## Velocity change in pipe due to abrupt diameter change

## Velocity change in pipe due to abrupt diameter change

(OP)

I would appreciate help with what seems like it is probably a pretty easy fluid mechanics problem. I need to calculate the velocity change in a pipe due to an abrupt diameter change (see attached figure). I have the velocity in the larger pipe, and need to calculate the velocity in the smaller pipe.

I need the velocity in the smaller pipe in order to calculate the Reynolds #, which I need in order to calculate the friction factor, which I need in order to calculate the damping coefficient, which I need to plug into my FEM... this is the first time I have dipped my toe in the world of fluid mechanics since I graduated 10 years ago, so I am a little rusty. Any help would be much appreciated. I am doing some googling, and am coming up blank...

I need the velocity in the smaller pipe in order to calculate the Reynolds #, which I need in order to calculate the friction factor, which I need in order to calculate the damping coefficient, which I need to plug into my FEM... this is the first time I have dipped my toe in the world of fluid mechanics since I graduated 10 years ago, so I am a little rusty. Any help would be much appreciated. I am doing some googling, and am coming up blank...

## RE: Velocity change in pipe due to abrupt diameter change

time to scrap those rusty brain cells . . .

## RE: Velocity change in pipe due to abrupt diameter change

Ratio of areas.

But friction and pressure losses on a sharp edged nozzle are quite different.

Remember - More details = better answers

Also: If you get a response it's polite to respond to it.

## RE: Velocity change in pipe due to abrupt diameter change

## RE: Velocity change in pipe due to abrupt diameter change

So I guess what I am asking is, are the friction factor curves on the below chart calculated from the Darcy-Weisbach equation? Or are they calculated using another equation, and then you can use the Darcy-Weisbach equation to calculate the head loss (not a number I need, just trying to figure out how the equations are intended to be used)

Moody Chart in Imperial Units: https://www.pumpfundamentals.com/php_pages/frictio...

## RE: Velocity change in pipe due to abrupt diameter change

## RE: Velocity change in pipe due to abrupt diameter change

But, as we usually want to find the head loss, we calculate the friction factor with other equations. I suggest you take a look at the Colebrook-White equation (https://en.wikipedia.org/wiki/Darcy_friction_facto...).

Daniel

Rio de Janeiro - Brazil

## RE: Velocity change in pipe due to abrupt diameter change

Good Luck,

Latexman

## RE: Velocity change in pipe due to abrupt diameter change

For laminar flow (Re < 2000) the friction factor is given by the Hagen-Poiseuille equation. In the critical zone between 2000 and 4000 there are some equations (such as Churchill) that give answers, but flow in this regime is not stable and you should not give too much credence to the numbers generated by these equations.

Back-calculating the friction factor from the Darcy-Weisbach equation would typically be done when you are not sure of the condition (i.e. roughness) of the pipe, but you are able to measure the pressure drop.

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

## RE: Velocity change in pipe due to abrupt diameter change

If not, just use pmover's advice: if Q1 = Q2 with 1 being the larger diameter and 2 being the small diameter and Q=VA.

If you care what the pressure drop is, the abrupt change may be small compared to the length of pipe before and after...

## RE: Velocity change in pipe due to abrupt diameter change

Katmar Software - AioFlo Pipe Hydraulics

http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

## RE: Velocity change in pipe due to abrupt diameter change

In this problem I'd use crane 'flow of fluids'. Go to page A-26, use sudden contraction with angle 90deg. Calculate resistance coefficient (K) in formula 2.

This will allow you to find head loss (pressure loss, KE energy loss), hL=(Kv^2)/2g.

Thereafter apply Bernoulli equation where hL is known, v1 is known, change in pressure should be already known (otherwise you won't know its velocity) and you are left with finding v2 (what you want to know).

NOTE: remember bernoulli equation conditions must be met (don't use incompressible bernoulli equation with compressible fluid)

Kind regards,

Sadik