Bernoulli’s equation, as developed
previously, may be stated in the following form:
z1 + h1 + v1 2 /2 g = z2 + h2 + v2 2 /2
g
All the three terms on each side of
Bernoulli’s equation have dimensions of length and are therefore
expressed in metres. For this reason the total value of the three
terms on the left-hand side of the equation is known as the initial
total head in just the same way as we used the word head to describe
the height h associated with any pressure p through the expression
p = rho x g x h
Similarly the right-hand side of the
equation is known as the final total head. Bernoulli’s equation for
an ideal situation may also be expressed in words as: Initial total
head = final total head
What happens when there is a loss of
energy due to friction with a real fluid flowing along a real pipe is
that the final total head is smaller than the initial total head. The
loss of energy, as heat generated by the friction and dissipated
through the liquid and the pipe wall to the surroundings, can
therefore be expressed as a loss of head.
Note that we are not destroying this
energy, it is just being transformed into thermal energy that cannot
be recovered into a useful form again. As far as the engineer in
charge of the installation is concerned this represents a definite
loss which needs to be calculated even if it cannot be reduced any
further.
What happens in practice is that
manufacturers of pipe system components, such as valves or couplings,
will measure this loss of head for all their products over a wide
range of sizes and flow rates.
They will then publish this data and
make it available to the major users of the components. Provided that
the sum of the head losses of all the components in a proposed pipe
system remains small compared to the total initial head (say about
10%) then it can be incorporated into a modified Bernoulli’s
equation as follows:
Initial total head – head losses =
final total head
With this equation it is now possible
to calculate the outlet velocity or pressure in a pipe, based on the
entry conditions and knowledge of the energy losses expressed as a
head loss in metres.
Once again we see the usefulness of
working in metres since engineers can quickly develop a feel for what
head loss= might be expected for any type of fitting and how it could
be compensated. This would be extremely difficult to do if working in
conventional energy units.
No comments:
Post a Comment