Sudden contraction
Where a liquid flows through a sudden contraction as shown in figure 8-1c the loss occurs almost wholly in the small pipe. The liquid in the large pipe converges smoothly as it approaches the sudden change in diameter and continues to converge for a distance of about before it starts to diverge again. The flow pattern breaks down into intense eddying and the main loss occurs in this eddying. As the loss occurs in the small pipe the expression for the loss will be in terms of and, as the contraction depends on the two diameters, will depend in some way on the ratio of the diameters or the ratio of the areas. Then, if the loss is given by , useful values of k are given in the table below.
|
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
0.95 |
|
|
0.09 |
0.16 |
0.25 |
0.36 |
0.49 |
0.64 |
0.81 |
0.9 |
|
|
0.36 |
0.35 |
0.32 |
0.27 |
0.22 |
0.14 |
0.05 |
0.015 |
A real fitting will have a shape that will cause less loss than the sudden contraction and so the figures above should be regarded as worst case values.
In figure 8-1e I showed that the loss at a mitre bend results from the contraction and subsequent divergence. When the bend is swept ie has a radius and the radius of a swept bend is greater than about 2.5 times the pipe diameter the contraction does not occur. The flow then exhibits the characteristics of free vortex flow in that the velocity on the inside of the bend is greater than that on the outside. The transition to this flow starts upstream of the bend and the transition back to normal flow takes place downstream of the bend. The loss is attributed to this double change in flow pattern.
The flow through such a bend is unpredictable even if the effects of the connections are suppressed in some way and generally it is found to be adequate to put the loss in a swept bend where the radius of the bend is greater than equal to .
Allowances for losses in other fittings can be made by choosing figures that are based on similar geometry to the figures given above. For example the loss in a tee used as a bend could be put equal to that for a mitre bend.