Pressure head loss within a tapered pipe due to friction
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
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
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Note that is the half angle of the taper.
Using the continuity equation:
The head lost over the elemental length is given by:
Thus the head lost over the total length is:
Thus the head lost can also be written as: