L = the length of pipe in feet.
w = the density of the entering air in pounds per cubic foot.
Reducing the pressure loss to inches of mercury and using in lieu of w, r which is the ratio of the average absolute pressure in the pipe to atmospheric pressure, this formula becomes:
Q = 310.3 √ pd⁵Lr
To permit the rapid calculation of the air quantity which can be passed through a hose, the author has prepared the diagram shown in [Fig. 48]. To use this table, look up the friction loss in the hose in the right hand margin, pass along the horizontal line to the left until it intersects the line inclined at an angle of 45° toward the left, indicating the length of the hose. From this intersection pass vertically to the line inclined at approximately 30° toward the left, representing the diameter of the hose. The quantity in the left-hand margin, opposite the horizontal passing through this intersection, represents the quantity of air which would pass through this hose in cubic feet at the average density in the hose. To correct this quantity to free air, step off the distance on the vertical line from the bottom of the table, representing the average degree of vacuum in the hose, to its intersection with the curved line near the bottom of table. Transfer this distance vertically downward on the left hand margin from the quantity first read on this margin. The quantity opposite the lower end of this distance will be the cubic feet of free air per minute passing through the hose under these conditions.
The line inclined towards the right, which passes through the intersection of lines representing hose diameter, and the horizontal line representing the cubic feet of air passing through the hose at actual density in same, shows the actual velocity in the hose in feet per second.
For friction loss over 10 in. of mercury, use the figures at the right hand of the lower margin, instead of those in the right hand margin, and pass vertically to the hose diameter. Then proceed as before. As these high frictions are seldom used in practice, this departure has been made in order to reduce the size of the diagram.
FIG. 48. CHART FOR DETERMINING HOSE FRICTION.
To illustrate how much the friction tables, based on air at atmospheric density, vary from actual results, two tests made by the author are given. In the first test it was desired to pass 68 cu. ft. of free air per minute through a ⁷⁄₈-in. diameter orifice at the end of 100 ft. of 1-in. diameter hose. Tests on larger hose showed that, to permit this quantity of air to pass through the orifice, a vacuum at the orifice of 2.6 in. mercury was necessary. The most rational table the writer could find indicated that the friction loss in the hose should be 18 in. mercury, and the final vacuum necessary at the hose cock would have to be 20.6 in. mercury. On test it was found that, with 24.8 in. vacuum at the hose cock, but 50 cu. ft. of free air per minute was passing, with a vacuum at the orifice of 1.6 in. mercury, showing a friction loss of 23.2 in. mercury. With the smaller quantity of air passing, the same friction table indicated a friction loss, with this quantity of air, of but 9.8 in. mercury, or 39% of that actually observed. Checking the results of the test with the diagram ([Fig. 48]) gives 50 cu. ft. of free air, with a friction loss of 23 in. mercury.