General Mean Values of Constants.
The general formula (Hagen's)-h/I=rno"/d'.2g-can therefore be taken to fit the results with convenient closeness, if the following mean values of the coefficients are taken, the unit being a metre:- This shows a marked decrease of resistance as the temperature rises. If Professor Osborne Reynolds's equation is assumed h=rnLV"/d'*“", and n is taken I-795, then values of rn at each temperature are practically constant-
Kind of Pipe. in x n
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Wrought iron, . -0131 -21 1-75
Asphalted iron . . -0183 1-12 1-85
Riveted wrought iron
New cast iron
Cleaned cast iron
Incrusted cast iron
Tin plate .... ~0I6Q I°I0 1-72
The variation of each of these coefficients is within a comparatively narrow range, and the selection of the proper coefficient for any given case presents no difficulty, if the character of the surface of the pipe is known.
It only remains to give the values of these coefficients when the quantities are expressed in English feet. For English measures the following are the values of the coefficients:- Kind of Pipe. rn x n 1
Tin plate . . 0265 1-10 1-72
Wrought iron . . 0226 I~2I 1~75
Asphalted iron . 0254 1-127 1-85 Riveted wrought iron . 0260 1-390 1-87 New cast iron . 0215 1-168 1-95
Cleaned cast iron 0243 1~168 2'0 Incrusted cast iron . -0440 I'160 2-0 § 78. bistribiztion of Velocity -in the Cross Section of a Pipe.—Darcy made experiments with a Pitot tube in ISSO on the velocity at different points in the cross section of a pipe. He deduced the relation
V-v = 11~3(r%/R), /i,
where V is the velocity at the centre and v the velocity at radius r in a pipe of radius R with a hydraulic gradient i. Later Bazin repeated the experiments and extended tl1CII1 (/llém. de VA cadérnie des Sciences, xxxii. No. 6). The most important result was the ratio of mean to central velocity. Let b= Ri/UZ, where U is the mean velocity in the pipe; then V/U =1+9-o3, / b. A very useful result for practical purposes is that at 0-74 of the radius of the pipe the velocity is equal to the mean velocity. Fig. 84 gives the velocities at different radii as determined by Bazin.
§ 79. Influence of Temperature on the Flow through Pipes.-Very careful experiments on the flow through a pipe 0-1236 ft. in diameter Temp. F. rn. Temp. F. rn.
57 0-000276 100 O~O0O244
70 0000263 1 IO O'000235
80 0-0002 57 120 0~ooo229
90 O'OOO250 130 0~0OO225
where again a regular decrease of the coefficient occurs as the temperature rises. In experiments on the friction of disks at different temperatures Professor W. C. Unwin found th-at the resistance was proportional to constant >< (1-0-o021t) and the values of rn given above are expressed almost exactly by the relation rn =o-o00311(1~o-00215 I).
In tank experiments on ship models for small ordinary variations of temperature, it is usual to allow a decrease of 3 22, of resistance for 10° F. increase of temperature.
§ 80. Influence of Deposits in Pipes on the Discharge. Scraping Water Mains.-The influence of the condition of the surface of a pipe on the friction is shown by various facts known to the engineers of Waterworks. In pipes which convey certain kinds of waterjoxidation proceeds rapidly and the discharge is considerably diminished. A main laid at Torquay in 1858, 14 m. in length, consists of 10~in., 9-in. and 8-in. pipes. It was not protected from corrosion by any coating. But it was found to the surprise of the engineer that in eight years the discharge had diminished to SI % of the original discharge. ]. G. Appold suggested an apparatus for scraping the interior of the pipe, and this was constructed and used under the direction of William Froude (see “ Incrustation of Iro11 Pipes, ” by W. Ingham, Proc. Inst. Mech. Eng., 1899). It was found that by scraping the interior of the pipe the discharge was increased 56 %. The scraping requires to be repeated at intervals. After each scraping the discharge diminishes rather rapidly to 10%) and afterwards more slowly, the diminution in a year being about 25 %. Fig. 85 shows a scraper for water mains, similar to Appold's but modified in details, as constructed by the Glenfield Company, at Kilmarnock. A is a longitudinal section of the pipe, showing the scraper in place; B is an end view of the plungers, and C, D sections of the boxes placed at intervals on the main for introducing or withdrawing the scraper. The apparatus consists of two plungers, packed with leather so as to fit the main pretty closely. On the spindle of these plungers are fixed eight steel scraping blades, with curved scraping edges fitting the surface of the main. The apparatus is placed in the main by removing the cover from one of the boxes shown at C, D. The cover is then replaced, water pressure is admitted behind the plungers, and the apparatus driven through the °°B . Les.:»;. :;: t-i., , s; swerves“~w~swwm®wa=<;a=::s===~; V333 ' 1 . -2,
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MM - wma =-2 r-~ D
er s C r 2 I
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FIG. 84. Fm. 85. Scale 215.
and 25 ft. long, with water at different temperatures, have been made by J. G. Mair (Proc. Inst. Civ. Eng. lxxxiv.). The loss of head was measured from a point 1 ft. from the inlet, so that the loss at entry was eliminated. The 1% in. pipe was made smooth inside and to gauge, by drawing a mandril through it. Plotting the results logarithmically, it was found that the resistance for all temperatures varied very exactly as v“795, the index being less than 2 as in other experiments with very smooth surfaces. Taking the ordinary equation of How /t= § '(4I¢/D)§ v2/2g), then for heads varying from 1 ft. to nearly 4 ft., and velocities
second, the values of g' were
ln the pipe varying from 4 ft. to 9 ft. per as follows:-
Temp. F. g* Temp. F. I
57 -0044 to -0052 loo ~oo39 to -0042 70 ~oo4z to -0045 110 0037 to 0041 80 -0041 to -0045 120 -0037 to -0041 go ~oo4o to -0045 130 -0035 to -0039 160 -0035 to -0038
main. At Lancaster after twice scraping the discharge was increased 56% %, at Oswestry 54% %. The increased discharge is due to the diminution of the friction of the pipe by removing the roughness es due to oxidation. The scraper can be easily followed when the mains are about 3 ft. deep by the noise it makes. The average speed of the scraper at Torquay is 2% m. per hour. At Torquay 49% of the deposit is iron rust, the rest being silica, lime and organic matter. In the opinion of some engineers it is inadvisable to use the scraper. The incrustation is only temporarily removed, and if the use of the scraper is continued the life of the pipe is reduced. The only treatment effective in, preventing or retarding the incrustation due to corrosion is to coat the pipes when hot with a smooth and perfect layer of pitch. With certain waters such as those derived from the chalk the incrustation is of a different character, consisting of nearly pure calcium carbonate. A deposit of another character which has led to trouble in some mains is a black slime containing a
good deal of iron not derived from the pipes. It appears to be an