Maximizing Flow: Understanding the Impact of Fittings on Water Velocity

[physea]

Hello!
When water flows through fittings like U bends, elbows, etc, is kinetic energy lost and velocity reduced?​

 

[BvU]

No

 

[physea]

No

How no?
Aren't there collisions in the bend that decrease the velocity of molecules?

 

[BvU]

Yes there are. However:
Water is practically incompressible, so it can't accumulate and speed has to be maintained. Something else has to give: the driving force.

 

[physea]

Yes there are. However:
Water is practically incompressible, so it can't accumulate and speed has to be maintained. Something else has to give: the driving force.

Why speed has to be maintained?
I am referring to a driving force that sends water at the beginning of a pipe and the end of the pipe is free. Will the liquid exit the pipe at the same velocity? Given diameter is constant, but there are fittings like bends and friction.

 

[russ_watters]

Why speed has to be maintained?
I am referring to a driving force that sends water at the beginning of a pipe and the end of the pipe is free. Will the liquid exit the pipe at the same velocity? Given diameter is constant, but there are fittings like bends and friction.

If the velocity dropped, volumetric flow rate would drop and you would have more water going into a pipe than coming out the other end. What would happen to this missing water?

 

[Baluncore]

I am referring to a driving force that sends water at the beginning of a pipe and the end of the pipe is free.

Potential energy is lost as the pressure reduces towards the open end. Conservation of diameter requires velocity be fixed and so KE is fixed.

 

[physea]

Lets have a tube connected to a tap and that tube has bends etc and ends freely so that the water drops.

Just after the tap, we have a flow meter that gives a specific velocity of the water.

Is that velocity the same across the whole tube up to the end including the bends?

 

[BvU]

Yes

 

[physea]

Yes

And when the tap generates a flow of 100kg/s, which corresponds to 1m/s (let's say) for 1m pipe diameter, will that velocity of the fluid be the average velocity across the whole pipe, if there are bends etc along the pipe?

 

[Chestermiller]

And when the tap generates a flow of 100kg/s, which corresponds to 1m/s (let's say) for 1m pipe diameter, will that velocity of the fluid be the average velocity across the whole pipe, if there are bends etc along the pipe?

Do you believe in conservation of mass? Do you believe that liquid water is very nearly incompressible?

 

[BvU]

And when the tap generates a flow of 100kg/s, which corresponds to 1m/s (let's say) for 1m pipe diameter, will that velocity of the fluid be the average velocity across the whole pipe, if there are bends etc along the pipe?

100 kg/s is 0.1 m³/s. A pipe diameter of 1 m is $\pi/4$ m². I get [edit] $0.4 / \pi$ m/s (ahem...after thinking ).
And: yes, that velocity will be the average velocity all over the pipe (provided the diameter is constant).

Can you imagine a very (very!) long pipe, so long that the velocity drops to zero before the end of the pipe is reached ?

 

[physea]

So turbulence does not affect mean velocity?

 

[sophiecentaur]

The important thing to remember about water flow in situations as described is that things take time to establish themselves and for the system to reach a steady state after the tap is opened. The pressure drops across the various fittings and pipe runs will always add up to the pump pressure (same as Kirchof’s second law for electrical circuits). Mass flow rate has to be the same all the way round if there is no reservoir / accumulator in circuit.

 

[Chestermiller]

So turbulence does not affect mean velocity?

Of course not.

 

[Andy Resnick]

Hello!
When water flows through fittings like U bends, elbows, etc, is kinetic energy lost and velocity reduced?​

I think this discussion went off in the wrong direction. It is true that fittings and bends can create a pressure drop that will reduce the volume flux- an extreme example is what happens when you kink a hose. I only have some third-hand ancient engineering books that cover the topic, but there are tables that incorporate pressure drops due to, for example, sudden changes in pipe diameter. The reason, IIRC, is viscous dissipation.

 

[russ_watters]

I think this discussion went off in the wrong direction. It is true that fittings and bends can create a pressure drop that will reduce the volume flux- an extreme example is what happens when you kink a hose. I only have some third-hand ancient engineering books that cover the topic, but there are tables that incorporate pressure drops due to, for example, sudden changes in pipe diameter. The reason, IIRC, is viscous dissipation.

I'm not following: reduce the volume flux vs what?

Versus before you put the kink in the hose? Sure: it's trivially true that different systems may have different flow rates.

Upstream vs downstream of the kink? No.

The difference between these two scenarios is often misapplied, but I don't think we're talking about two different scenarios...though frankly it sounds like you switched back and forth between them in your answer.

 

[gmax137]

I think this discussion went off in the wrong direction. It is true that fittings and bends can create a pressure drop that will reduce the volume flux- an extreme example is what happens when you kink a hose. I only have some third-hand ancient engineering books that cover the topic, but there are tables that incorporate pressure drops due to, for example, sudden changes in pipe diameter. The reason, IIRC, is viscous dissipation.

Yes, the fittings and bends cause pressure drop, and the overall pressure drop affects the flow rate, but it affects the flow rate all along the hose. The velocity downstream of the kink is the same as the velocity upstream, assuming the hose diameters are equal up- and down-stream.

 

[physea]

Yes, the fittings and bends cause pressure drop, and the overall pressure drop affects the flow rate, but it affects the flow rate all along the hose. The velocity downstream of the kink is the same as the velocity upstream, assuming the hose diameters are equal up- and down-stream.

The velocity downstream and upstream a bend may be equal, but IN the bend? Won't it get affected?
And the turbulence created after the bend, won't affect the mean velocity nearly after the bend?

So, I understand that any losses inside a pipe will be exhibited as pressure drops and not velocity drops? (again I mean average velocity).

 

[Chestermiller]

The velocity downstream and upstream a bend may be equal, but IN the bend? Won't it get affected?
And the turbulence created after the bend, won't affect the mean velocity nearly after the bend?

So, I understand that any losses inside a pipe will be exhibited as pressure drops and not velocity drops? (again I mean average velocity).

See my post #11.

 

[boneh3ad]

The velocity downstream and upstream a bend may be equal, but IN the bend? Won't it get affected?
And the turbulence created after the bend, won't affect the mean velocity nearly after the bend?

So, I understand that any losses inside a pipe will be exhibited as pressure drops and not velocity drops? (again I mean average velocity).

Think of it this way. Let's say you have a pipe network with no branches (one inlet, one outlet) and you are pumping in water at a steady volumetric flow rate of $Q$. Along the entire length of that pipe network, regardless of the fittings, the volumetric flow rate must still be $Q$, otherwise you would have mass missing (total mass flow out has to equal total mass flow in).

Now, volumetric flow rate is related to cross-sectional area, $A$, and the average velocity, $V_{avg}$, over that area by $Q = V_{avg}A$. So, regardless of fittings or turbulence or anything else, in order to make sure mass is conserved, the average velocity is always $V_{avg} = Q/A$. If you pick two positions with the same cross-section, then the average velocity will be the same, even if there is a fitting between them, since $Q$ is constant.

Now, across any cross-section of the pipe, the velocity will not be constant. it will vary from zero at the wall to some maximum at the centerline (or at least near the centerline), and this fact is not reflected in the use of $V_{avg}$. Perhaps this is where you are getting confused. The relationship between the velocity at a specific point at that average velocity is
$$V_{avg} = \dfrac{\oint_A V(r,\theta)\;dA}{\oint_A dA} = \dfrac{1}{A}\oint_A V(r,\theta)\;dA.$$
So, in short, fittings and turbulence can affect the distribution of $V(r,\theta)$, but they won't change the value of $V_{avg}$ because that would break the law of conservation of mass.

For example, a laminar flow in a straight pipe will have a parabolic $V(r,\theta)$ profile centered at the centerline with no $|theta$ dependence. A turbulent flow would have a smaller maximum $V(r,\theta)$ but the profile would be "fuller", i.e. it would have a sharper gradient near the wall and a flatter profile near the centerline. A bend would tend to move the maximum point off of the centerline. Fittings could do any number of things depending on the type. The one universal law here is that $Q$ is constant but $V(r,\theta)$ is not.

 

[sophiecentaur]

The velocity downstream and upstream a bend may be equal, but IN the bend? Won't it get affected?

It is true to say that, if the volume flow rate is the same and the cross sectional area reduces then the velocity of the water must be higher (Area times speed = flow rate).
But the flow rate has to be the same all the way round - where else could water go to or come from?

 

[russ_watters]

The velocity downstream and upstream a bend may be equal, but IN the bend? Won't it get affected?

If there is a diameter change, yes. This the premise of the Venturi Effect.

And the turbulence created after the bend, won't affect the mean velocity nearly after the bend?

Correct. The mean volumetric flow rate has to be the same everywhere, everywhere and everywhere along the pipe.

So, I understand that any losses inside a pipe will be exhibited as pressure drops and not velocity drops? (again I mean average velocity).

Correct.

 

[physea]

But the cross sectional area shouldn't be always perpendicular to the flow? In a bend, it's not, so maybe there is always a change in the cross sectional area in bends, even though the bore of the pipe is the same?

 

[BvU]

So don't bother looking there. Before and after the bend, if the pipe diameter is the same then the v are also the same.

 

[physea]

What happens with rotameters in turbulent flow? Do they over-estimate velocity? Is there any data on this?

 

[BvU]

Brooks has plenty white papers I expect.

 

[russ_watters]

But the cross sectional area shouldn't be always perpendicular to the flow? In a bend, it's not, so maybe there is always a change in the cross sectional area in bends, even though the bore of the pipe is the same?

No. "Cross" is short for "across". As in "perpendicular". Now you're trying to break a definition in order to support a nonsensical and pointless idea you don't want to let go of.

 

[russ_watters]

What happens with rotameters in turbulent flow? Do they over-estimate velocity? Is there any data on this?

Flow in pipes is turbulent. Flow meters work. Yes, there's data on it (any flow meter spec sheet provides its accuracy). Please stop trying to argue your way out of a reality you don't like and just accept it.

 

[Chestermiller]

@physea You still haven't answered this: If you have water flowing continuously into your piping system at a constant flow rate and water coming out of your piping system continuously at a lower constant flow rate, what happens to all that extra water that is continuously building up within your piping system? For example, if you have water going in at 30 gallons per minute (gpm) and water coming out at 20 gpm, then the rate of buildup is 10 gpm. So after 1 minute, you would have an extra 10 gallons in your system. No big problem yet (maybe). But, after a day, you would have an extra 14400 gallons in your piping system. This would be enough to fill my entire living room. Where did it all go?

 

[Andy Resnick]

The difference between these two scenarios is often misapplied, but I don't think we're talking about two different scenarios...though frankly it sounds like you switched back and forth between them in your answer.

That could be. My understanding is that when unsteady flow is created (for example, just after a discontinuous expansion or flow through an orifice in a pipe, either one resulting in a vena contracta), the flow field that exists prior to resumption of steady flow is associated with viscous energy losses. My (ancient) book spends a chapter or so on hydraulic grade lines and energy grade lines. It describes "minor losses" and 'head losses', but isn't very specific on *what* is being lost.

 

[russ_watters]

That could be. My understanding is that when unsteady flow is created (for example, just after a discontinuous expansion or flow through an orifice in a pipe, either one resulting in a vena contracta), the flow field that exists prior to resumption of steady flow is associated with viscous energy losses. My (ancient) book spends a chapter or so on hydraulic grade lines and energy grade lines. It describes "minor losses" and 'head losses', but isn't very specific on *what* is being lost.

Unsteady flow is what you have when the flow field is in the process of changing, caused by the system setup changing. E.G., for the second it takes to bend a hose into a kink or few seconds it takes to actuate a valve or variable orifice. Durign this time, the volumetric flow rate is changing and is indeed also not constant along the pipe.

The OP asks about flow through fittings, which are welded/soldered in place before the system is even turned on. So I don't see a way to apply an unsteady flow to it. And I don't think it is really what you mean:

It sounds like you are describing undeveloped or developing flow. This is where the velocity profile across the pipe is changing along the pipe due to a discontinuity (in the image in the wiki, an entrance). After the discontinuity, where the pipe becomes uniform again, the velocity profile is still changing, but the average velocity is not.
https://en.wikipedia.org/wiki/Entrance_length#Hydrodynamic_entrance_length

 

[Asymptotic]

What happens with rotameters in turbulent flow? Do they over-estimate velocity? Is there any data on this?

Do a search on "flow meter installation guidelines".

How much turbulence affects flow meters depends on how they operate, and ranges from 'practically no effect' to 'significant'. Turbine (paddlewheel) sensors are ubiquitous, but sensitive to turbulent flow, and require (sometimes significant; up to 50, although usually no less than 10 upstream/5 downstream pipe diameters) of straight run to operate well.

Read sensor manufacturer literature (and post #21 and #32) for clues to the 'whys', but changes in average flow rate isn't one of them.

 

[boneh3ad]

That could be. My understanding is that when unsteady flow is created (for example, just after a discontinuous expansion or flow through an orifice in a pipe, either one resulting in a vena contracta), the flow field that exists prior to resumption of steady flow is associated with viscous energy losses. My (ancient) book spends a chapter or so on hydraulic grade lines and energy grade lines. It describes "minor losses" and 'head losses', but isn't very specific on *what* is being lost.

What is being lost is "total head", which is a code word for total pressure. If you think about it in terms of the modified Bernoulli equation, the total head would be
$$h_{total}=\dfrac{p}{\rho g} + \dfrac{V^2}{2g} + z,$$
where $z$ is a height. The relationship between two points in the flow is then
$$\dfrac{p_1}{\rho g} + \dfrac{V_1^2}{2g} + z_1 = \dfrac{p_2}{\rho g} + \dfrac{V_2^2}{2g} + z_2 + h_{loss}.$$
Generally, $V$ is set by conservation of mass through the system, so the losses are manifested as a loss in either pressure or elevation.

 

[Andy Resnick]

What is being lost is "total head", which is a code word for total pressure.

It sounds like you are describing undeveloped or developing flow. This is where the velocity profile across the pipe is changing along the pipe due to a discontinuity (in the image in the wiki, an entrance). After the discontinuity, where the pipe becomes uniform again, the velocity profile is still changing, but the average velocity is not.

I guess this is the source of my confusion: if there is a pressure loss associated with, for example, a sudden constriction, how is this manifested in the flow?

http://images.slideplayer.com/24/7380603/slides/slide_94.jpg

The figure above mentions that velocity increases but the kinetic energy decreases...??