# Pressure along the pipe

## Homework Statement

In this notes , i was told that there is an increase in pressure along the inner wall

## The Attempt at a Solution

IMO , it should be there is increase in pressure at the outer wall , as we can see , the outer wall is longer , so the water would flow slower, resulting in the increases in pressure , am i right ?

#### Attachments

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BvU
Homework Helper
If the outer wall is longer, then the stuff has to move faster there, isn't it ?

Cf river bends: on the outer edge sand is being eroded, on the inner sand is being deposited. That's how you get meandering.

foo9008
If the outer wall is longer, then the stuff has to move faster there, isn't it ?

Cf river bends: on the outer edge sand is being eroded, on the inner sand is being deposited. That's how you get meandering.
i still dont understand , can you explain further?

BvU
Homework Helper
the outer wall is longer , so the water would flow slower
It's this assumption you want to reconsider.
I don't know if the context is for laminar flow or for turbulent flow. The latter is easiest to imagine: radial pressure profile flat in the straight sections. To make the longer path for the outer turn the liquid has to flow faster. And on the inside the shorter path necessitates a slower flow. So there is a pressure profile (Bernoulli) in the 45 degree plane (lower right to top left in your picture) : higher pressure on the inside to lower pressure at the outer point. The guide vanes can prevent the liquid from responding to that pressure difference with an outward flow (so in an undesired drection) by 'pushing' it in the right direction (f = dp/dt).

foo9008
It's this assumption you want to reconsider.
I don't know if the context is for laminar flow or for turbulent flow. The latter is easiest to imagine: radial pressure profile flat in the straight sections. To make the longer path for the outer turn the liquid has to flow faster. And on the inside the shorter path necessitates a slower flow. So there is a pressure profile (Bernoulli) in the 45 degree plane (lower right to top left in your picture) : higher pressure on the inside to lower pressure at the outer point. The guide vanes can prevent the liquid from responding to that pressure difference with an outward flow (so in an undesired drection) by 'pushing' it in the right direction (f = dp/dt).
do you mean if the flow is turbulent , the water at the outer region of pipe(longer) is flowing faster , why is it so ?

BvU
Homework Helper
On the lower left of the picture, planes of equal pressure are horizontal. On the right vertical. They have to change orientation but are reluctant to do so (inertia).

On the inside, the liquid has to 'brake': it wants to flow faster but is held up. So pressure is rising.
On the outside the pressure drops to accelerate the liquid.
Velocity profile follows (Bernoulli)

I've only drawn a few blue arrows to suggest this.
In the horizontal direction something similar happens

On the lower left of the picture, planes of equal pressure are horizontal. On the right vertical. They have to change orientation but are reluctant to do so (inertia).

View attachment 99457

On the inside, the liquid has to 'brake': it wants to flow faster but is held up. So pressure is rising.
On the outside the pressure drops to accelerate the liquid.
Velocity profile follows (Bernoulli)

I've only drawn a few blue arrows to suggest this.
In the horizontal direction something similar happens
whaty do you mean by On the inside, the liquid has to 'brake': it wants to flow faster but is held up.??? how can the liquid be held up ?

BvU
Homework Helper
Hehe, you ask good questions. I'll have to look up a few things that I seem to have imagined wrongly... (what I wrote is contradicted by figure 2..., but I do like figure 3, at least if my interpretation is right...)

Hehe, you ask good questions. I'll have to look up a few things that I seem to have imagined wrongly... (what I wrote is contradicted by figure 2..., but I do like figure 3, at least if my interpretation is right...)
ok , let me know if you have found out the new explaination .

Hehe, you ask good questions. I'll have to look up a few things that I seem to have imagined wrongly... (what I wrote is contradicted by figure 2..., but I do like figure 3, at least if my interpretation is right...)
hi , do you have any idea about the question that i asked earlier?

haruspex
Homework Helper
Gold Member
I didn't reply to this thread originally because it made no sense to me either. I was hoping someone more expert might explain it. Anyway, here's my inexpert 2c.
One problem with the "has to go faster" argument is that there is no obvious reason why it has to keep up.
The referenced text mentions centrifugal forces. The argument from that, surely, is that a net radially inward force must exist, which implies higher pressure on the outside. Since that implies the outside flow would slow down into the bend (relative to the inside flow, at least) it suggests the creation of a counterclockwise eddy.

I didn't reply to this thread originally because it made no sense to me either. I was hoping someone more expert might explain it. Anyway, here's my inexpert 2c.
One problem with the "has to go faster" argument is that there is no obvious reason why it has to keep up.
The referenced text mentions centrifugal forces. The argument from that, surely, is that a net radially inward force must exist, which implies higher pressure on the outside. Since that implies the outside flow would slow down into the bend (relative to the inside flow, at least) it suggests the creation of a counterclockwise eddy.
so , the notes is wrong ? the pressure at the outer wall should higher than the inner wall ?

haruspex
Homework Helper
Gold Member
so , the notes is wrong ? the pressure at the outer wall should higher than the inner wall ?
That's how I see it, but, as I wrote, I do not consider myself expert in hydrodynamics.

foo9008
BvU
Homework Helper
I looked at the link in post #8 with interest, and also at ref.1 therein (*).
Hehe, you ask good questions. I'll have to look up a few things that I seem to have imagined wrongly... (what I wrote is contradicted by figure 2..., but I do like figure 3, at least if my interpretation is right...)
Clearly, even my interpretation of fig. 3 was wrong ands the pressure at outer wall is higher -- and consequently (?) the velocity is lower. So the first paragraph of your notes is disproved and my defence was ill-advised.

I still think
the outer wall is longer , so the water would flow slower
that this is not a cause-effect relation, but that's only as a physicist (and obviously I'm not a fluid flow expert ).

Some aspects of this elbow flow are counter-intuitive, others make sense. Thank you for bringing it up in this critical manner !

(*)
I particularly like the (page 14)
It is this horizontal gradient that is ultimately responsible for keeping the flow turned along the axis of the pipe
and it would be interesting to check (by calculation or from experiment) the claim in your notes that the insertion of guide vanes eases the situation and reduces the pressure drop. My bet is that it does.

foo9008
haruspex
Homework Helper
Gold Member
I particularly like the (page 14)
It is this horizontal gradient that is ultimately responsible for keeping the flow turned along the axis of the pipe​
This strikes me as essentially the same as the mention of centripetal acceleration in the text cited in the OP. It may be that the claim there that the pressure is therefore greatest on the inside of the bend is simply a typo.
) the claim in your notes that the insertion of guide vanes eases the situation and reduces the pressure drop.
Again, that is consistent with the centripetal acceleration view. The vanes can supply the centripetal force locally, instead of the entire force having to be transmitted from the outside of the elbow.

I found the velocity map on page 13 particularly interesting. It shows that the flows follow two counter-rotating helices around the curve.

foo9008 and BvU
I looked at the link in post #8 with interest, and also at ref.1 therein (*).
Clearly, even my interpretation of fig. 3 was wrong ands the pressure at outer wall is higher -- and consequently (?) the velocity is lower. So the first paragraph of your notes is disproved and my defence was ill-advised.

I still think that this is not a cause-effect relation, but that's only as a physicist (and obviously I'm not a fluid flow expert ).

Some aspects of this elbow flow are counter-intuitive, others make sense. Thank you for bringing it up in this critical manner !

(*)
I particularly like the (page 14) and it would be interesting to check (by calculation or from experiment) the claim in your notes that the insertion of guide vanes eases the situation and reduces the pressure drop. My bet is that it does.
Ok, since this is not an cause and effect relationship , why the pressure at the outer wall of pipe is higher?

This strikes me as essentially the same as the mention of centripetal acceleration in the text cited in the OP. It may be that the claim there that the pressure is therefore greatest on the inside of the bend is simply a typo.

Again, that is consistent with the centripetal acceleration view. The vanes can supply the centripetal force locally, instead of the entire force having to be transmitted from the outside of the elbow.

I found the velocity map on page 13 particularly interesting. It shows that the flows follow two counter-rotating helices around the curve.
can you explain, why the pressure at the outer wall of pipe is higher?

haruspex
Homework Helper
Gold Member
can you explain, why the pressure at the outer wall of pipe is higher?
Do you understand that a centripetal force is needed to get the flow around the elbow?

Do you understand that a centripetal force is needed to get the flow around the elbow?
Yes

haruspex
Homework Helper
Gold Member
Yes
So where will that force come from?

So where will that force come from?
the force of water to make the water to rotate around the bend ?

haruspex
Homework Helper
Gold Member
the force of water to make the water to rotate around the bend ?
But something has to apply the force to the water.

foo9008
But something has to apply the force to the water.
so, how it relate to pressure at the outer and inner wall of bend?

haruspex
Homework Helper
Gold Member
so, how it relate to pressure at the outer and inner wall of bend?
Consider a part of the flow that's adjacent to the outer wall. That gets a normal force from the wall to push it around the bend. Now consider a part next to that, just a bit further from the wall. At constant velocity it would run into the first part, creating a higher pressure. That higher pressure creates the normal force that pushes it also around the bend, and so on.

foo9008
Nidum
Gold Member
BvU
Consider a part of the flow that's adjacent to the outer wall. That gets a normal force from the wall to push it around the bend. Now consider a part next to that, just a bit further from the wall. At constant velocity it would run into the first part, creating a higher pressure. That higher pressure creates the normal force that pushes it also around the bend, and so on.
do you mean higher pressure(normal forces) from the outer wall of the bend is required too keep the water to move around the bend (centripetal forces) ?

Consider a part of the flow that's adjacent to the outer wall. That gets a normal force from the wall to push it around the bend. Now consider a part next to that, just a bit further from the wall. At constant velocity it would run into the first part, creating a higher pressure. That higher pressure creates the normal force that pushes it also around the bend, and so on.
What do you mean by at constant velocity, it will run into the first part??

haruspex
Homework Helper
Gold Member
do you mean higher pressure(normal forces) from the outer wall of the bend is required too keep the water to move around the bend (centripetal forces) ?
Yes.
What do you mean by at constant velocity, it will run into the first part??
According to Newton, in the absence of a net force, masses keep constant velocity, i.e. a constant speed in a constant direction. Think of the total flow as a number of separate parallel flows. The flow next to the wall is deflected by the normal force from the wall. The flow next to that, if not subjected to a net force, would keep going in a straight line and collide with the first flow. The tendency to do that raised the pressure. The resulting pressure gradient, from high next to the outer wall to low near the inner wall, provides the forces to deflect all these flows around the bend.

foo9008
Yes.

According to Newton, in the absence of a net force, masses keep constant velocity, i.e. a constant speed in a constant direction. Think of the total flow as a number of separate parallel flows. The flow next to the wall is deflected by the normal force from the wall. The flow next to that, if not subjected to a net force, would keep going in a straight line and collide with the first flow. The tendency to do that raised the pressure. The resulting pressure gradient, from high next to the outer wall to low near the inner wall, provides the forces to deflect all these flows around the bend.
Can you sketch a diagram showing the flow in pipe??

haruspex