MODIFIED BERNOULLI'S EQUATION BASIC INFORMATION AND TUTORIALS


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.

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