The causes of losses in fittings.

The common feature in the flow through these devices is that, at some point, the flow breaks down to eddy in a way that causes a greater loss than would have occurred in the ordinary laminar or turbulent flow. In order to see what leads to the breakdown in the flow we must consider each device separately.

I drew the diagrams in figures 8-1a to 8-1f 20 years ago and I am not really satisfied with them because

they do not show the region of eddying sufficiently accurately but I cannot, with any confidence improve them. Fortunately for me we are not really interested in the flow pattern beyond knowing qualitatively how the loss is caused.

 

Figures 8-1a, b, c, d, e, and f represent the typical fittings. The diagrams have been drawn with square corners for two reasons. The first is that these represent the worst case so that any data for such fittings would overstate the loss. The second is that these shapes can be described in the fewest dimensions and words. Typically the sudden enlargement shown in figure 8-1d can be described in terms of the diameters of the two pipes and perhaps the word "square". A real enlargement would in fact be a transition piece and be profiled with two radii if only to facilitate manufacture. These radii improve the flow pattern in the transition and so the loss caused by the real fitting would be less than that caused by the sudden enlargement.

 

 

In looking at the diagrams of figures 8-1 it must be remembered that the approach flow would normally contain fine grain turbulence and the flow lines depicted would not be shown up by injecting dye. However the lines do represent the mean paths of the liquid and in each case show how the shapes of the solid boundaries lead to the breakdown of flow.

 

In the cases of the sharp-edged entry to a pipe, the sudden contraction and the mitre bend, the flow lines separate at the corners, over-contract, and then, breakdown occurs when the liquid expands again to fill the pipe. The random eddies decay into fine grain turbulence as the liquid continues along the pipe until the former turbulence level is re-established.

 

When liquid flows from a pipe into a reservoir a secondary flow is entrained by the emerging stream and the two flows mix as indicated in figure 8-1b. Ultimately the mixing flows spread out into the main body of liquid and the kinetic energy that the liquid has as it leaves the pipe is dissipated to increase the stock of internal energy. The flow through a sudden enlargement is clearly allied to the flow into a reservoir with the larger pipe suppressing the secondary flow but some of the eddying flow moves back upstream into the corner to circulate back into the flow. The function of a partially open valve is the control of the rate of flow through a pipe. This is done by creating a controllable loss and the dissipation of energy into the structure of the fluid. The valve is really a sudden contraction followed by a sudden enlargement with the throat area being variable. Figure 8-1f shows the section through a partially open gate valve. The main loss occurs downstream of the valve. This can be so intense that valves have to be designed to control the flow during the divergent phase just in order for the valve to have a reasonable working life.