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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