To find the head of fluid for a given diameter and length of pipe and discharge in gallons per minute: Find, in above table, head for length of one yard opposite discharge in gallons; multiply by given length in yards. Example.-Find head necessary to deliver 100 gallons per minute by a pipe 3 in. diameter and 200 yards long. Solution. 0.169 X 200 = 33.8 feet head. To find the diameter of a pipe for a given head, length of pipe, and discharge, divide head in feet by length of pipe in yards and find in the table opposite the figure for the discharge, the number nearest the quotient; take the diameter from the head of the column in which such number stands. Example.-What diameter should a pipe have to deliver 100 gallons a minute through a pipe 200 yards long under a head of 34 feet? Solution. 34: 200= 0.17; number nearest this quotient opposite 100 gallons discharge is 0.169; diameter at head of column in which this number stands is 3, which is the required diameter. To find the discharge in gallons for a given head, length of pipe and diameter of same: Divide head of fluid in feet by length in yards; find the nearest number in the table under the given diameter and read off the number of gallons in the first column of the table. Example.-How many gallons of water will a 3-inch pipe of 200 yards under a head of 34 feet deliver per minute? Solution. 34 : 200 = 0.17. nearest number under diameter 3 inches is 0.169; corresponding number in first column, 100, which is the required number of gallons. To find the length of pipe for a given head, discharge, and diameter of pipe, divide the given head by the head for one yard as given in the table for the given diameter and discharge; the quotient is the required length. Example.-How long should a 3-inch pipe be to deliver 100 gallons a minute under a head of 34 feet? Solution. 34: 0.169=201, which is the required length. APPROXIMATE FLOW OF PIPES. A simple way to calculate the approximate discharge of a pipe is by means of Prony's formula. Multiply the head in inches by the diameter of the pipe in inches, and divide by the length of the pipe in inches hx d e Then find the number nearest the quotient thus obtained in the first column of the subjoined table, and the required discharge will appear in gallons per minute opposite this figure under the diameter of the pipe. APPROXIMATE flow of pipes (PRONY'S FORMULA). 0.00002402 0.025 0.0511 0.1150 0.2045 0.3196 0.4602 0.626 0.818 UPWARD OR DOWNWARD FLOW OF PIPES. The formulas given are for horizontal pipes or hose. Where there is a difference in height between the point of entry of the pipe and the point of discharge, the formula remains the same, 7.031 10.12 13.77 18.00 28.12 40.50 7.670 11.04 15.02 19.64 30.68 44.18 11.96 16.28 21.27 33.23 47.86 12.88 17.53 22.91 35.79 51.54 38.34 55.23 40.90 58.90 but the value of the head will be different. The head for a horizontal pipe is the height of the surface of the liquid above the point of entry into the pipe, which point is on a level with the point of discharge. Where the pipe falls or rises from the point of entry to the point of discharge or nozzle the head on the fluid is different. The head is always equal to the vertical difference between the surface of the fluid and the point of discharge. Where a pipe falls, after leaving the point of entry, the head will increase; where it rises, the head will diminish. Thus, where a fluid is run from a tank on one floor to a vessel on a floor below, the total head is the difference in altitude between the surface of the fluid in the upper tank and the point of discharge in the lower, so that the head is largely increased over that of an horizontal pipe or hose. Where, on the other hand, the fluid is discharged at a point higher than the point of entry into the pipe, the head will be diminished as against that of an horizontal pipe. Example 1-What will be the discharge of a 3-inch pipe carrying a fluid from a tank in which it stands 8 feet high, and being emptied into a vessel 8 feet high, standing on a floor 20 feet below the first tank, both tanks standing on the respective floors without feet or other supports raising them above the level floors. The first tank stands at one end of the floor, the second at the opposite end of the one below, giving the pipe a length of 210 feet. The fluid in the supply tank is kept at a uniform height by a constant inflow of fresh fluid. Solution.-Assuming the water to be delivered at the top of the lower vessel, the head of the fluid will be the height of the upper tank (8 ft.) plus difference in altitude of floors, less height of lower vessel (20 8 ft.). 8208 20 ft. Reduce length of pipe in feet to yards: 210:3 = 70. Inserting these values according to above rule for finding the discharge in gallons for a given head, length of pipe and diameter, gives 20:70 0.29: nearest number in table under diameter 3 inches 0.286; corresponding number in first column 130. Answer.-Required discharge in gallons per minute = 130. The capacity of the tank to be filled being known, this affords a simple means of computing the time that will be required to fill it from the supply tank. RULES FOR LAYING PIPES OR HOSE. The shorter the pipe, the greater the discharge; hence unnecessary length of pipe is to be avoided where time is of any moment. Angles and curves are to be avoided for the same reason, as they materially interfere with the flow of fluid through pipes. Hence the hose, where such is used, should be of just the requisite length to avoid a waste of time or pressure. In the case of wort or beer this is all the more important since the viscosity of the material augments the friction in the pipe. Sharp angles are to be avoided entirely in pipes and hose, as well as contractions and enlargements of bore. Where curves or elbows cannot be avoided they should be well rounded and of large radius. In that case they offer so little resistance to the fluid that no account need be taken of them in computing time of discharge. By radius is meant the radius of the arc formed by the axis or central line of the bend. This should not be less than five times the diameter of the pipe. Where the respective values can be ascertained, the following formulæ can be used: t = value given in table, next below, for each diameter. Q = number of cubic feet discharged per minute. To find d; given 7, h, Q. t = Q Vx, find value for d opposite t in table THE MECHANICS OF GASES. Elastic Force of Gases.-Gases are in the highest degree elastic. The volume of a gas depends upon the pressure exerted upon it. If the pressure is increased two, three or four times, the volume decreases at the same rate, that is, the gas that under a certain pressure occupies one cubic foot will, when the pressure increases four times, occupy one-fourth of one cubic foot. As soon as the pressure is released the gas will resume the original volume. |