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TABLE OF THE LOSSES BY FRICTION IN PIPES. FRICTION LOSS IN LBS.
PRESSURE PER SQUARE INCH FOR EACH 100 FEET IN LENGTH OF CAST-IRON PIPE DISCHARGING THE STATED QUANTITIES PER MINUTE. COMPUTED BY G. A. ELLIS, C.E.
3.3 0.84 31 1 2 8 13.0 3.16 1.05 .47 .12 12 28.7 6.98 2.38 97 .27
50.4 12.30 4.07 1.66 .42
27.5 9.15 3.75 .91 30
16.1 6.52 1.60 .51
100 48.1 14.9 4.89 1.99 .51
125 124 21.2 7.00 2.85 .69 .10
150 145 28. 1 9.46 3.85 .95 .14
37.5 12.47 5 02 1.22 .17 207 47.7 19.66 7.76 1.89 .26
250 249 28.06 11.20 2.66 37 .04 .005
300 290 33.41 15.20 3.65 .50 .01 .05 .007
350 42.96 19:50 4.73 .65 .15 .06.01
400 373 25.00 6.01 .81 .20 .08 .02
30.80 7.43.96 .25 .09 .04 .017 .009.005 500 621
14.32 2.21 .53 .18 08.036 .019.011 750 830
3.88 .94 .32 .13.062 .036 .020 1,000 1,037
1.46 .49 20.091 .049 .028 1,250 1,245
2.09 .70 .29.135.071 .040 1,500 1,450
.95 .181 .095 .054 1,750 1,660
.234.123.071 2,000 1,867
.297 .153.086 2,250 2,075
.77 .362 .188 .107 2,500 2,490
III 515 .267 .150 3,000 2.905
.697 -365 .204 3,500 3.320
.910 .472 .263 4,000 3,735
-593 .333 4.500 4,150
The frictional loss is greatly increased by bends or irregularities in the pipes.
The speed at which the water flows inside a pipe has, as will be inferred from the proportionated losses and quantities in the above table, a directly increasing effect on the loss, and the results, over a considerable range of speed and size of pipes, are given in the succeeding table.
OUTFLOW OR DISCHARGE OF WATER FROM A 100-Foot LENGTH OF DIFFERENT PIPES, UNDER VARIOUS
VELOCITIES, WITH CORRESPONDING FRICTIONAL LOSSES.
Internal Diameter of Pipe,
Internal Diameter of Pipe,
Cubic Feet of Feet Dis- Fall: Lost charged in Over
per coming Minute. Friction.
Lost by Friction.
This is calculated, as is the table on page 46, upon a basis of a length of pipe of 100 feet, convenient for decimal multiplication or division, and from it may be gathered the loss of fall or head in conveying a given quantity of water through a certain pipe, leaving the net outflow or discharge to be expected at the end of the length of pipe. The Measurement of Streams.
I.—This can be effected by causing the water to pass over an artificial dam or weir : thus, a board sunk level across the stream, well puddled all round, and having a notch
cut out, broad enough and deep enough for all the water to pass through and fall perfectly free on the other side. Rule.-Cube the depth of water flowing through notch, extract square root, multiply by 5, which will give quantity in cubic feet flowing over each foot in width ; but it saves time to consult the following
TABLE GIVING THE QUANTITY OF WATER IN CUBIC FEET PER MINUTE
PASSING OVER A DAM OR WEIR FOR EVERY INCH OF WIDTH.
Depth of Weir Water.... 1 in. 2 in. 3 in. 4 in. 5 in. 6 in. 7 in. 8 in. 9 in. 10 in. 11 in. 12 in.
EXAMPLE.—A weir 36 inches wide and 6] inches deep. The table gives for 612 inches 6.68 cubic feet of water per minute ; this, if multiplied by 36 inches, will give the total quantity of water (6.68 by 36 = 240.48 cubic feet) per minute passing down the stream. The depth of the water must be taken 2 or 3 feet up the stream ; there drive in a peg until level with the bottom of the notch, then measure the depth of water flowing over the top of the peg.
The weir must be made with the up-stream side vertical. The crest should be horizontal and the ends vertical. The edges presented to the current must be sharp; if the upstream edge be beveled or rounded in any degree the result will not be correct.
The stream must not touch the weir except at the edges. The height of the crest above the tail-water, below the weir, should be equal to one-half the depth of the stream flowing over the weir.
II.- BY DISCHARGE THROUGH ORIFICES.—This is a very useful method of measurement, and is particularly applicable to existing mills. The gate or shuttle is raised to the exact height necessary to pass all the water which is coming down. The width and depth of the opening is then carefully measured and the area calculated in square inches; the head or depth from the centre of the opening to the surface of the water above is also noted. The result obtained is termed so many “inches ” of water at such a head.
EXAMPLE.—A shuttle, 4 feet wide, takes the full flow of the stream when raised 2 feet, with the water standing 5 feet above the sill, that is 4 feet above the centre of the opening. The width of the opening, 48 inches, multiplied by its depth, 24 inches, gives an area of 1,152 square inches. The actual discharge under a head of 48 inches, taken from the tables, is 4.27 per square inch. Multiplying 1,152 by 4.27 we obtain 4,919 cubic feet per minute, as the actual discharge.
This plan may also be used for estimating the winter supply of a mill which can only be visited in the dry weather. The miller can generally give the exact height to which the shuttle of the by-pass must be raised to discharge the water during the rainy months.
III.—BY THE VELOCITY OF THE CURRENT AND SECTIONAL AREAS OF THE STREAM.—Select a length of the stream, of say 50 feet, of as nearly a uniform section as possible ; ascertain the area of the section by multiplying the width by the average depth taken in feet and decimals. The result will be more accurate if sections be taken at each end of the selected length of channel, and at one or more equidistant places between them; the average of these sections being used for the purposes of calculation.
Stakes should be placed on both sides of the stream, to mark the chosen length of 50 feet; and lines stretched across stream a few inches above the water make the observation more accurate.
A float consisting of a cork or piece of wood should be thrown in a few feet above the first line, and the time which it takes in traversing the distance between it and the lower one is carefully noted. To obtain accurate results a succession of floats are employed, and the mean time taken.
The calculation required to reduce these observations will be best illustrated by an example :
If the section of the stream measures 13 square feet, and the time occupied by the float in travelling the 50 feet is 28 seconds, the section 13 square feet, multiplied by the length 50 feet, would give 650 cubic feet passing in 28 seconds. Multiplying by 60, and dividing by 28, we obtain 1,393 cubic feet (nearly) as the amount per minute. But as the velocity has been measured on the surface of the water in the centre of the stream, this quantity must be reduced by one-eighth to allow for the retarding influence of the sides and bottom. We should then obtain 1,219 cubic feet as the quantity flowing per minute.
In irregular streams it may be necessary to use a short length, say 10 feet, for the purposes of measurement.
It is always desirable that the time should be taken with a chronograph or stop watch.
There is always a perceptible difference between the surface velocity of a stream and its mean velocity.