Sheet metal drafting/Chapter 4

by Ellsworth M. Longfield

 

CHAPTER IV
INTERSECTING CYLINDERS

Objectives of Problems on Intersecting Cylinders.

Problem 15
TEE JOINT AT RIGHT ANGLES

32. The Tee Joint at Right Angles.—The name commonly applied to two pipes that intersect is "Tee Joint." Some forms of these joints are known in various localities as "Y-Branches" and "Tee Y's." One of the scoops, Fig. 72, was a cylinder cut by a curved plane. A study of Fig. 95 will reveal a similar condition, the branch pipe being cut by the curved surface of the main pipe.

Side Elevation.—The side elevation should be drawn according to the dimensions given in Fig. 96. The profile should be drawn above the side elevation to avoid a confusion of lines. The profile must be divided into sixteen equal parts, and each part numbered, Fig. 96. Extension lines are dropped downward from each division of the profile until they intersect the circumference line of the main pipe. These intersections, A, B, C, etc., are lettered as shown.

Front Elevation.—Extension lines are used to locate properly the front elevation. Fig. 97. A profile is drawn above the front elevation. This profile is divided into as many equal spaces as there are in the profile first drawn. Both profiles must be of the same size since they represent the same pipe. The profile. Fig. 97, should be numbered as shown. It should be noticed that number 1 of the profile of Fig. 96 is at the bottom, while number 1 of the profile of Fig. 97 is on the left-hand side of the horizontal diameter. This is an important fact, and is true of every drawing that has two elevations. Whatever is directly in front in the side elevation appears on the left-hand side in the front elevation. The true shape of the miter line in the front elevation cannot be shown until it is developed. To do this, extension lines are carried over into the front elevation from points A, B, C, etc., of the apparent miter line, Fig. 96. Extension lines are also dropped from each division of the profile in Fig. 97. Starting at point 1 of the side elevation profile, the extension line is traced downward to the apparent miter line, and then horizontally to a correspondingly numbered line dropped from the profile of Fig. 97. This point is marked with a small circle. All other points of the profile of Fig. 96 should be traced in like manner. A curved line drawn through these intersections will give the developed miter line.

Pattern for the Tee.—After drawing the line of stretchout, the spacing of either profile (both profiles are the same size) is

Figs. 95–99.Tee Joint at Right Angles.

transferred and numbered to correspond. The measuring lines of the stretchout should also be drawn in. Starting at point 1 of the front elevation profile, the extension line should be followed to the developed miter line, and thence to the correspondingly numbered line of the stretchout. This intersection is marked with a small circle. In like manner all the remaining points in the profile of Fig. 97 should be traced and the intersections of each with its corresponding measuring line in the stretchout determined. A curve traced through these intersections will give the miter cut of the pattern.

Opening in Main Pipe.—A line of stretchout, Fig. 98, is first drawn at right angles to the main pipe. The spacings of the apparent miter line, Fig. 97, are set off upon this line, and these divisions lettered to correspond to the lettering of the apparent miter line. Measuring lines from each point are drawn at right angles to the fine of stretchout. The intersections of the developed miter line, as shown in Fig. 97, should now be lettered. It should be noticed that the position of the lettering is changed as was the numbering of the profile, and for the same reason. A line is dropped from point E of the developed miter line until it intersects line E of the stretchout in Fig. 99. The intersection is marked with a small circle. In like manner intersections for all other points of the developed miter line should be located. A curve drawn through these intersections will give the true shape of the opening in the main pipe, Fig. 99.

Problem 16
TANGENT TEE AT RIGHT ANGLES

33. The Tangent Tee at Right Angles.—When a straight line and the circumference of a circle touch each other at but one point, the straight line is said to be tangent to the circle. Their point of meeting is called the point of tangency. A straight line from the center of the circle, meeting the tangent at an angle of 90°, locates the point of tangency. In Fig. 101, the tangent and the point of tangency are plainly indicated.

Tangent Tee.—When the tee joint is so placed upon the main pipe that one side of the tee is tangent to one side of the main, as in Fig. 100, the fitting is known as a "Tangent Tee." The use of this type of fitting enables the designer to keep the distance from the ceiling to the top of every horizontal pipe uniform throughout the entire system. All hangers for the piping can be made the same length and the entire job will have a neater and more workmanlike appearance.

Side Elevation.—A side elevation should be drawn according to the dimensions given in Fig. 101. After drawing a profile, it should be divided into sixteen equal spaces, and extension lines from each division carried to the apparent miter line. The divisions of the profile should be numbered, and the intersections of the apparent miter line lettered as shown in Fig. 101.

Front Elevation.—The front elevation can be located by extension lines. Another profile should be drawn above the front elevation. It must be divided into the same number of equal spaces as the profile of Fig. 101. It is to be numbered, placing number 1 on the left-hand side. Extension lines are dropped from each division of the profile, Fig. 102. Other extension lines are carried over from the intersections of the apparent miter line. Fig. 101, until they intersect the extension lines drawn from the profile. Starting from point 1 in profile of Fig. 101, the extension line should be traced downward to the apparent miter line, and thence to a correspondingly numbered line dropped from the profile of Fig. 102. In like manner, ah the divisions of the profile, Fig. 101, can be traced and each intersection marked with a small circle as shown in Fig. 102. A curved line passing through these points will give the developed miter line. One-half of the developed miter line is dotted to represent that part of the line that cannot be seen from the front.

Figs. 100–104.Tangent Tee at Right Angles.

Pattern for the "Tee."—Draw the line of stretchout, Fig. 103. The spacing of the profile should be transferred and the divisions numbered to correspond to the numbers of the profile. The measuring lines of the stretchout should be drawn. Starting at point 1 of the front elevation profile, the extension line is to be followed to the developed miter line, and thence to a correspondingly numbered measuring line in the stretchout. This intersection should be marked with a small circle. All the other points in the profile of Fig. 102 are traced in like manner, and the intersections for each measuring line in the stretchout determined. A curve traced through these intersections will give the miter cut of the pattern.

Opening in Main Pipe.—A line of stretchout, Fig. 104, must be drawn at right angles to the main pipe. The spacing of the apparent miter line is to be set off upon this line. These divisions are lettered to correspond to those of the apparent miter line. Fig. 101. Measuring lines, at right angles to the line of stretchout, are drawn from each point. The intersections of the developed miter are lettered as shown in Fig. 102. The position of the letters must be changed in the same way as the numbers in the profiles of Figs. 96 and 97. A line should be dropped from the point E of the developed miter line until it intersects the line E of the stretchout in Fig. 104. The intersection of the two lines is marked with a small circle. In like manner, intersections for each division of the developed miter line, as shown in Fig. 102, can be located. A curve traced through these intersections will give the true shape of the opening in the main pipe.

Problem 17
TEE JOINT NOT AT RIGHT ANGLES

34. The Tee Joint Not at Right Angles.—The tee joint not at right angles is used for conveyor systems, and in heating and ventilating work. The abrupt change of direction in the Tee Joint at right angles causes a drop in velocity that seriously affects the working of an entire system. The greatest angle of deflection allowable in a Tee Joint not at right angles is 45° from the direction of flow as in Fig. 105. Many firms use an angle of 30°.

Side Elevation.—The side elevation should be drawn using the dimensions given in Fig. 106. The branch pipe is represented as being broken in this view, because the upper part of the branch plays no part in developing the pattern. A profile, Fig. 106, divided into sixteen equal parts, which are numbered, is now drawn. Extension fines are carried downward from each division until they meet the apparent miter line. The intersections of the apparent miter line A, B, C, etc., are lettered as shown in Fig. 106.

Front Elevation.—The front elevation. Fig. 107, should be drawn in outline. The "tee" is set at an angle of 45° to the main pipe as shown. The profile of the "tee" should be drawn and divided into sixteen equal parts. An extension line from each division of this profile is carried downward and to the right; that is, parallel to the sides of the branch.

Developing the Miter Line.—Horizontal extension lines from each intersection of the apparent miter line are carried over into Fig. 107. If a view were to be taken along these lines in the direction of the arrow, the eye would see two points, D and F for instance, on each line. But Fig. 106, the side elevation, represents such a view; therefore the intersections of the front half of the apparent miter line must each have two letters. Starting at the point A in Fig. 106, the intersections of the apparent miter line must be lettered as shown. Starting from point 1 in the profile of Fig. 106 the extension line can be traced downward to the apparent miter line, and thence to the correspondingly numbered line, dropped from the profile of Fig. 107. In like manner, the other intersections for the developed miter line are located and the curve drawn.

Pattern for the "Tee."—After the line of stretchout is drawn at right angles to the tee in Fig. 108, the spacing of the profile should be set off on it and the divisions numbered to correspond. The measuring lines of the stretchout are put in at right angles to the line of stretchout. Since the branch is at an angle of 45°, all of this construction work can be drawn with the T-square and the 45" triangle. Extension lines parallel to the line of stretchout are

Figs. 105–109.Tee Joint Not at Right Angles.

carried from each intersection of the developed miter line until they cut corresponding measuring lines in the stretchout. A curved line through these intersections will give the miter cut of the pattern.

Opening in Main Pipe.—A line of stretchout, Fig. 109, is drawn at right angles to the main pipe of Fig. 107. The spacings of the apparent miter line are set off on this line and the divisions lettered to correspond. Measuring lines are drawn from each point at right angles to the line of stretchout. The intersections of the developed miter line should be lettered as shown in Fig. 107. An extension line is dropped from point E of the developed miter line, until it meets line E of the stretchout. In like manner, intersections for all other points in the developed miter line are located. A curve drawn through these points will give the true shape of the opening in the main pipe.

Problem 18
TANGENT TEE NOT AT RIGHT ANGLES

35. The Tangent Tee Not at Right Angles.—Figure 111 shows a side elevation which has the same appearance as the side elevation of Fig. 106. The branch pipe, however, is tipped towards the eye as will be seen by studying Fig. 112. Every tangent tee at other than right angles must have the entire miter line developed. The method of drawing this problem does not vary from that of the preceding one. Consequently, the method need not be repeated here. The student is cautioned to follow each step carefully.

The student has perhaps noticed a similarity of method for developing the patterns for all cylinders. Such pattern problems come under the head of "Parallel Line Drawing," which takes its name from the fact that the sets of extension and construction lines are parallel to one another. The following general rules apply to parallel line developments, and, if carefully followed, can be applied to any problem of this class with success.

Rule 1.—Draw a side elevation, if necessary, to show a true miter line.

Rule 2.—Draw a front elevation, if necessary, to show a true miter line.

Rule 3.—Draw necessary profiles.

Rule 4.—Divide the profiles into equal spaces, and number the divisions.

Rule 5.—Carry extension lines from each division of the profile to the miter line.

Rule 6.—Develop a miter line if necessary.

Rule 7.—Draw a line of stretchout, transfer the spacing of the profile to this line, and number to correspond.

Rule 8.—Draw the measuring lines of the stretchout.

Rule 9.—Carry the extension lines over into the stretchout, from each division of the true miter line.

Rule 10.—Trace the intersections of the stretchout, beginning at the profile, thence to the miter line, and from there to a correspondingly numbered line in the stretchout.

Front elevations. Figs. 107 and 112, could be dispensed with in tee joints at right angles. As a matter of fact, experienced layer-outs never draw them. They are included here for instructional purposes.

36. Related Mathematics on Tangent Tees and Tee Joints.—Altering the Main Pipe Size.—In a blow-through system, whenever a branch is taken from the main pipe, the diameter of the main must be reduced beyond that point. Also, if a branch pipe is added on to the main of an exhaust system, the diameter of the

Figs. 110–114.Tangent Tee Not at Right Angles.

main must be increased. By so doing, the original velocity and static pressures are preserved and the system exerts an equal "pull" at all points.

Rule for Altering the Size of Main.—The area of the main must be increased, or diminished, by an amount equal to the square inches of cross-sectional area of the branch. In other words, the cross-sectional area of the main must at all times be equal to the combined cross-sectional area of all its branches.

Sample Problem.—Two heaters are to be connected to a chimney flue by one pipe. One heater has a 7-inch, and the other a 9-inch neck. How large must a main pipe be to care for both heaters?

Formula for area,	A=	D2×.7854
Substituting,	A=	72×.7854
	A=	38.485 sq. in., area of 7" pipe
and	A=	92×.7854
	A=	63.617 sq. in., area of 9" pipe.

Since this is an exhaust system the areas must be added to get the equivalent area of the main.

Equivalent area=38.485+63.617=102.102 sq. in.

Transposing the above formula,
$\scriptstyle {D={\sqrt {A\div .7854}}}$ (Problem 8, Article 24.)

Substituting in this formula,
$\scriptstyle {D={\sqrt {102.102\div .7854}}}$

		.7854	102.1020	130
			78.54
			23.562
			23.562
	$\scriptstyle {{\sqrt {130}}=11.4''}$				11.4" Ans.

In actual practice we would make the pipe 11½" in diameter.

Problem 18A.—Two heaters are to be connected to a chimney flue by one pipe. One heater has an 8-inch, and the other a 10-inch neck. How large must the main pipe be to serve both heaters?

Problem 18B.—A battery of three steam heaters having 8½" smoke necks are to be connected to the chimney by one main pipe. (a) What will be the diameter of the main between the second and the third heaters? (b) What will be the diameter of the main between the third heater and the chimney?

Problem 18C.—Six blacksmith forges are to be connected to one smokestack. Each forge has a 6-inch neck. Give the size for the main pipe as each forge is "picked up."

Problem 18D.—In a shavings removal system a "sticker" is to be provided for. Two hoods on the "sticker" have 5-inch necks, and two other hoods have 4-inch necks. How many square inches should be added to the area of the main pipe to care for this machine?

Problem 18E.—A forced draft heating system in a factory has a 9" diameter outlet every 20 feet. The main pipe as it leaves the fan is 20" in diameter, (a) How many 9" branch outlets will this main serve? (b) What will be the diameters of the main after each branch is taken off?

Problem 18F.—Two boilers are set side by side. Each boiler has a rectangular smoke neck measuring 14"×37". How large must the round pipe be made that is to convey the gases from these boilers to the stack?