« 이전계속 »
will give the same value to v, in the two vi' f's ml? m'l) _p,'-P.' equations. That will be the desired
(21) 29 T, 37,'
28,P, value of the velocity of exit from the pipe, all resistances being considered. But when the flow is strictly iso
In practice these equations for strictly thermal we have y=1 in eq. (14), or adiabatic flow cannot be applied to very m=0 in eq: (21), all of which reduce to long pipes, because the flowing gases the eq. will acquire same
measure of heat. Hence, as the resistance at the orifice of v,'f's,_P,'-P.'
(22) entry becomes greater in comparison 2g a with the frictional resistance as the pipe
Should it be desired to take into is shortened, it appears that when (14) is
account the resistance of the orifice of to be employed (17) should be also.
III. Let the pipe be considered as so entry in calculations for flow through long that an appreciable amount of heat pipes by any of the latter formulas, it is transferred to the gas while in transit may be done by use of eq. (3) or (17), as
whether the fall of pressure is slight or through it, and yet not sufficient to make the flow isothermal. Then some where (22) is applicable, however, it will
considerable at the entry. In cases modified value of y might be used, as lying between 1.408 and 1.
scarcely be found necessary to consider
the resistance at entry, because then the But it may be more convenient to express the temperature as it varies pipe will be relatively very long, making along the length of the pipe as a func. able. Eq. (22), indeed, is applicable to
that resistance comparatively inapprecition of l, or, taking r for the absolute the case of conveying compressed air temperature,
into tunnels as at Hoosac, Mont Cenis, T=F(1).
St. Gothard, &c., or as proposed by In this case, instead of eq. (13), we H. H. Day, in a scheme for compressing should write
air at Niagara Falls, to be used at PTP, F(t)
Buffalo, Rochester, &c. For such extra
(19) ordinary lengths the resistance at entry v,
would vanish. The flow could then be and hence we should have, instead of regarded as strictly isothermal, provided the equation next following (13), the the pipes were at constant temperature following, viz:
throughout, a condition nearly realized
by burying the entire line of pipe, Forv,' fs / P, FO
mula (27) has been employed in my 29 a P р т.
(20) 29 a T, P,
In the preceding the leading object an expression which is integrable when has been to state the true relation bethe form of F(l) is known.
tween the quantities treated. As regards As an example suppose the tempera- II and III, more convenient forms for ture increases uniformly with the dis- application to practice will be considered. tance along the pipe from the exit up. First, we notice that in the use of Then, for T, at exit,
such quantities as before us, frequent T=(T, + ml)=F(1)
reference to tables of physical constants,
&c., is necessary, and these are usually I being here variable as representing various lengths of the pipe. If l' is the given for the temperature of melting icē. whole length of pipe, and if , is the temperature at the entrance to pipe, we Let P., 0, and 7, represent the specific have
pressure, specific den
sity and absolute temT, T,
perature for the temper
ature of melting ice. Hence (20) becomes
FORMULAS FOR PRACTICE.
Pi, d,, and t, the same for the gas in Po (P-P2) (P, +p.) the reservoir at the point 0.7.
2 of departure in the flow.
P.-P. p, d, and t the same just inside the
(26) orifice of entry.
P" P2, 0, and 7, the same at the instant where Pm=the arithmetical mean of the of exit.
P.: V, and the velocity of the stream For small differences of pressure P.
of gas at the entrance and p,, we have pm=p, nearly, and (26) and exit.
becomes a, s ,l, sectional area, perimeter
P. P.-P. of section and length of
8.7. P flowing stream. The term specific pressure, is taken to thermal flow through cylindrical pipes.
For air the equation (22) for iso mean the pressure in units per unit of
becomes surface, as lbs. per square ft. Specific density is the weight in units per unit of v,' =284943 . Źr, Pm P.: . . . (27) volume, as lbs. per cubic ft.
P. For gases sensibly perfect, like air, 1 being the radius of the pipe, and the illuminating gas, &c., we have the well- coefficient of friction being taken at known relation
This equation (27) has been compared 8.7, 8, 7, 8, 7,
with the results of experiment as indi53.15, air; or = 88. illuminating gas; column of calculated velocities at exit
cated in the accompanying table, the for lb. ft. F. units, true for a given gas having been obtained by aid of this under all circumstances, whether expanding adiabatically, or in any other formula. The comparisons indicate that
But for many cases the three the coefficient of friction is in some quantities p, & and 7 vary, as, for instance, cases less in value than the .006 asin the adiabatic condition.
sumed, notably for the St. Gothard In eq. (14) the density 8, is unknown, experiments, for which .004 would have but as the entire flow is supposed adia- given results agreeing more closely. But batic, quantities in the reservoir are con
it is difficult to discover a law relating f nected with those at other points accord
with r or v, or both; which will reconcile
the discrepancies shown in the table. ing to (13). Hence
For instance, compare the Italian experi8.7. P. (P2
ments with the St. Gothard, for velocid=d
(24) ties of 15 to 20 ft. and diameter of pipe P. P. T
7.87. Like velocities and diameters 8, and p, being quantities in the reser- being found in both, it appears that t, voir.
stated in terms of v and r, would be the The flow of weight, or weight of gas same for both and could not be otherdischarged, is always
wise. Hence f cannot be stated in terms ayo=av, 8=av,8,=w
of v and r alone, so as to satisfy all the (25)
experiments. so that the weight can be found for the If f be taken as a function of p, so as adiabatic flow, by use of (14), (17), (24), to reconcile the two cases above conand (25). When the resistance of the sidered, the same will be wrong for makorifice of entry is neglected, (17) is an ing the results of experiment of Henson necessary, and p, in (14), becomes p., and calculation agree. The experiments
The second members of (21) and (22) of Henson were made with lead pipe. may be put in the following form:
If we assume that the St. Gothard p-p P. T, (P-1)
experiments are more trustworthy than
the others, this would argue a smaller 0.T.' 2
value of f. But from these experiments, pe T,
all considered, probably no better value 0.
of f=.005 could be assumed.
TABLE OF VELOCITIES OF COMPRESSED AIR AT THE EXIT FROM LONG PIPES.
OBSERVED AND CALCULATED
PRACTICAL FORMULAS FOR
FOR ANGLE BLOCKS AND
BRACES OF BRIDGES.
Written for VAN NOSTRAND'S ENGINEERING MAGAZINE.
The exact values of x and y can be value of x. We therefore compute y found from (1) and (2), only by solving first. an equation of the fourth degree.
Also from the above we have ab>xy, A very simple and almost exact solution is, however, easily effected as fol- therefore >
d lows: Substitute
Now eliminating x from (1) and (2) I
dl (3), and h=
y-10y' +80.25y +54-56=0. VD? +1?
By Horner's method (.831 being an for x and y in the second member of (2), approximate root of the above equation) which equation then becomes
I find y=.845. Then 2 =.535, and
tion given above, decrease as Now (1) and (5) give:
decreases, or as (6)
approaches unity. (D-6)*+(-a)
Still the errors are almost inappreciable, d (l-a)
and are of no practical significance, even
(7) in the above very unfavorable case. V (D-6)* +(2-a)
When the length only is wanted, eq. Then L=V(D-y)' +(120)" ..
(10) is most convenient and is suffi
ciently exact. 2xy
It is easy to see that:
; () d
BD=EN+2BK + a small quantity,
2ab 2 ab
say e', and that
=2BK+a small quanor L=VD' +
2ab Let us compare these with the true tity, say e”, .: BD-5=EH+ (e' -e');
which shows that the error involved in Let d=1, D=10 and 1=15. eq. (10) is the difference of two small Eq. (3) gives a= .557;
quantities. Eq. (4) gives b=.831 (6) 5354
THE SOCIETY OF CIVIL ENGINEERS OF Eq. (7) y=-.8444 PARIS AND FRENCH PORTS.—The tonnage L=17.1187
of the following ports during the year (9) L=17.1183
1879 was given in a paper read before (10) L=17.1148
this society by M. Hersent: Of Antwerp a and b are special values of x and y it was 5,614,243 tons; Dunkerque, 726,found from (1) and (2) by interchanging 401 ; Le Havre, 1,888,099; Rouen, 582,x and y in the second member of (2), or Bordeaux, 871,930; Marseilles, by omitting them from that member. 2,591,052; Genes, 2,068,973. He also
called special attention to the value of Supposing y>x then is (>D;
the docks projected under M. Freycinet D
at the port of Dunkerque. M. A. Pyotteand
Beyaert, of that port, worked hard many
1-X and since a'+bo=x++y*; x<a and y<6. years in the endeavor to get the neces
sary dock and harbor improvements carLet bry-e; then by virtue of the ried out to give back to Dunkerque the preceding equation, and since e is small, important position it once held among
the ports of France. As long ago as y a=Xte very nearly
1868 he caused fully matured plans and
estimates to be lithographed and largely Hence b is less than, and also nearer circulated in the endeavor to improve the true value of y than a is to the true the port.
ON SOME ELECTRO-MAGNETIC ROTATIONS OF BAR MAG
NETS AND CONDUCTING WIRES ON THEIR AXES.
By G. GORE, F.R.S.
Proceedings of the Royal Society.
In all the published forms of Ampère's Although the action of the portion of experiment of the electro-magnetic ro- the current in the mercury and the fixed tation of a vertical bar magnet or con- conductor in contact with it upon
the ducting wire upon its axis by Ampère, movable current in the rotating wire or Faraday, Sturgeon, and others, the mag- magnet is a cause of the movement, there net or wire has either been immersed a are other circumstances which co-operate large portion of its depth in mercury, or to produce the rotation, and which are its middle part has been connected by a themselves capable, without assistance, wire with a surrounding annular channel of producing it. Wiedemann and myfilled with mercury, and the electric cur- self have shown that an electric current rent passed into or out of the magnet or passing from one end to the other of a wire by means of that liquid, and the magnetized iron rod or wire having dismercury has formed an essential part of similar poles at its two extremities prothe arrangement.
duces torsion of the wire (the two ends In different treatises on electro-mag- of the wire moving of course in opposite netism, either no explanation or different directions), and that reversing the direcones are given of the cause of the rota- tion either of the current or of the magtion of the magnet or wire. The most netic polarity, reverses the direction of usutal cause assigned is the action of the the twist. In all published cases of roportion of current in the mercury and tation of bar magnets on their axis by the fixed conductor immersed in it upon the influence of electric currents, the the current in the rotating wire or mag- two ends of the magnet have had disnet; and the correctness of this expla- similar poles. By meditating upon cernation is proved by the simultaneous tain facts connected with this subject, I movement of the mercury in the opposite concluded that, by passing a current direction.
from one end to the other of a magnetDe la Rive, in his Treatise on Electri- ized rod or wire having similar poles at city (English edition, 1853, vol. i., page its two ends, the magnet would probably 259) very correctly remarks: “It must rotate ; and experiment has demonstrated not be supposed that the phenomenon of that conclusion. rotation is due, as has been erroneously Upon a thin wooden tube 15 centims. stated, to the action upon the magnet of long and 7 millims. bore I wound a cotthe portions of the current that traverse ton-covered copper wire 1.7 millim. diit, or that traverse the conducting wires ameter from one end of the tube to the attached to the magnet and move with middle, then reversed the direction of it. In fact, how could a solid system winding and continued to the other end be set in motion by a force emanating and back to the middle, again reversed from a portion of the very system itself, and coiled to the first end of the tube; and connected with it in an indissoluble by which arrangement the passage of a manner? The action can only arise from current through the coils produced two a part of the current which is independ- similar poles at the ends of the tube, and ont of the system that moves. This two others of the opposite kind at the part is the portion of the circuit which is middle. not connected with the magnet that is The tube being now fixed in a vertical set in rotation, and which consequently position, a straight iron wire 15 centims. is situated independent of the system in long and 1.8 millim. diameter, pointed motion. This kind of action has been at its lower end and surmounted by a calculated by M. Ampère in a perfectly brass mercury cup 5 millims. diameter, rigorous manner.”
containing a drop of mercury, was sup