Dec., I 9 16
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING CHEMISTRY
with water-agar a t the t o p and CHC18-agar beneath. T h e bottom layer consists of a snow-white porous, spongy mass, occluding large quantities of chloroform. On heating, the mass becomes less bulky, loses its chloroform, a n d apparently reverts t o ordinary agar. The precipitating action of alcohol and acetone has already been described. S U M RIA R Y
I-The sources, preparation and composition of agar have been discussed. 11-The analysis of sixteen samples of agar, obtained from widely different sources, show a remarkable uniformity in composition. High ash or silica content is indicative of a n inferior product. Considerable amounts of nitrogenous substances were found in all of t h e samples. P a r t of this nitrogen, a n d possibly some of t h e other nutrients may serve as a food for microorganisms, if grown on a medium containing agar. Some aqueous solutions of agar are acid t o phenolphthalein. 111-A method of preparing a “purified” agar is described. It consists essentially in washing t h e agar shreds in a solution of dilute acetic acid, washing out t h e acid and precipitating, while hot, a 5 per cent
1.133
solution of t h e agar, by means of a large volume of alcohol or acetone. It is shown t h a t much of t h e nitrogenous matter of t h e agar is removed by this method of purification. The method is recommended t o be Eollowed for t h e preparation of agar substrata t o be used in refined bacteriological work, especially where a jellifying medium containing a minimum of nutrients is desired. IV-Solutions of agar will solidify at all concentrations of HC1 and NaOH between 4 . j per cent HC1 a n d 5 per cent NaOH. Heating a t one atmosphere pressure for 1 5 minutes in a n autoclave narrows t h e range of solidification t o from z per cent acid t o 4.5 per cent alkali. Peptone increases t h e jellifying power of agar. KC1 appears t o decrease i t slightly. The author wishes t o take this opportunity t o t h a n k Dr. J. G. Lipman, of Rutgers College, for his valuable suggestions and kindly interest in t h e work, and Dr. E. M. Chamot, oE Cornel1 University, under whose guidance t h e work was begun. Thanks are also due t o t h e various companies, and t o Mr. Y . S. Djang, of China, who so kindly furnished samples of agar. AGRICULTURAL EXPERIMENT STATION NEW BRUKSWICK, NEW JERSEY
LABORATORY AND PLANT FORMULAS FOR THE FLOW OF GASES By
W. K. LEWIS
Received August 5, 1916
I n t h e formulas ordinarily employed for t h e flow of gases through orifices, pipes, and conduits, use is seldom made of t h e simplifications which t h e gas laws make possible, with t h e result t h a t in our engineering handbooks a n d textbooks we find formulas for t h e flow of steam, other formulas for t h e flow of air, and occasionally formulas for use with illuminating gas. On t h e other hand, all these formulas can be expressed in terms of fixed constants (the same for all gases) a n d t h e molecular weight of t h e particular gas with which t h e engineer is dealing. While such modification of t h e formulas involves nothing new in t h e dynamics of gases, none t h e less such simplification is of great value, most especially t o t h e chemical engineer, who frequently deals with gases other t h a n those familiar t o mechanical engineering practice. This is t r u e t o such a degree t h a t i t seems worth while t o develop and present such formulas in general form so as t o make them available t o t h e profession. The mechanical engineer always uses t h e gas law in t h e form pV = R T , applying this formula t o one pound of t h e gas in question. On the other hand, t h e chemist has learned t o use t h e gas law in t h e form pV = n R T , where a is t h e number of mols of gas in question a n d R is t h e gas constant, the same for all gases. The chemist, it is true, has hitherto used this formula exclusively in t h e metric system, but its advantages over t h e older form are no less real in t h e English system t h a n in the metric, and throughout t h e following we shall therefore express t h e gas law
in this way, pV = n R T , using throughout English engineering units, so t h a t p = t h e pressure on t h e gas in lbs./sq. ft., V = the volume of gas in question expressed in cu. f t . , n = the amount of gas in pound mols, one pound mol being a weight of t h e gas in question in pounds equal t o its molecular weight, R = t h e gas constant in English units, 1545, a n d T t h e temperature in O F. absolute. By t h e use of this formula and this nomenclature all t h e ordinary formulas for t h e flow of gases may be written in a common form applicable t o all gases, merely inserting into t h e formula t h e molecular weight or average molecular weight of t h e gas or mixture of gases in question. The molecular weight of a gas may be defined as the weight in pounds of 359 cu. ft. of t h e gas reduced t o or measured under standard conditions, this definition being identical with t h e ordinarily accepted definition familiar t o t h e chemist. The measurement of gas by volume when this is not absolutely necessary is intolerably bad practice, especially on t h e part of a chemical engineer. T o state t h e volume of gas tells nothing of its amount unless its temperature and pressure also be given. It is true t h a t gas quantities may be expressed as weight, but weight relationships in gases are always complicated in comparison with molal relationships, and t h e rational way t o express gas quantities is in mols. Inasmuch as most engineering work has t o be done in t h e English system, t h e most satisfactory unit is t h e lb. mol, i. e . , a number of pounds of t h e gas equal t o its molecular weight. The formulas for t h e number of pound mols of gas are therefore given below, and in general it will be found t h a t these are the easiest and best t o use.
T H E JOL'RNAL O F I N D U S T R I A L A N D E-VGINEERING C N E M I S T R Y
1I34
D E R I V A T I O N OF F O R M U L A S
Bernoulli's theorem in hydro-mechanics is merely t h e statement of t h e equality of input or output of energy into a n y section of a system through which a fluid is flowing. As applied in hydraulics and in t h e hydro-mechanics of liquids in general, i t is usual t o equate the mechanical energy a t inlet and outlet, inasmuch as there is no transformation of heat energy into mechanical energy or vice ~ ' ~ Y sexcept u, t h a t due t o i'riction; where friction loss occurs this is subtracted from t h e energy input before equating t o t h e energy output. On the other hand, whenever a compressible fluid, e. g., a gas. enters and leaves a section under differing pressures, t h e gas must have expanded within the section itself from the higher t o the lower pressure or viLe versa. I n such a n expansion, a gas mill do work upon itself, thereby increasing its mechanical energy a t t h e expense of t h e heat content of t h e gas itself or of its surroundings. and its expansion work must be added t o the input of mechanical energy in the gas in order t o get t h e output. This expansion work is evidcntly t h e integral of p d v . and Bernoulli's therefore becomes
The integral may have all possible x-alues from zero u p t o t h e value of a n isothermal expansion a t t h e highest temperature in t h e apparatus in question and t h e actual value will frequently be difficult, if not impossible. t o ascertain. On the other hand, this term can rarely be neglected and Bernoulli's theorem for the flow of all conipressible fluids must be corrected b y t h e inrroduction of this integral I n the flow of gases it is usually allowable t o neglect the variations in z , because gases are so light t h a t t h e differences in level above d a t a encountered are usually negligible compared with t h e other terms in Bernoulli's equation. On the other hand, if t h e pressure differences encountered are small. t h e vertical distances may no longer be negligible. We shall, however, neglect these terms consistently in the following discussion.
compared with the total pressure of t h e gas, i. e . , not exceeding I O per cent of t h a t total pressure.' T h e best results are obtained in manipulating such a n orifice when t h e orifice chamber is very large compared with t h e orifice itself. This makes ztl negligible compared with u2. To secure this condition i t has been found experimentally t h a t t h e *cross section of the orifice chamber should be not less t h a n twenty times the area of the orifice itself. 'Under this condition our equation becomes ui = z g b T h p J f i 2 . If hz ( I -j- iz) be expanded b y Maclaurin's theorem h2 19 -h4 etc.; if lz be small this series i t gives lz -2 3 4' is sensibly equal t o h itself. Since pl is very nearly equal t o p 2 , the logarithm of p l / p 2 may be written
+
IN
ISOTHERK4L
FLOK
OF
A
(
I
+2-
= I)
:2
2gv2(P1
which may be written
--
2gc2A2
P2)
72 =
2
28
2
T r i t i n g Bernoulli's theorem, zi$Piui+ 2g a
pdv
=
'd2
PI
D1
P2
bTln- = bTIn--.
This condition of isothermal flow is practically quantitatively realized for t h e passage of air through a n orifice through which t h e drop in pressure is small
- UL 2
2g
T h e velocity changes are therefore determined b y the expression on the right-hand side of this equation. For isothermal expansion this function is Pi01
In
Et
and for adiabatic
' [ e) !
The ratio of these two expressions, 'nI
k-1
-
1
T ]
1 t lk-1 . is unity if pi = pi, as is shown b y the calculus; i. e., fov small Pressure chaizgcs the velocity changcs arc ihe same whelher the process be isothermal or adiabatic. So nearly coincident are these curves t h a t even though the pressure change be 10 per cent of the initial pressure, the difference in the velocity changes for the two curves is only '1% per cent, i. e., isothermal expansion represents the result within the usual experimental error. Wherever the pressure change is less t h a n 10 per cent, or frequently even 20 per cent, the assumption of isothermal expansion is entirely justified. This statement applies t o calculating t h e power output of fans a n d the performance of all apparatus handling gases under low pressure drops. fit/
2
'dl
cAd&
,.............
11)
p1v11np1/p2.
=
=
c A ~ z g P ~p p ~) .
