# How do different angle bends in pipes affect flow?

#### LeftRightGoodnight

Hi,
I am currently doing an experiment where a piece of 5mm diameter plastic tubing has different angle bend in it (e.g. 10 degrees, 25 degrees... 90 degrees etc.) and was wondering what equations to use to figure out what affects the rate of flow when water is going through it? Do i use friction, momentum, or things like Bernoulli's principle?

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#### oz93666

I'm not an expert on this , but I'll hazard a guess ...

It must depend on the sharpness of the bend . Suppose you wound your 5mm tube around the outside of a 100mm drain pipe , say 10 meters of tubing round and around tightly packed , so all the tubing was spiral , All 10 meters of it in a gently bend . I don't think it would effect the flow rate too much compared to a strait tube.

I know the blue plastic plumbing fittings come in two styles of right angle bend ,one is very sharp , the other a gentle curve (both change the flow through 90deg) this second one must be to create less resistance to flow.

#### studiot

Good morning leftrightgoodnight and welcome to PhysicsHelpForums.

I see you mention Bernoulli and momentum so you know some fluid physics, which is good.

There are two effects one involving Bernoulli and one involving momentum.

All pipes have some friction which is usually measured as a pressure drop per metre or per fitting or per bend. Manufacturers publish tables of such data which is empirical.

This pressure drop is usually recorded as a drop in pressure head and then added in series to the Bernoulli equation used in pressured head format.
This is a bit like resistors in series in an electric circuit or the voltage drop calculations electricians make for wiring.

The second point is momentum.

Yes momentum calculations show that momentum is destroyed at bends and changes of pipe section, resulting in a force on the pipe.
This can cause movement of the pipe or opening of the joints unless the pipework is restrained. Very large pipes have thrust blocks set at bends to oppose this force.

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1 person

#### LeftRightGoodnight

Good morning leftrightgoodnight and welcome to PhysicsHelpForums.

I see you mention and Bernoulli momentum so you know some fluid physics, which is good.

There are two effects one involving Bernoulli and one involving momentum.

All pipes have some friction which is usually measured as a pressure drop per metre or per fitting or per bend. Manufacturers publish tables of such data which is empirical.

This pressure drop is usually recorded as a drop inpressure head and the added in series to the Bernoulli equation used in pressured head format.
This is a bit like resistors in series in an electric circuit or the voltage drop calculations electricians make for wiring.

The second point is momentum.

Yes momentum calculations show that momentum is destroyed at bends and changes of pipe section, resulting in a force on the pipe.
This can cause movement of the pipe or opening of the joints unless the pipework is restrained. Very large pipes have thrust blocks set at bends to oppose this force.
So what kind of calculations/equations would i be looking to do for a tube with only one bend in it, and with no vertical differences?

#### agammessi10

In a filled(steady state) pipe, nothing changes

In a completely steady state fluid, which is assumed when you apply Bernoulli equation,
there will actually be no effect.

What I mean by that is, the speed will only be different for the different pipes when the water is just initially going through and coming out,
but once it is in a state where it completely fills the pipe at all points in time, the speeds will more or less be the same(within experimental error).

[This can be proven using Bernoulli's equation Area1.Volume1=Area2.Volume2 which works regardless of the shape of the pipe]

But this'll only work if you create a steady state fluid, practically managing that may be a little difficult.

Hope I could help.
Thanks

#### Woody

Bernoulli strictly only applies for incompressible inviscid fluid flows.
This actually applies very well for many practical situations, where the compressible and viscosity effects are substantially smaller then the Bernoulli effect.

However, in bends the flow on the outside of the bend is travelling a different distance to the flow on the inside, which (in a viscous fluid) creates turbulence which uses energy (it heats up the fluid slightly).

These are the additional (empirically derived) terms that studiot mentioned.

#### benit13

There's a lot of interesting physics about fluid flows through pipes of different geometry, especially when it comes to convective heat transfer or laminar/turbulent flow. You might gleam a lot of information by grabbing a book about heat transfer processes or convection, since they often worry about these sorts of flow problems.