The loss of head, due to bends in a pipe, depends upon three factors. First, loss due to change of direction of the water in the pipe; second, loss from friction as in an ordinary straight length of pipe; third, loss due to enlargements or contractions in the bend, such as are formed when the unreamed ends of pipe are screwed into ordinary elbows.

The second and third losses also apply to couplings and tees, and the loss is about the same as for bends of equal diameters. The loss of head for change of direction differs with the angle and with the radius of the bend. That is, there is less loss for change of direction in a 45 degree bend than in a 90 degree bend, and the loss is greater in a bend of one diameter radius than in one with a radius of two diameters. The loss in a 90 degree bend with a radius of five or more diameters and uniform smooth interior bore is no greater than in an equal length of straight pipe. In other words, there is practically no loss for change of direction in a bend of greater radius than 5 diameters.

The head lost in a 90 degree bend of less than 5 inch diameter and of the radius commonly found in practice (Radius=Diameter) with square unreamed ends of pipe screwed into the fitting, Fig. 64, is found by experiment to equal the head lost in a length of pipe of about 100 times the diameter of the fitting.* The loss of head is divided into:

Fig. 64

*Thus 100 diameters of 2-inch pipe=200 inches of straight 2-inch pipe.

In pipes of larger diameter than 5 inches, these values would hold true only for the loss of head due to change of direction, as the pipes are not relatively as thick, nor the enlargements of the elbows relatively as great.

The loss of head when the ends of the pipe screwed into the fitting are reamed, as shown in Fig. 65, is found by experiment to be equal to the loss of head in a pipe equal in length to about 50 diameters of the fitting. This loss of head is divided into:

Fie. 65

Loss of head due to change in direction.....38 diameters

Loss of head due to enlargement of the bend ... 8 diameters

Loss of head from friction due to length of fitting . . 4 diameters

Total................50 diameters

The loss of head in a bend of five or more diameter radius, with flush interior joints, Fig. 66, is equal to the loss of head in a length of pipe four diameters of the fitting. This is comparatively shown as follows:

From the foregoing it will be seen that the least possible head is consumed by using fittings of large radius with flush joints. That when common fittings are used the loss can be reduced to one-half by reaming the ends of the pipe with a triangular-shaped reamer, the length of which is just double the base.

Table XXV - Values Of Coefficient n

Fig. 66

The loss of head due to bends can be calculated by the formula:

v2 h=n 2g

In which h=head lost in feet v=velocity in feet per second g=32.16 acceleration due to gravity n=a coefficient for the bend.

The value of coefficient n depends upon the ratio between the radius r of the pipe and the radius R of the bend. Table XXV gives values of n corresponding to various values of the ratio r .

Example

What will be the loss of head in a column of water flowing with a velocity of 8 feet per second through a 4-inch bend that has a radius R of 4 inches?

Solution

The radius r of a 4-inch bend = 2 inches, therefore, R which is 4 inches will=2r which gives for n the value .29 (Table XXV).

Substituting values in the formula then gives, h=.29 X 64/64.32 =.287 foot.

Answer.