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Tapered Pipe

Pressure head loss within a tapered pipe due to friction
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Overview

23287/uniform_run_off_and_tapered_pipes_004.png
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Let the velocity and diameter at the sections 1 and 2 be as shown on the diagram. Consider the head lost over a short length which is st a distance from position 1, and let the velocity and diameter associated with this short length be and .

The head lost over the element

But,
Note that is the half angle of the taper.


Or,
Using the continuity equation:

Or,

The head lost over the elemental length is given by:

Thus the head lost over the total length is:

Putting:

Thus the head lost can also be written as: