Major Losses

Important Equations

[1]  

[2]  

[3]  

[4]  

[5]  

(Note: this page assumes you’re up to scratch with Pipe Loss Equations and the Reynolds Number. We recommend you have a look over them if not :) )

Major pipe losses are pressure (or head, depending on the question) losses in a flow due to friction from the pipe walls. Despite having the label ‘Major’, they can still be dwarfed by Minor Losses, so don’t get tricked!

The process of finding the pressure loss (if flow rate is given/can be calculated) in a pipe can be broken down into 3 stages:

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• 1. Calculate the Reynolds Number. Is it turbulent? Is it laminar?

  2. Calculate the Head Loss. Which equation or method you use will depend on whether the flow was laminar or turbulent (See below)

  3. Calculate the Pressure Loss using equation [1] (Unless the question just wants Head Loss).

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Step 2: Laminar Flow

So you’ve got a Reynolds Number that says the flow is laminar, now what? We use Equations [1] and [2], in that order, to get that value of hloss. The velocity needed for Equation [2] would have been previously used to calculate Re.

Step 2: Turbulent Flow

The process is unfortunately less streamlined for turbulent flow.

• • Is it a smooth pipe? If so, we can use Equation [3] to calculate the friction factor, and head straight to Step 5. If not…

  • Ah heck, it’s a rough pipe. Unless they’re being particularly horrible, there should be a given absolute roughness value associated with the pipe material (noted as Ɛ). Be careful, since this value is often given in millimetres.

  • This absolute roughness needs converting to relative roughness (a ratio) by dividing it by the pipe’s internal diameter (also in millimeters!). This is Equation [4]

  • Time to refer to the Moody Diagram (see below). Mark on a vertical line for your value of the Reynolds Number. Then, find a line on the Relative Pipe Roughness axis that closest corresponds to the value you’ve calculated. If nothing’s close enough, you can sketch/imagine a line parallel to the others.

  • Follow this line across until it intersects the Reynolds Number line. From this point, draw a line directly across to the Friction Factor axis, and read off that value

• • Now with the Friction Values, you can just plug everything into Equation [2], and finish with Step 3

But what if flow rate, and to that extent, velocity, isn’t given? Now, the process becomes more iterative:

• 1. Calculate the Relative Pipe Roughness the same as before. Then, estimate a value of Re.

• • 1. is a recommended value

• 1. Back to the Moody Diagram. Using the estimated Reynolds Number and the Relative Pipe Roughness, find the Friction Factor for these set of values

  2. Time for some equation wizardry. Combine and rearrange Equations [1] and [2] to eventually end up with :

• 1. Sub everything in, and stick the new value of velocity into the Reynolds equation. How far off were you? If your estimated and calculated values of the Reynolds Number are more than 10% apart, increase or decrease your estimated value accordingly, and try again until you make it into the 10% tolerance.

5. Finish the question. That is, some might just ask for the velocity, but some may want a flow rate etc etc.