That the flow of a fluid from a branch pipe into a main pipe may meet with as little resistance as possible, a branch pipe may be required to join on to a main pipe, as in Fig. 14. Here it will be seen that the cut on the branch pipe where it joins the main pipe is somewhat peculiar, its shape at the back taking the form shown by the dotted line.

Fig. 14.

The patterns for the segments of the curved portion of the branch pipe can, of course, be set out, as in the former cases.

The striking out of the pattern for the branch pipe cut, and the hole in the main pipe, is shown in Fig. 15. Before a pattern can be made, an elevation of the intersecting line of branch and main pipes must first be obtained. This is done by describing a semicircle on the branch pipe in the side elevation, dividing into six parts, and running lines up parallel to the centre line as shown. These lines are cut off by drawing lines up from the points on the semicircle in end elevation until they meet the main pipe circle, then running along until they cut the same numbered line on the side view.

Thus, the line through point 10 on the semicircle in the end elevation gives point 10' on the main pipe circle, the horizontal dotted line through this point then intersecting with the line drawn through point 10 on the semicircle in the side elevation, and so on for all the other points required for the elevation of the joint line. The pattern for the branch pipe is now marked out in the usual way by measuring lines from the base to the joint line, and setting these lengths up on the correspondingly numbered line on the pattern. It should be noticed that two lengths are measured off each line in this side elevation, except the two outer lines. Thus, to take one case, the height of line for position 8 on the pattern will be measured from the base up to the dotted curve, and that for position 4 up the same line to the point marked 4", and so for each pair of lines.

Fig. 15.

To mark out the hole, a girth line, 3' to 9', is laid down, the parts of this being equal in length to the length of the correspondingly numbered arc on the main pipe circle. Through each of the division points lines square to the girth line are drawn. Now to get the lengths of these. Draw a line, A B, as shown in the elevation, and, using this as a base to measure from, measure the distance of the different points on the joint curve from this, and set along the corresponding line on the hole. Thus the line 2' 4 on the hole will be the same length as 2" 4"/ on the elevation, and, again, 3' 3 will be equal to A 3", and so on for all the other lines. All the points on Fig. 15 have not been numbered, as this would probably have led to confusion; but the reader should find no difficulty in following the construction, as having obtained one set of points and lines, all the rest will follow the same rule.

In bending the plates, care must be taken that they are bent the proper way, so that the pipes will fit together correctly at the joint. This, of course, holds for all cases of tee-pipes in which the branch does not fit on the middle of the main pipe.