wall just after the bend may lead to flow separation at these points, giving rise to a large increase in pressure losses. Even for fairly large-radius bends, the flow field in the bend will be severely distorted as illustrated by the data of Rowe (1970) shown in Figure 2.

The pressure losses suffered in a bend are caused by both friction and momentum exchanges resulting from a change in the direction of flow. Both these factors depend on the bend angle, the curvature ratio and the Reynolds Number. The overall pressure drop can be expressed as the sum of two components: 1) that resulting from friction in a straight pipe of equivalent length which depends mainly on the Reynolds number (and the pipe roughness); and 2) that resulting from losses due to change of direction, normally expressed in terms of a bend-loss coefficient, which depends mainly on the curvature ratio and the bend angle. The pressure loss in a bend can thus be calculated as:

<snip>

 

[erobz]

I'm studying fluid dynamics. do you believe coiling would lead to slower flow rate

Look at post#9. I think it's reasonable assumption one would have to try and make a mathematical model for that prediction.

 

[Lnewqban]

there is an experiment I have to design to test the difference in flow rate in a tube of 3mm internal diameter of 100cm length where initial pressure is 300mmHg
the second pipe I would coil over a 10cm diameter cylinder shortening the initial length from 100cm to 30cm. all other properties kept the same

Locating both pipes in a vertical position will create the problem of different heights (and hydrostatic pressures) for outlet and inlet for both.
100 - 30 = 70 cm or 0.7 m column of water, which is a pressure difference of 6865 Pascals.
That pressure differential will be a 17.1% of the input pressure, which will be 39997 Pascals (300 mm Hg).

 

[mahdis]

Locating both pipes in a vertical position will create the problem of different heights (and hydrostatic pressures) for outlet and inlet for both.
100 - 30 = 70 cm or 0.7 m column of water, which is a pressure difference of 6865 Pascals.
That pressure differential will be a 17.1% of the input pressure, which will be 39997 Pascals (300 mm Hg).

why would the column of water differ, they will both contain the same amount, as they are both 100cm length except one is coiled in the middle so that the new measured length from its inlet to outlet is 30cm

 

[Lnewqban]

Same volume of water, same length of pipe.

 

[erobz]

why would the column of water differ, they will both contain the same amount, as they are both 100cm length except one is coiled in the middle so that the new measured length from its inlet to outlet is 30cm

The hydrostatic head only depends on the difference in elevation between two points.