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COI

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Originally appearing in Volume V14, Page 65 of the 1911 Encyclopedia Britannica.

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COI 0.1 0.2 0.3 0.t 0.5 o.6 0.7 o.8 0.9 1.0 /w = cc = .624 .632 .643 .659 .68, .712 .755 .813 .892 1.00 c = 22 5.9 47.77 30.83 7.801 1.753 1.796 .797 .290 .060 .000 r • 4 (4) Elbows.-Weisbach considers the loss of See also:

head at elbows (fig.91) to be due to a contraction formed by the stream. From experiments with a See also:

PIPE

pipe i; in. See also:

DIAMETER (from the Cr. &a, through, µErpov, measure)

diameter, he found the loss of head = ',v2/2g ; = 0.9457 +2.047 See also:

sin' 10. Hence at a right-angled See also:

ELBOW

elbow the whole head due to the velocity very nearly is lost. Bends.-Weisbach traces the loss of head at curved bends to a similar cause to that at elbows, but the coefficients for bends are not very satisfactorily ascertained. Weisbach obtained for the loss of head at a See also:

BEND

bend in a pipe of circular See also:

section fb=i-bv2/2g; (6) where d is the diameter See also:

TEA (Chinese cha, Amoy dialect t€)

tea. of the pipe and p the Valves, Cocks and Sluices.-These produce a contraction of the See also:

WATER

water-stream, similar to that for an abrupt diminution of section already discussed. The loss of head may be taken as before to be ~v = 3',v2/2g; (7) where v is the velocity in the pipe beyond the See also:

VALVE (Lat. valva, a leaf of a double or folding door, allied to volvere, to roll, as of a door on its hinges)

valve and i•,, a coefficient determined by experiment. The following are Weisbach's results. Sluice in Pipe of Rectangular Section (fig. 92). Section at sluice =w1 in pipe =w. wl/w = I.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 i'e = 0.00 •09 '39 '95 2.08 4.02 8.12 17.8 44'5 193 Sluice in Cylindrical Pipe (fig. 93).

Ratio of height oft I.o I 1 I } I I } } opening to diameter J} of pipe wtlw = 1.00 0.948 .856 .740 .609 .466 .315 .159 1•n = 0.00 0.07 0.26 0.81 2.06 5.52 17.0 97.8 See also:

COCK, EDWARD (1805-1892)

Cock in a Cylindrical Pipe (fig. 94). See also:

ANGLE (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Gr. ayKOS, a bend; both connected with the Aryan root ank-, to

Angle through which cock is turned =B. B = 5° 10° 15° 20° 25° 30° 350 Ratio of •85 0 '772 •692 '613 '535 .458 See also:

CROSS

cross •926 sections j y. _ '05 '29 .75 1.56 3.10 5'47 9.68 B= 40° 45° 5.'° I 55° 6o° 65° 82° Ratio of •385 .315 •250 .190 .137 •091 0 cross sections )} 17.3 31.2 52.6 106 206 486 co - Throttle Valve in a Cylindrical Pipe (fig. 95) f a B = 5° to° 15° 20° 25° 30` 350 1 4G° '24 .52 '90 1. J4 2.51 3.91 6.22 Io•8 9 = 450 50° 55° 60° 65° 70° 900 - = 18'7 32.6 58.8 118 256 751 co § 84. See also:

PRACTICAL

Practical Calculations on the Flow of Water in Pipes.-In the following explanations it will be assumed that the pipe is of so See also:

GREAT

great a length that only the loss of head in See also:

FRICTION (from Lat. fricare, to rub)

friction against the See also:

SURFACE

surface of the pipe needs to be considered. In See also:

general it is one of the four quantities d, i, v or Q which requires to be determined. For since the loss of head h is given by the relation h=il, this need not be separately considered. There are then three equa- tions (see eq. 4, § 72, and 9a, § 76) for the See also:

SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of such problems as arise:- ~'=a(I+I/I2d); where a =0.005 for new and =0.01 for incrusted pipes.

02/2g = 4di. (2) Q = . rd2v. (3) Problem I. Given the diameter of the pipe and its virtual slope, to find the See also:

DISCHARGE (adapted from the O. Fr. discharge, modern decharge, from a med. Lat. discargare, to unload, dis- and earn care, to load, cf. " charge ")

discharge and velocity of flow. Here d and i are given, and Q and v are required. Find from (1) ; then v from (2); lastly Q from (3). This See also:

case presents no difficulty. By combining equations (I) and (2), v is obtained directly:- v=v (gdi/2i-) =v (g/2a)) {di/{1+I/12d} ]. (4) For new pipes . / (g/2a) =56.72 For incrusted pipes . . =40.13 For pipes not less than I, or more than 4 ft. in diameter, the mean values of are For new pipes 0.00526 For incrusted pipes 0.01052. Using these values we get the very See also:

SIMPLE

simple expressions- v=55'31,/ (di) for new pipes =39.11V (di) for incrusted pipes S Within the limits stated, these are accurate enough for practical purposes, especially as the precise value of the coefficient i- cannot be known for each See also:

SPECIAL

special case.

Problem 2. Given the diameter of a pipe and the velocity of flow, to find the virtual slope and discharge. The discharge is given by (3); the proper value of i- by (I); and the virtual slope by (2). This also presents no special difficulty. Problem 3. Given the diameter of the pipe and the discharge, to find the virtual slope and velocity. Find v from (3); from (I); lastly i from (2). If we combine (I) and (2) we get =(v2/2g) (4/d) =2a{I+I/12d}v2/gd; (5) and, taking the mean values of i' for pipes from i to 4 ft. diameter, given above, the approximate formulae are i=0.0003268 v2/d for new pipes ] (5a) =0.0006536 v2/d for incrusted pipes Problem 4. Given the virtual slope and the velocity, to find the diameter of the pipe and the discharge. The diameter is obtained from equations (2) and (I), which give the quadratic expression d2-d(2 av2/gi) - av2/6gi = o. d =av2/gi+v { (av2/g2) (av2/gi+I/6)}. (6).

For practical purposes, the approximate equations d = 2av2/gi+ 1 / 12 (6a) =0.00031 v2/i+•083 for new pipes =o 00062 v2/i+.o83 for incrusted pipes are sufficiently accurate. Problem 5. Given the virtual slope and the discharge, to find the diameter of the pipe and velocity of flow. This case, which often occurs in designing, is the one which is least easy of See also:

DIRECT

direct solution. From equations (2) and (3) we get- d' =32'Q2/g7r2i. (7) If now the value of in (I) is introduced, the See also:

EQUATION (from Lat. aequatio, aequare, to equalize)

equation becomes very cumbrous. Various approximate methods of See also:

MEETING (from " to meet," to come together, assemble, 0. Eng. metals ; cf. Du. moeten, Swed. mota, Goth. gamotjan, &c., derivatives of the Teut. word for a meeting, seen in O. Eng. Wit, moot, an assembly of the people; cf. witanagemot)

meeting the difficulty may be used. (a) Taking the mean values of given above for pipes of i to 4 ft. diameter we get d=V (32i'/g7r2)J (Q2/i) (8) =0.2216;1 (Q2/i) for new pipes =0•2541V (Q2/i) for incrusted pipes; equations which are interesting as showing that when the value of ° is doubled the diameter of pipe for a given discharge is only in-creased by 13 %.

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