July, 1916
T H E J O U R N A L O F I N D r S T R I A L A IV D E N G I N E E R I N G C H E M I S T R Y
111-It is shown t h a t sodium nitroprusside can be used as a n internal indicator t o show t h e end-point of the disappearance of t h e sulfide in t h e titration with iodine. IS’-This work affords further evidence of t h e interesting fact t h a t when an iodine solution or a dilute acid is carefully added t o a solution containing calcium polysulfide and thiosulfate, t h e polysulfide can be quantitatively decomposed before t h e thiosulfate is attacked. S‘-A rapid accurate method of weighing t h e pre-
627
cipitated sulfur in t h e iodine and hydrochloric acid titrations of a lime sulfur solution is proposed. VI-Two methods ( B and C ) , not heretofore used for t h e determination of thiosulfate in lime-sulfur solutions, are described, both being theoretically and practically sound and accurate. VII-The accuracy of t h e iodine titration method (or Harris method) for t h e analysis of such solutions is confirmed. EXPERIMENT STATION LEXINGTON, KENTUCKY
A%GRICULTURAL
LABORATORY AND PLANT THE FLOW OF VISCOUS LIQUIDS THROUGH PlPES
I
By W. K. LEWIS Received May 2, 1916
Y p
The carrying capacity of pipes for water under various pressure drops has been experimentally studied b y many engineers and while the results are not very concordant on account of the extreme sensitiveness t o varying conditions, none the less our knowledge of t h e resistance t o flow o€ k a t e r through pipe lines is relatively satisfactory and complete. On the other hand, practically no work has been published on t h e resistance t o flow through pipes of liquids other t h a n water despite the fact t h a t information of this sort is of vital importance t o the chemical engineer, Davis, in his “Handbook of Chemical Engineering, ” points out t h e extremely small carrying capacity of pipes for viscous liquids such as sulfuric acid a n d glycerin as compared with their capacity for water, b u t he gives no suggestions as t o methods of estimating t h e size of pipes required for specific cases. There are in this country thousands of miles of pipe lines transmitting mineral oils as well as t h e piping systems of chemical plants handling acids, solvents, a n d all sorts of liquids in large quantities. While a wealth of information along this line is undoubtedly available t o t h e engineers of individual corporations, t h e lack of a n y published figures a n d t h e importance of t h e whole problem led this laboratory t o undertake a n investigation along these lines which has extended over t h e last four years. After certain preliminary work, a series of tests was made studying t h e flow of mineral oils of varying viscosity a t relatively low velocities. T h e results of this work are reported as Series A. Later, in order t o supplement the results of these first experiments b y s t u d y of flow a t higher velocities, another separate investigation was carried out which is reported as Series B. While t h e results are limited t o relatively small pipes and low viscosities, certain generalizations can be drawn which are so well confirmed t h a t their use, even beyond the scope of t h e present experimental range, seems justified, especially as a working basis upon which t o develop further investigation. N0M E N C L A T E R E
P
’
= =
pressure drop in grams/cm2. or lbs./sq. f t . coefficient of absolute viscosity in sec. dynes/cm2. or sec. poundals/’sq. f t .
1 1
= = =
length of the pipe in cm. or ft. radius of pipe in cm. or ft. density of the fluid. mean velocity a t point where sinuous flow changes t o parallel flow,cm./sec. or ft./sec. mean velocity in cm.,’sec. or ft./sec. hydraulic frictional coefficient.
{
v,
=
V,
=
f
=
G E NE R A L DISC US S I 0S
It has long been known t h a t , for t h e flow of fluids through capillary tubes u p t o 4 or j mm. in diameter, the formula of Poiseuille, P =
8 pzv
---?, RY2
holds quantita-
tively. Though for t h e flow o f liquids other t h a n water through large tubes or pipes, quahtitative d a t a have not been published, t h e paths along which t h e particles of liquid travel have been studied qualitatively b y introducing air or dyes into t h e fluids and photographing the effects produced by forcing t h e m , through glass containers of various shapes and sizes.‘ These observations show t h a t a t low velocities liquids move in straight lines parallel t o t h e axis of the tube, b u t when t h e velocity is sufficiently increased, t h e lines of flow become distorted, the filament forming violent eddies of constantly changing form and position. A t t h e walls of t h e container there is always a film of liquid which is retarded b y t h e friction of t h e solid surface, so t h a t it continues t o move in straight lines. The mean velocity of the fluid, a t t h e point where t h e change in type of motion takes place, is commonly known as the critical velocity and all flow below this point is called parallel, direct, or viscous motion, while t h a t above is known as turbulent, indirect, or sinuous flow. From this i t is obvious t h a t a t least two different laws must govern t h e flow of fluids, the one above and t h e other below t h e critical velocity, with the possibility of a third for an intermediate state. Poiseuille’s law would be t h e one t o use below the critical point, since his formula applies entirely t o straight line motion. For flow above t h e critical point, we have but one suggestion as t o t h e manner in which flow may t a k e place, from observation of the formulae for t h e flow of steam, air, and water above the critical rate. 1
These equations may all be written P
=
H. S.Hele-Shaw, Engineering, 66 (1898), 420, 444, 477, 510.
fpls‘, -~
er
,
T H E J O U R - V A L OF I L V D U S T R I A L A N D ENGI.!VEERl~VGC H E M l S T R Y
628
,A ',B
TABLEI-RESULTS
several bends and drops were necessary t o accommodate the pipe t o the receivillg tank. ,4s it tvas desired, however, t o study flow in
OF
TYPICAL R u m (SERIESA) Per cent
Run
No, (c)
Coeff. Dens. Abs. of Visc. Fluid P
DeviaPRWSURE tion DRoP(a) Obs. Lbs. Dynes
P
v01. 8, *YO.7
a t approximately its theoretical capacity. MoreoTTer, the driving motor was running a t from j o t o 60 per cent overload, thus causing great difficulty in properly regulating t h e pressure. A t the highest
If a tube is smaller a t one end than a t t h e other, as from t h e method of manufacture is usually t h e case, t h e liquid will flow much more rapidly when the large end is a t t h e bottom than when t h e tube is reversed. Furthermore, Gurney's correction terms, although small and perhaps negligible, are of doubtful validity.
0.005plW
For example, the term
-~~- - - - ,
which is used for frictional resistance, holds for non-viscous fluids flowing in turbulent motion and is incorrect for parallel flow. M7e propose a new method of calculation suggested b y Lang (Thesis, Mass. Inst. Tech., 1914), which can be obtained directly from t h e fundamental equation of Poiseuille. Let t h e tube (Fig. 11) be so adjusted t h a t the capillary head, Dq, is maintained constant. Let t h e fluid be raised t o h and allowed t o flow b y gravity from A t o C. Por capillary tubes, as 8 plV previously stated, Poiseuille's formula, P =,-;; holds quantitatively. Therefore, as pressure is proportional t o the density oi the fluid, hp =
aPiv gv*
For tm-o different fluids, 1 and 2,
Dividing (1) by (21,
( a ) T h e conversion in. is 6.87 X lo4. (6) T h e conversion factor l o r changing lhs. per min. t o cc. per sec. is 7.95. (6) In R u n s 1-60 and 95-187, the I-in. standard steam p i p e teas used. T h e '/*-in. standard steam pipe nras used in t h e remaining runs. ( d ) Calculated b y Poiseuille's equation.
Five lubricating oils of different viscosities were used, the oil being pumped into a constant head t a n k b y means of a Gould rotary pump and thence into t h e pipe line. After passing through t h e line, t h e oil was discharged into a t a n k supported b y platform i T h e work in this series of runs was carried o u t by Messrs. Greenough and Dinsmore in 1914 and submitted as a thesis in partial fulfilment of the requirements for the S.B. degree a t the Massachusetts Institute of Technology.
Solving, Therefore, if t h e tube be standardized by measuring the time of efflux of a liquid between t w o fixed points, B and C, the viscosity of any other fluid m a y be obtained by simply measuring its density a n d time of flow between t h e same points, providing p and !J are k n o w n for the first liquid. This automatically corrects for unevenneyc. of bore. W e would suggest, as did Gurney, t h a t the fluid be raised each time t o A a3 described above, b u t t h a t the time be taken between B and C for greater accuracy in time of starting. For high precision over wide ranges of temperature, the standardizatioll and t h e viscosity determination should be carried out a t nearly t h e same temperature, or the following correction may be made for expansion of t h e glass:
Tz =
TI(?--+- 4, (1
4-2ait)
where a = linear coefiicient of expansion of glass, a n d 1 = temperature difference between t h a t employed and the temperature of standardization.
July, 1916
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
the experimental error for runs at high velocities was therefore large. , I n order t o determine t h e critical velocity of t h e oils and also t o ascertain whether t h e equation P = cf)V" would hold above t h e critical velocity, we plotted
629
critical velocity is a point of unstable equilibrium a n d seldom reached in practice; hence when critical velocity1 is referred t o in this article, t h e lower pointt h e change from turbulent t o nonsinuous motionwill be understood. I t is t o be noticed t h a t t h e curves do not deviate from straight lines u p t o the point of intersection, or, in other words, there is no intermediate flow between straight and turbulent motion. The average value of n from t h e two curves is approximately 2 and we therefore make the same assumption made in hydraulics, namely t h a t P
=
PflZ2 -,
gr realizing t h a t neither oil nor water follows this law without a varying constant. The frictional coefficients for those runs above t h e critical velocity were found t o be nearly t h e same as those for water under the same conditions of flow. Ail exact work on flow above the critical velocity is, however, taken from Series B. I n this first series of runs it was impossible t o carry t h e velocities of flow far above the critical point and in all runs a t these high \-elocities, t h e experimental error was great, owing t o inadequate equipment. I n order t o study the flow of liquids a t varying velocities a t rates well above the critical point, a second entirely separate series of runs was undertaken, using
1 I n order t o derive a n equation for t h e critical velocity of any fluid, let us consider the pressure-velocity plots for Poiseuille's and t h e sinuous formula. If a fluid is moving through a pipe below t h e critical velocity Poiseuille's formula, a s above stated, holds quantitatively or, in other words, P = kV. T h e pressure-velocity plot is therefore a straight line (Fig. IV) passing through t h e origin and determined experimentally b y
3 the logarithm of t h e pressure drop against t h e logarithm of t h e ve1ocity.l I n Fig. 111, Curve I represents t h e least viscous oil ( p = 0 . 089) flowing above t h e critical velocity. Curve z represents t h e oil ( p = 0 . 23) flowing above and below t h e critical velocity. Curve 3, plotted from d a t a collected b y Osbourne Reynolds on t h e critical velocity of water, gives a means of comparison between water and a fluid twenty times as v'1scous. Even a casual glance a t t h e two latter curres will reveal their extraordinary similarity. Each liquid has two critical velocities: the first represents t h e higher one, where nonsinuous motion becomes sinuous; the other shows the point where turbulent flow changes t o direct motion. Usually, in industrial practice, a fluid enters a pipe with a turbulent motion produced by a rotary or centrifugal pump, compressed air or by some other means whereby violent eddies are set up in t h e field. We: however, were able t o realize both conditions because of the introduction of a constant-head t a n k between our p u m p and t h e pipe line. This t a n k was provided with a n air dome and insured fairly uniform and quiet conditions a t t h e mouth of t h e pipe line. Nevertheless, this higher 1
For if P = kVn, log P = log k
line having the form r = a by log k and is equal to n.
+ n log V, the equation of a straight
P + n y , the slope being log - which is unaffected log v
V
F/G*Tlf r" P locating points between a and b. Let the same liquid flow above t h e critical velocity and accordingly follow the sinuous formula P = kV2 This curve is a parabola passing through the origin with all experimentally n), where n was determined points lying between B and D. If P = k V ( 2 plus or minus a small decimal, the curve BD xould cease to be a parabola b u t would remain a curve which nevertheless has t h e same general shape and in t h e following discussion would make no difference. Between points a and B, the velocity is greater for a given pressure drop in turbulent motion than in straight line flow, while above B the reverse is true. It is clear t h a t for a liquid moving with a greater velocity per unit pressure, less power is necessary t o transmit a given amount of this fluid through a pipe. Below t h e point B therefore more energy is consumed b y viscous t h a n b y sinuous flow. Above point B t h e reverse is true. This experimental work has, however, proven t h a t below B the flow is viscous and sinuous above. In both cases the flow takes place in t h a t way involving t h e greater energy consumption. This may be looked upon a s a specific instance of the general rule t h a t if a change can take place in a variety of ways the change tends t o follow t h a t path which corresponds t o t h e greatest decrease in free energy. At the critical velocity t h e two types of motion give identical pressure drops, i. e . , n fpluc 8plVc pc = -- =
+
gr
-.
8P
If t h e value of 2 be assigned t o n, Vc = - *
fp i
T h e value t o use for f will be developed under Series B.
630
T H E J O V R A ~ A LO F I X D C S T R I A L A X D E.VGINEERISG
CHEMISTRY
voi.
a, xo
not only higher XTelocities, but also a 2-in. pipe in addition t o the smaller pipes of the previous series.
Friction-velocity curves were constructed from the experimental d a t a b y plotting the pressure drop against t h e relocity. It v a s found t h a t for each S E R I E S B' pipe the pressure drop @ varied with a power of t h e From a supply t a n k of 400 gals. capacity liquids velocity 1,) or, p = a#. were pumped by a Duplex Steam P u m p into an air The value of n vc.as determined by plotting log p dome a n d thence through four pipe lines one of 2-in. against log 1 and determining the average slope of wrought iron, one of I-in. wrought iron. one of 1i2-in. t h e curves of t h e four pipes. The lines were nearly wrought iron, and one of I/2-in. steel pipe. I n each parallel with an average slope of I . 8 j . To determine case t h e liquid passed through a length of straight t h e variation of the pressure drop with the diameter, pipe around a return bend and back t o t h e starting values of log ( p 'ill 85) were plotted against the point, where it flowed into a slightly larger pipe which logarithm of the diameter for oils of the same delivered it through two quick opening valves t o two TABLE 11-PRESSURE DROP:I,BS PER SQ Ix-. PER 100-FT. LENGTHOF tanks set on platform scales. PIPE (SERIESB) A by-pass was used t o shunt part of t h e liquid from SIZE O F PIPE Velocity in feet per second--':*-in. Steel 4 6 8 10 12 14 16 18 the pump directly back t o t h e supply t a n k in order COLDOIL' t o regulate the pressure as desired. The initial presObserved 20.8 49.0 32.5 71.2 98.8 . . . ... Calculated 20.1 51.5 .. 71.8 34.0 71.8 . . . .., sure was taken b y calibrated gauges, t h e drop in Deviation . . -3.3 + 4 . 6 + 5 . 1 +O 8 -2.8 ... WARMOIL' pressure around t h e bend by a difierential manometer Observed 47.7 21.5 33.6 64..1 8 3 . 0 104.2 . . . Calculated 45.7 17.8 30.2 64.8 8 5 . 2 109.0 . . . and t h e back pressure b y a U-tube manometer. As in Deviation 4 1 . 1 f 2 . 6 +4.6 -4.2 -10 HOT OIL: all hydraulic experimentation, this work was subject Observed ,. 1 9 . 3 29.9 43.3 59.9 79.2 101 .O . . , Calculated .. 16.3 27.6 4 1 . 8 5 8 . 4 7 8 . 0 9 9 . 8 . . . t o more or less error. T h e reciprocating pump would Deviation .. . . -7.2 -5.8 - 2 . 5 -1.5 -1.7 ... C O L D WATER: not gire absolutely constant pressure even m-ith t h e Observed .. 13.2 22.2 33.1 46.3 79.2 61 .: 99.8 help of an air dome with I O cu. ft. capacity. The Calculated .. 14.3 24.2 36.6 51.2 73.2 93 , 109.0 Deviation . . 4-8.3 $9.0 +9.5 +10 +I6 4-16 +19 best average values were obtained by throttling the HOT WATER: Observed ,. 3 0 . 5 43.0 1 2 . 0 2 0 . 0 5 8 , 2 i 6 : 5 9 7.3 gauge and t h e readings mere again averaged b y the Calculated . 14.2 51.0 24.1 36.5 7 3 . 0 9 3 . 5 108.0 Deviation ,, +22 7 11 A 1 8 +20 ~ 2 0 +18 4-25 graphical consideration of t h e data, b u t the \ d u e s of Wrought Iron p cannot be relied u p t o better t h a n j per cent. T h e 1-in.COLD OIL: Observed 4.5 1 9 . 0 29.3 41.5 5 5 ~ 0 68.8 10.2 li2-in. wrought iron pipe, aIthough new, m-as very Calculated 5.5 19.8 30.0 41.9 56.0 71.7 1,l.j Deviation 4-22 4-4.2 4-2.4 4-0.9 -11 f 1 . 8 +4.2 rough and gave in all suns about 2 j per cent greater XVARM OIL: friction loss t h a n t h e steel. I n small pipes the condiObserved 17.8 26.7 36.7 4 8 . 0 60.4 . . . 5.1 10.7 Calculated 36.7 49.0 6 2 , 8 . . . 1 7 . 4 26.3 4.8 10.3 tion of t h e surface plays such an important part in Deviation -5.9 0 . 0 -2.2 -1.5 -3.7 L 2 . 1 i-3.8 . . . HOTOIL: the friction loss and t h e roughness varies so greatly Observed 23.7 32.6 4 3 . 2 5 5 . 2 68.0 10.4 16.2 5.8 33.0 44.2 5 6 . 6 7 0 . 2 15.7 23.7 4.4 9.2 with different pipes t h a t me have assumed t h e 11'2-in. Calculated Deviation -2.70 1 . 2 -3.1 0 0 4-2.3 4-2.5 $ 2 . 9 -10 steel pipe as a standard for this size. T h e liquids 2-in. Wrought Iron COLDOIL: used were water and gas oil. The viscosity of t h e Observed 2.64 5.50 9 . 0 8 13.67 ., . . , ~. . . . . Calculated 2.46 5.22 8.85 13.40 ,, ... . .. ... former was obtained f r o m t h e d a t a of Thorpe and Deviation -6.8 -5.1 -2.5 -1.5 . .. . .. . . . %'ARM OIL: Rodger as found in Landolt-Bornstein. The ris1.64 4.29 8.05 12.79 .. . . . . .. . Observed Calculated 2.15 4.56 7.78 11,70 . . . . . . . ~. cosity of the latter was determined as in the previous Deviation 3 1 . 0 i 6 . 3 -3.8 -8.3 .. , .. ... series. T h e temperature and therefore the viscosity H O T OIL: .. . .. Observed 1.41 3.82 6 . 9 0 10.37 14.19 . . . of the oil and water was changed b y means of a steam ... ... 6.92 10.50 14.60 . . . Calculated 1.92 4.09 + 2 . 6 . . . . . . .. . 1-0.3 f 0 . 9 Deviation 26.7 + 7 . 0 coil in t h e supply tank. Series of runs were made with hot and cold water aqd with hot, m u m and cold oil, t h e viscosity being determined in each case from viscosity and again nearly parallel lines were the average temperature of the series. T h e viscosities obtained. T h e average slope of these was - I . 2 2 , jzys are as follows: i. e . , p varies inversely as or P = d l , 2 2 I
Cold oil.. . , , . . , , . . , , . . , Warm oil., , . . , , , . , , . , . . , Hot oil.. , , . , , , , , . , . . , . , Cold water.. , , , , , . . . . . , H o t water., . , , , , . , , . . . . .
TemD. Dvnes/cm2. PoundaldIn.2 24.5O C. 0.169 0.0000789 40.0' C . 0.1045 0.0000488 60.0' C . 0.0596 0.0000278 20,0° C. 0,0100 0.00000466 48.5' C. 0.0056 0.00000261
I t is t o be noted t h a t a wide viscosity range was covered as t h e cold oil was over 30 times as viscous as t h e hot water. Runs were made at velocities u p t o 2 0 f t , per sec. in t h e and I-in. pipes and as high as 1 2 ft. per sec. in t h e a-in pipe. The gauge pressure of each run was kept constant b y the regulation of t h e by-pass Val\-e. The results appear in Table I I . T h e work in this series of runs was carried out b y Messrs. Haylett and Lucey and submitted a s a thesis in partial fulfilment of t h e requirements for the S.B. degree a t the Massachusetts Institute of Technology in 1915, 1
is the equation obtained where j varies with t h e viscosity of t h e liquid. This last relation was determined b y plotting j against t h e viscosity, by which a straight line was obtained for t h e I - and 2-in. pipes and another parallel to it for the l:p-in. steel pipe. The equation of these lines was of t h e form f kw c. T h e slope k 7 ~ 2 sfound t o be I I j and the intercept c, 0 . 0 1 14-for the I - and n-in. pipes (0.0140 for the ' 1 2 in.). Thus, t h e completed equation becomes p = ( 1 1 5 ~ =I
u1.85
0.
o r 14) d,;i2, xl-here
+
+
p is the pressure drop due t o fric-
tion expressed in lbs. per sq. in. per I O O f t . of pipe, p the absolute viscosity in poundals per sq. in,, II the velocil-y in ft. per sec. and d the diameter of the pipe in sq. f t ,
July. 1916
T H E J O C RX A L O F I37 D C S T RI A L A ,V D E AVGIY EE RI N G C H E M I S T R Y
Table I1 contains illustrations of the results of these runs giving the velocity in f t . per sec., t h e observed pressure drop in Ibs. per sq. in. per I O O f t . of pipe, t h e pressure drop calculated b y t h e use of the above formula, and t h e percentage deviation between t h e two. T h e equation ~p = -( I I j/J. ' f 0 . 0 114)V''85 a1.22
m a y be the form of a general law,
for all sizes of pipes, with varying velocities and different degrees of internal roughness. T h e constants, however, doubtless vary, as do all hydraulic constants, and only experimental d a t a can possibly give t h e ones t o use for a n y particular case. However, until further research has been carried o u t in this field, these laws, with t h e derived constants, will serve as a first approximation. F R I C T I O N A L C O E F F I C I E K T S FOR
VISCOUS
LIQUIDS
We have shown t h a t flowing liquids of all viscosities when in sinuous motion follow substantially t h e same equation, differing only in t h e coefficient of t h a t equation: i. e . , t h e flow of a n y liquid in sinuous motion may be expressed as a constant times some function of velocity, length, a n d radius. T h e constant f depends upon t h e viscosity of t h e liquid flowing, b u t t h e function of t h e velocity, length a n d radius is independent of t h e viscosity. I n all ordinary hydraulic calculations it is assumed t h a t this function of velocity, length, and radius is
v21p -,
and t h e fact t h a t the flow gr does not exactly follow this formula is provided for b y t h e use of tables for t h e coefficient f, these tables showing t h e value of f as determined b y radius and velocity, t h e two factors which influence it. Inasmuch as we have shown t h a t t h e flow of viscous liquids has t h e same function of velocity, length and radius as the flow of water, it follows t h a t t h e ratio of t h e cons t a n t t o be employed for t h e flow of viscous liquids t o t h a t of water itself is t h e same as t h e ratio of t h e constant employed in t h e more exact exponential formula which we have derived above. If f w be t h e hydraulic coefficient for t h e flow of water through a pipe and f t h a t of a n y liquid, both t o be employed on t h e assumption t h a t t h e lost head or pressure drop is directly proportional t o t h e length, t o t h e square of the velocity and inversely t o t h e radius, it follows that d f -_-0.0114 _______ 1 1 5 p dfw 0 . 0 1 1 44- I1j(o.00000467)* P = 0.95j 0.045--o.00000467' Or, df = fw(0.955 0.045z), where z is t h e relative viscosity of t h e liquid in question t o water. The best way t o determine z is t o measure the relative time of efflux of t h e liquid and water through t h e same capillary tube. The t u b e should not be constricted a t t h e ends and the use of the Gurney
viscosimeter as outlined above for this purpose is recommended. We believe t h a t t h e use of this formula
f
+
* Viscosity of water a t ordinary temperature
(ZOO
(2,).
= jw(0.9jj
f
0.0452)
is a t present t h e best means of estimating the carrying capacity of a pipe for viscous liquids. From t h e formula it is evident t h a t for liquids of low viscosity t h e capacity is exactly t h e same as t h a t for water, b u t for high viscosities t h e capacity rapidly decreases. We have experimentally confirmed t h e accuracy of this formula by t h e d a t a given above u p t o viscosities of 20-fold t h a t of water. Up t o this point, the correction t e r m for viscosity in the formula above is small, but for very high viscosities, such as are encountered in heavy mineral oils, glycerin, etc., this t e r m becomes very great. We personally doubt t h e validity of this formula for high viscosities, believing t h a t t h e pressure drops will be decidedly less t h a n this formula indicates. On the other hand, t h e use of this formula should be safe, inasmuch as t h e actual carrying capacity of a pipe designed b y its use will exceed t h e calculated rather t h a n otherwise. We have hitherto not been in a position t o confirm the use of this formula for more viscous liquids. C A L C U L A T I O N O F C A R R Y I K G CAPACITY
T o estimate t h e carrying capacity of a pipe line for a n y liquid, proceed as follows: Determine t h e density of t h e liquid a n d its viscosity relative t o water, doing t h e latter either with t h e Gurney viscosimeter or b y measuring t h e time of efflux through a capillary t u b e for which the time of efflux of water or of a n y other liquid of known absolute viscosity has been measured. The relative viscosity times 0.0671' gives t h e absolute viscosity in poundals/ sec./sq. f t . Now employ the two formulae,
+
where j = fw(o.95j 0.045~). Chocse t h a t result which indicates t h e greatest resistance t o flow. A single illustration will make the procedure clear. It is required t o find the velocity of an oil of sp. gr. 0.91 through 600 it. of standard I-in. pipe (inside diameter, 1.07 in.) under a head of 30 ft. The time of efflux of the oil at 20' C. from a pipette which is not constricted at the tip is 108 sec., water flowing from the same pipette in 4.90 sec. p = hp = 30(0.91)(62.3) = 1 7 0 1 lbs./sq. ft. I 08
z=-=
p = 0 . 0 6 7 1 ~= 1.478
22.05
4.90 I .07 ___-
+
+
63 1
(I2)(2)
g =
- 0.0446
32.2
Assume that fw, from hydraulic tables for the pipe in question, is 0.0075. For viscous flow, v
(I
=
701 ) ( 3 2 . 2 1 (0.0446)
=
( 8 ) ( 1 . 4 7 8 )(600)
o.0153 ft./sec.
For sinuous flow, v =
-\i---
(30)(32.2)(o.o*)p = 0.045(22.05)1 (0.0075)
(600) [0.995
+
2,22
ft,Jsec.
T h e flows in viscous motion being b u t a small fraction of t h a t required for sinuous flow, viscous motion 1
The viscosity of water a t 20' C.
632
T H E J O U R T A L O F I X D G S T R I A L A N D ENGIMEERIiVG C H E M I S T R Y
will resulc and t h e low discharge is t h e one which must be expected. H a d the sinuous formula given the lower value of v, the result b y the formula for viscous flow would have been rejected.
T‘ol. 8, NO. 7
since .the earliest ages, if not by name a t least b y its characteristic properties. The first authentic record t h a t we possess of t h e manufacture of this gas was in 1783 when Van Marum: a Dutch scientist, termed it ‘la smell of electricity,” as a result of its production S I Z E O F P I P E F O R VISCOUS L I Q U I D S by this means. Liquids of even moderate viscosity flowing under I t was not, however, until t h e exhaustive studies of lorn heads follow viscous motion unless the pipes be Schoenbein in 1840 t h a t t h e active properties of ozone very large. It is very important t o keep in mind were well understood or a n y analytical methods were the fact t h a t , so long as t h e motion is viscous, doubling the size of t h e pipe increases t h e velocity 4-fold a n d devised for measuring this gas. Schoenbein recognized this active oxidizing agent as a distinct gas t o which the discharge 16-fold for t h e same pressure drop. he gave t h e name of ozone. For t h e same discharge a pipe twice t h e size requires For more than fifty years after Schoenbein’s reonly one-sixteenth t h e pressure drop and therefore but one-sixteenth t h e power. If a pipe is carrying searches nothing was accomplished in placing ozone liquid in viscous motion, increase in size of the pipe within. the scope of a commercial possibility, although its active and oxidizing power was well known. With IS always well worth consideration, owing t o this very great effect on carrying capacity and power consump- t h e development of t h e alternating current generators tion. Decrease in size will ultimately result in con- and transformers, which so materially reduced the cost verting the flow into sinuous motion, after which of production, and t h e increasing knowledge of the bacteriology and chemistry of water, ozone T?”S recogthe effect of size is greatly lessened, being inversely nized as a water purification agent of great value. proportional t o only t h e first power of t h e diameter. Berthelot, a French chemist, in 1890 undertook, with S C XM A R Y some degree of success, t o apply this method of water Liquids flowing through pipes flow either in straight purification, and from then on Europe, as well as line motion in which case they follow Poiseuille’s America, has been practically flooded with numerous 8 ,ulz designs of generators and patented appliances for formula, p = , or in sinuous motion. t h e pressure g1.2 v a t e r treatment. All t h e ozonizers t h a t have been devised are based drop being represented by p = J1pv2. The flow will upon t h e same genera! principle, ziz., t h e production gr follow t h a t formula which requires t h e higher pressure of t h e allotropic form of oxygen, 03,from the oxygen drop, t h e higher radius, or gives t h e lower velocity, of the atmosphere. This is accomplished by passing as the case may be. Both formulae must therefore a current of air over a brush discharge u-hich takes be employed and t h e result chosen according t o t h e place between electrodes connected t o a high volabo77-e rule. T o obtain the coefficient j of the formula’ tage alternating current circuit; these usually ha\-e for sinuous motion: look up, in suitable hydraulic a solid dielectric interposed between them. There tables, t h e value of t h e coefficient for water flowing are, of course, many other ways of generating this in the same size pipe a t t h e same velocity a n d multi- gas, b u t none of these processes other t h a n the one ply this coefficient b y t h e expression (0.95j 0 . oqjz) described has proven a commercia! success. wherein z is the viscosity relative t o water of t h e liquid Numerous theories h a r e been advanced t o account flowing. for t h e production of ozone in this manner b u t t h e one These formulae have been experimentally substan- generally accepted is based on the theory of molecular tiated only for use in pipes u p t o 2 in. in diameter m0tion.l This theory, as stated b y Dr. C. P. Steinand for t h e flow of liquids of viscosity (relative t o metz, regards the chemical effect of all ether radiations water a t zoo) of 20. They are probably safe for use recognized b y light, heat and electrical waTTes as more in larger pipes and a t higher viscosities, b u t more or less specific for various compounds t o definite exact expressions for these conditions must be de- frequencies of their movement setting up resonance termined b y further experimentation. effects upon t h e natural molecular or atomic motion. RESEARCH LABORATORY OF APPLIED CHEMISTRY Pure ozone is colorless, has a distinct and peculiar INSTITUTE OF TECHXOLOGY MASSACHUSETTS odor and instantly decomposes a t 260’ C. I t can be BOSTON liquefied b y a pressure of 1840 lbs. per sq. in. and a t a T H E DESIGN AND OPERATION O F OZONE WATER C. I n this condition it is temperature of -103’ PURIFICATION SYSTEMS highly magnetic b u t is not so powerful an oxidizing By SHEPPARDT. POW ELL^ agent as t h e gas. Received February 7 , 1916 The great affinity of ozone for organic matter renders Although t h e first attempt t o purify water on a it peculiarly suited for water purification, in t h a t it practical scale b y means of ozone was made less t h a n not only removes the bacteria by direct oxidation b u t thirty years ago, still this gas was generated and its will eliminate t o a considerable degree other organic chemical and physical properties have been studied substances ‘contained therein. b y many investigators for more t h a n a century. In A11 ozonation plants for the purification of water all probability ozone has been recognized by scientists ozone generator and consist of two distinct parts-the
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1 Chemist a n d bacteriologist of the Baltimore County Water and Electric Company, 100-102 West Fayette Street, Baltimore, Md.
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Engineering S e w , 65 (1910). 488.
