Minor Losses

Important Equations

[1]

[2]

[3]

[4]

So now that you have learnt about how to calculate the major losses in a pipe you’re now ready to learn about… MINOR LOSSES!!!

Minor losses is where you calculate the pressure losses as a fluid passes through different bends, expansions, contractions, inlets, exits, fittings, valves and elbows. These interrupt the flow of the liquid and may cause separation from the smooth flow and therefore lose energy.

These losses are referred to as minor since they are usually much smaller losses than the major losses (shock).

Minor losses can be expressed with the loss coefficient KL. This relates to headloss with the equation [1]:

This equation can be rearranged easily to find pressure loss using the equation

Sudden Pipe Expansion

Oh no! Your fluid has come across a sudden pipe expansion… but how will the separation in your flow affect your pressure loss?

FEAR NOT! Because the Borda-Carnot equation [2] is here to help!

Using this equation combined with equation [1] can help you find KL for this component of the pipe. You can also use this equation if A2 is infinite, which will mean that:

If A1=A2 then the pressure loss will be zero, since there’s no change in the pipe diameter.

A way to reduce the inevitable KL that comes with a pipe expansion is to include a diffuser (see right). The smaller the angle of the diffuser the more the flow follows the edge of the pipe and reduces separation.

In a diffuser, KL depends on the area ratio and the angle of the diffuser:

Sudden Pipe Contraction

Oh boy, not a pipe contraction. The separated flow occurs just after the contraction of the pipe! But don’t be fooled by how complicated it may look. You can simply use the following table to compare the diameter ratio of the to its relevant KL.

Bends

There are many different types of bends in a pipe, thankfully there’s many different ready-made solutions here for you to use at any point

If a pipe is flanged or threaded refers to the way that two pipes are connected. A flanged pipe allows for the fluid to flow smoother and therefore has a lower loss coefficient. However a threaded pipe means there’s more slight disruptions to the flow in addition to the pipe component.

Solving the minor losses problems?

So now that you have all the information about the different losses in pipe components the

power is in your hands to solve the problem.

Step 1: Identify all the different components that are stated in the problem. E.g. identify any bends, expansions, contractions etc in the pipe.

Step 2: Using the information above calculate the loss coefficient (KL) for each component in the pipe separately.

Step 3: Add up the loss coefficients for each component

Step 4: Use the sum of the loss coefficients in equation [1] and the equation

to find the velocity or the head loss / pressure loss.

Step 5: Because you have just solved a minor loss problem.

But wait.

What about the major losses in pipes?

Just combine the equation for the head loss during minor losse with the equation for head loss during major losses

Therefore in a problem with multiple major losses and minor losses you add up the sum or the major head loss with the sum of the minor head losses. The general equation for this is:

But if D is constant then the equation can be simplified to:

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