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I am solving pipe flow problems and it came to my mind how does one find out the minor loss associated with the splitting of pipe.

enter image description here

Here how does one find the minor loss associated when the flow is in either direction.it is the same as contraction/expansion loss or a 90° elbow loss.

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Generally speaking, there are 2 kinds of losses along the pipe, the "friction" with the pipe wall, and the "friction" at corner and junction. Note that the term "friction" might not be technically correct, but I use it because it is easy to understand.

The pressure loss along the pipe is $p(loss1)=1/2*ro*v^2*f*l/D$ and the pressure loss at the corner is $p(loss2)=1/2*ro*v^2*E$

with ro as the density of the fluid and E is the "curly" letters denoted the loss coefficient at corner.

Your question only asks for loss at the junction "Tee", so the "E" value is between 0.2 and 2.0. Check this pdf file for more details

  • Line flow, flanged E=0.2
  • Line flow, threaded E=0.9
  • Branch flow, flanged E=1.0
  • Branch flow, threaded E=2.0

Based on the drawing you provide, it is the line flow, and perhaps it is "flanged" (smooth pipe, for the lack of better word). Therefore, the value applied is 0.2.

The diameters of the branches are half of the main line's diameter, therefore, the cross section of the main line A1 is 4 times as big as the branch ones. Applying the conservation of mass (assuming the density is unchanged), you have $4*A2*v0=A2*v1+A2*v1$. Solve this, and you have the final fluid speed in each branch pipe increased by 2 times.

If the fluid has changing density, well, then write down the Navier-Stokes equations and solve for the relationship between speed in the big pipe and speed in the small pipe.

With known value for final speed, you can plug it in the equation at the beginning p(loss2) and solve for the needed value.

Oh, just a side note. If the question also asks for loss along the pipe, then you should use Moody Chart. The link I provide also explains how to use it.

Best of luck, mate.

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I'm pretty certain that would qualify as a "tee" fitting, so the minor loss coefficient would range from 0.2 to 2.0 per this source depending upon the fitting type.

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