Introduction

In chapter 3 I concluded with the statement that, for steady, one-dimensional flow, the total energy/unit weight at point 1 in the flow equals the total energy/unit weight at point 2 down stream of 1 plus the energy/unit weight that has been lost between 1 and 2. This can be written in symbols:-

                            +  the loss between 1 and 2.

 

Now I have to extend this idea to the point where the loss between 1 and 2 can be evaluated for a pipe system.

 

I find that it is difficult to know how to start explaining the behaviour of pipes so that it is a logical progression because, of course, it did not evolve logically. It seems to me that I have to start by anticipating the outcome and observe that this empirical science has developed by evaluating each loss in the pipe as some fraction of the kinetic energy per unit weight in the flow. Then I can look at various pipe-fittings and see how the loss in incurred and put a magnitude to it.

 

We already have, from chapter 7, a way of finding the loss of head in steady flow in a pipe. Now we want ways of taking into account other losses due to bends, changes in section, valves and so on.

 

In chapter 3 we showed how the total head equation for a flow line could be adapted to the steady flow of a fluid through a pipe. We first put the total energy per unit weight at point 1 equal to the total energy head at point 2 plus the loss between 1 and 2. We then put the potential energy equal to its value on the axis of the pipe, regarded the pressure as uniform across every section, and let the kinetic energy head at any section equal to . Then we had to find a way to evaluate the loss of head to friction between points in the pipe.

 

In chapter 3 we also noted that pipes were normally constructed of lengths of straight pipe coupled by various fittings. We noted that this meant that we would require expressions for head loss in straight pipes in forms that can be used directly with the energy equation. We said nothing about the loss of head in the fittings. We must now adapt the total head equation still further to allow for these fittings. In order to do so we must consider the reasons for the loss of energy to friction in pipe fittings, find ways of measuring the losses and of storing the resulting data. We shall find that there is little justification for attempting to find expressions for the loss of head in pipe fittings when the flow is laminar so this chapter will be limited to the case of turbulent flow.