Let us look at a typical pipe fitting to see where the energy loss arises. The sudden contraction of the flow caused by joining two pipes of different diameters gives rise to regions of recirculating flow or eddies.

The liquid which enters these regions is trapped and becomes separated from the rest of the flow. It goes round and round, repeatedly hitting the pipe walls and losing kinetic energy, only to be restored to its original speed by robbing the bulk flow of some of its pressure energy.

The energy is dissipated as heat through the pipe walls. If the overall pressure drop was critical and the head loss needed to be kept to a minimum, then a purpose-built pipe fitting could be designed to connect the two pipes with much less recirculation.

Essentially this would round off the sharp corners.

Since it is kinetic energy which is lost in the collisions which are a feature of recirculating eddies, it follows that faster liquids will lose more energy than slower liquids in the same situation.

In extensive experiments it has been found that the energy loss in fact depends on the overall kinetic energy of the liquid as it meets the obstruction.

The proportion of the kinetic energy that is lost is approximately a constant for any given shape of obstruction, such as a valve or a pipe fitting, irrespective of the size.

For the purposes of calculations involving Bernoulli’s equation it is convenient to work in terms of the velocity head (i.e. the third term v2/2 g in Bernoulli’s equation) when considering kinetic energy.

Therefore a head loss for a particular type of pipe fitting is usually expressed as:

Head loss = loss coefficient × velocity head
hloss = k × (v2/2 g) (3.2.8)

Some typical values of k are shown below, but it must be remembered that they are only approximate.

Approximate loss coefficient k for some typical pipe fittings

90° threaded elbow 0.9
90° mitred elbow 1.1
45° threaded elbow 0.4
Globe valve, fully open 10
Gate valve,
fully open 0.2
3/4 open 1.15
1/2 open 5.6
1/4 open 24

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