William Macfarland Patton.

A treatise on civil engineering online

. (page 130 of 145)
Online LibraryWilliam Macfarland PattonA treatise on civil engineering → online text (page 130 of 145)
Font size
QR-code for this ebook


1528 SUPPLEMENT.



Data should be obtained for very slow, medium, and high veloettieft; and to
obtain tbe high velocities it will be necessary to pull tbe skiff with a i-indi
cotton rope, which can extend from the bow of the skiff to the <mpo8ite bank of
the pond ; but if this is done the oarsman should be retained in the atiiff to
stop it from running into the bank and to return it to the starting poation. If
the pond is very wide, a long stake may be driven out in the pond, and it can be
made rigid at its top with small guy-ropes, which can lead diagonally down lo
the bottom of other stakes, which are driven around it, the ropes being tied to
tbe stakes before they are driven, then all attached to the centre sti^e. The
skiff can then start from this stake, and the pulling-rope can lead to the shore.
If the skiff is propelled at all velocities with a rope in this way the rating will
be more accurate, as the motion of tbe oarsman in rowing rocks the skiff and
thus causes the meter to travel through a curved path which is longer than tbe
distance measured with the tapes. Just before each trip is made over the bme
the meter- wheel should be turned till it is about midway between two clicks, so
that the first click will be heard by the observer before all of the short tape is
paid out. The wheel will make 40 revolutions in about 103 feet. A longer
wire can be used to lengthen the tape, so that a measurement for 60 or more
revolutions may be made.

The amount of error in such a rating, supposing the skiff to move at the same
velocity at the instant the first and last clicks are made, depends entirely on the
time intervals used by the observer in starting and stopping his watch, and in
stopping the reels after he hears the click of the meter. In order to eliminate all
error, the time consumed by him to do this must be the same at the beginning as
at the end of tbe trip.

When the data are reduced to revolutions of the meter- wheel per second
and velocity in feet per second, and then plotted on cross-section paper, takiog
the revolutions per second as abscissas, and the velocities in feet per second as
ordinates, the plotted points will lie in a curve. A line can best be drawn
through these points by bending a true steel straight-edge between three heavy
paper-weights till one side of it coincides with the points. It has been the usual
practice to assume that this line should be straight, and expressed by the equation

y =: oo; + 6,

from which it is easy to compute a reductiour table; but when more accurate
ratings are made, so that all the plotted points are in their true positions, it is
found that the elastic curve formed by the bent straight-edge passes precisely
through them all. This curve departs so much from a straight line, it is seen,
that to compute the reduction-table upon the assumption that the line should be
straight is a very inaccurate method. By an inspection of the curve, it will be
seen that for successive higher velocities the revolutions per second increese
faster than the velocities in feet per second. This indicates that the slip of the
wheel or the screw, as in a steamship propeller, becomes less as the velocity
increases ; and we can think of a velocity so great that the water would become
in effect so near a solid there would be no slip, and beyond that point the rating
would be a straight line.

The friction of the bearings of a meter should be so slight that the wheel will
begin to revolve when a very low velocity is attained. For the first pneumatic
meter constructed this velocity was 0.042 foot per second. In order to make a
reduction-t^le from a meter rating, form a three-column table and write in the
first column the times in seconds of 100 revolutions of the meter-wheel, from 20
seconds to 400 seconds, or more if very slow velocities are to be measured. Then
compute the revolutions per second corresponding to those times of 100 revolu-
tions, and 'write them in the third column. Then from the plotted curve scale



Digitized by



Google



RIVEE AND HARBOR SURVEYS. 1629

off the velocity in feet per second corresponding to those revolutions per second,
And write them in the second column. In using the meter, measure the time of
100 revolutions, and look in the table for the corresponding velocity. Such
tables are usually furnished by the manufacturers.

In Engineering News^ March 2, 1893, a current-meter with an electric regis-
tering attachment, was described invented by the author of the above article.
The pneumatic meter above described is a much simpler and cheaper device, and
is recommended as preferable for use in shallow rivers and canals.

The price of tliis meter is only about $50.

THE RrrCHIE-HASKELL DIRECTION CURRENT-METER.

In conducting the hydrographic surveys for harbor and river improvements
it is often desirable to know the direction as well as the velocity of the prevailing
currents in order to calculate their value for good or harm. In tidal streams,
for example, for some time before the turning of the tide, an '* under run" of
the flood-tide is going on while the surface is still ebbing. These subcurrents of
tidal waterways are of extreme importance in their effects upon the sea bottom,
and need to be determined with considerable accuracy both in direction and
velocity. For determining the velocity of currents one of the common methods,
viz., by floats, gauge-tubes, or current-meters, may be used, but the last two
xnethods give nothing concerning the direction of the current. The Ritchie-
Haskell meter is designed to record simultaneously both the direction and velocity
of any character of subsurface currents.

The principal differences of appearance between this and the ordinary form of
current- meter are the propeller-wheel and the fish-shaped body, inside of which
is placed the magnetic needle and other mechanism for actuating the recording
apparatus in the hands of the operator.

The velocity-wheel is of the screw or propeller type, and is made conical in
form to prevent the catching of weeds, grass, and other floating debris.

This wheel may have any desired pitch to suit any kind of work, but thus far
-only two sty las of wheels have been made, the first covering a range of from 0.2
foot to 6 feet per second in velocity, and the second a range of from 0.6 foot to
12 feet per second in velocity. Of course a meter can have both of these wheels
furnished with it, so that either one can be attached as desired. The electric
Tnechanism for transmitting the number of revolutions of the wheel to the veloc-
ity register is, as stated above, placed inside the fish- like body of the meter. In
the velocity register starting the watch closes the circuit, and stopping the watch
i>reak8 the circuit, thus giving an absolute record of the time and the correspond-
ing number of revolutions made in that time.

The apparatus for determining the direction of the current and actuating the
direction register is also placed in the fish-like body of the instrnment. This
apparatus consists primarily of a compass, whose needle is free to assume the
magnetic meridian at all times, immersed in an oil-chamber to prevent rust. An
expansion-bag compensates for changes in temperature, and establishes equality
of pressure between the inside and outside of the chamber when submergeii. By
the use of an electric current the angle, to the nearest degree, between the direc-
tion of the current and the compass needle is shown on a dial. This dial is
graduated in azimuth from south to west, and also has the points of the compass
given. The total length of the meter, which has a low-pitch wheel 1\ inches in
diameter, is 36 inches, and its weight is 30 pounds, exclusive, of course, of the
lead weight, which can be adjusted to weigh 20 pounds, 35 pounds, or 50 pounds,
as desir^. The cable for suspending the meter is of galvanized Bessemer steel,
-i\ inch in diameter, with a core formed by three insulated wires — three circuits



Digitized by



Google



1530



SUPPLBKEKT.



mn
































It^








i 1 1 1 1 1 1 1

DRAINAOC CURVCS.
Od» q - MI«B«ir«liypJo». «|-

JloOoab q - 8J9W6(«I»kA)^

MelUtk q - .TBztJSCUsllOi:)''

O'Oowien Q . -tf.7W + 0n97Jlx 4S7JtsllOA)» .

FkudBf Q . tNA.'<

▲ w KnmbMrofigiMramaMdralMi.

L - U»g1h»» " »• "
N - OoulMt-lJt

1 1 1 1 1 1 1 1 1 >














i


^




ooo














/






«000












/








9O0O










>


V








B0OO
5100
OOO
6000
ttOO








^


7^














J


7^








y






A


y








y


;?^




J


7








y


^








y/


r






/


^/


r






4000
























;;^


/






J


^/


/








mo






















/^


/






J


^


f






























^






J


//


/












«00


















J




/






/y


/






























//








/


/






























«


A


V






/


/
































/


^


i






/




















«00
















^






































/J


V




■ N




































/


y


/


y









,




















-










/


/




/


/
































/


h


f




/




























900
1000


.








/


/


























____^


X












u


A





























^




1 1800








T





/-












c^-^.


^


^


"^














a iJ/Mi




J




A


/










^


^


5^




^


^


















Jt




Y








^


^




^^


\^


^
















j^iaoo




T'j_




r




^








,^


JJJ






















i:




U




y


y






^


X




























(/


/






^


x^'






























I"




Y




^


X






































y


-p'






































-













































▲ores. 900 loooisooaoooasooaoooaoootfoo ttoosooo 5900600069001000 Tmsooowonooiro

itJOiM.&m LW MM &ui nm 4M i^Mi UK rxn 7JB UN u» xoomanyiumnflouwauMiuoB

Fio. 456.



.GooqIc



WATER REACHING STREAMS AND SEWERS. 1531



being required for both recording registers — from the meter to the recordings
apparatus. The total cost of the apparatus, including both velocity and direc-
tion registers, is $280. Extra wheels cost $25 each. The meter, without the
direction-recording apparatus, can also be secured in various sizes and styles.

In an instrument especially designed for gauging brooks, creeks, and irriga-
tion ditches the suspending cable is replaced by a graduated hand rod, and a foot-
plate is provided to prevent the wheel from sinking into the mud of the bottom.
This instrument cost $180, is 14 inches long, with a 4-inch-diameter wheel, and
weighs 7 pounds. It will register velocities varying from 0.4 foot to 5 feet, and
from 1 foot to 10 feet per second, with the low and high pitch wheels respectively.

These meters are now used by many of the United States engineers in their
hydrographic work, and have also been adopted by a number of large irrigation
companies.

In the Gk>vemment work Mr. Haskell has used the direction current-meter in
measuring the currents in New York Harbor, Long Island Sound, the Gulf
Stream, and the Gulf of Mexico since 1887, and states that he believes it to be
reliable under all conditions.

CURVES SHOWING AMOUNT OF WATER REACHING STREAMS AND SEWERS.

The amount of water reaching streams and sewers will, for simplicity, be
called the ** Run-off."

The author is indebted to Col. W. E. Cutshaw, City Engineer of Richmond,
Va., for the following remarks on the run-off from the ground surface, and also-
for the accompanying diagrams.

In Fig. 456 will be found the Drainage Curves, embracing a wide range of
drainage surfaces in acres and square miles, together with the more common
formuke in use. This diagram shows the cubic feet of water per second reach-
ing the watercourses.

Diagrams Figs. 457, 458, 459, 460 are intended to represent curves showing the
number of cubic feet of water per second per acre reaching sewers from rainfalls-
of 1, 2, 8, and 4 inches per hour, together with the formulsB in more oommoa
tise. ' These various diagrams fully explain themselves, and the formulse will be-
readily understood.

Col. Cutshaw writes that these diagrams show what may be done about drain-
age and sewerage in the way of finding what allowances should be made for storm
discharges.

The practice now is to determine by one formula the amount of storm-water to
provide for, and then to calculate the sewer or channel to discharge it by another
formula. Though most cities use this method, some have used a single combined
empirical formula for determining the diameter or sizes of sewers.

The mn-off depends on such conditions that the variations of formulsd aswelli
as the ditBculties of applying them to small city areas and to large country area*
alike make the applications unsatisfactory. The same imperviousness of surface
and the same degree of saturation will not obtain for like areas; and the surface
slope varies to such an extent with the rolling features of the country that the
constants introduced into all these formulsB are difficult to settle upon, even after
comparisons ?rith extended observations of rainfalls and channel discharges.

Formula now applying approximately well for city areas do not apply to
country areas, where the storm discharges are carried off by creeks and rivers.
The curves on the diagrams should be particularly noticed in this respect.

The best formulae now tised seem to be based on variable areas, variable
slopes, and variable rainfalls, the powers, roots, and constants used in each giving
it its special merit.



Digitized by



Google



153-,»



SUPPLEMENT.




CURVES
•irowiNQ KMoirNT or wkrtn

RCACriTNQ tCWCR PROM



Bttrkll-Zlegler -«=>»cr(^y;

Adamg ^='<»5r(^)^;

Hawksley ... C = aW6r(^)*.

McMath Q = «.488r(|)^

^ = cu. ft. water per second per acre retcb-
log sewer;

8 = sine of surface slope;

r 3= rainfall in inches per hour;

A = number of acres drained;

c = constant varying from 0.85 to 0.60 ac-
cording to the nature of the ground:
here taken = 0.60.



Curves for 1/100 surface slope .
'* 2/100 '• *^

" 8/100 " " .



Shown thus



Digitized by



Google



WATER REACHING STREAMS AND SEWERS. 153$

Automatic rainfall records for short periods of heavy rainfalls and the sewer
gaugings of run-oflP corresponding are now being observed more closely in the
cities where combined sewers are used, and these observations are beginning ta



I
I

2

I

I

6



Fig. 458.



settle which formula best applies to each city. Go\. Outshaw's purpose in prepar-
ing these diagrams was, by comparisons of curves of run-off, to determine which
is best to use in Richmond. Even with the four best formulae for run-off, three
of them,— Hawksley's, McMath's, and Bttrkli-Ziegler's, — it will be noticed, give
curves for small areas (under five acres) showing more run-off than rainfall; and



Digitized by



Google



1534



SUPPLEMENT.



Pfr 459.



.GooqIc



WATER REACHING STREAMS AND SEWERS.



1535



yet BUrkli-Ziegler's and McMath's are more generally used, because of a better
4igreement with observed run-off from areas, say, above 60 or 60 acres. None of



^00
1.90
1.90
1.8S
1.80
1.75
1.70
l.tt
1.60



X



|1JIS

^1.45
I 1.40
^1.85
|lJ0r

a>ij»

I 1.15
J 1.10
^1U)6
^1.00

|.«

S .90
S .85

.80
.75
.70
.65
.60
.55

.45



\ 1



A



^



\\



>;\



CURVES

•MOWING AMOUNT OP WATCH

RCACHINQ SCWCR

PROM

POUR INCHES RAINPAtL.



^,



\



^



ts.



m.



Y



V



^



>s



%.



^ift



9r



hf)



M.



■^



^^1



^



^?^






:^



-m



'"^^



^



iJSL



^k^



'^*^ —



ley_



::2:^m^ti^^



- ^jfiku



2'm



• l^



J^-i



-^Wl



^^n



^.tler



100



500



700 900



1100 1300 1500
Acres

Pig. 460.



1700



2100



3300 2500



these formulae, and still worse, none of the various flood -discharge formulae, are
satisfactory in very large country areas, as will be seen from the attempt to ap-



Digitized by



Google



1536 SUPPLEMENT.



ply them to Stony Brook, near Boston: there they were found to give from about
540 cubic feet per second in the lowest to 5600 cubic feet per second in the
highest, and this discrepancy on an area of about 8000 acres. The Board of
Engineers, investigating the drainage of the stream, discarded all the formols,
and assumed, from a very unusual set of observations extended over a very large
area, that 12 inches in 24 hours, or i inch per hour, was the rainfall over this
area, and that three fourths of it ran off; in other words, that 3000 cubic feet per
second should be provided for. A similar result was worked out for Rock Cred[
at Washington City, where some 49,000 to 50,000 acres were involved; and using
some five or six flood-discharge formul»» the cubic feet per second, as calculated
varied from 4707 to 25,640, and was finally taken at between 18,000 and 25,000,
cubic feet per second, practically assuming i-inch rainfall per hoar, on the whole
area of 49,863 acres. It is to be noticed that McMath has his formuhse modified
so as to apply to city areas for sewers and to country areas for streams.

Eutter's formula for mean velocity from which to determine the sizes of
sewers or channels seems to be about the best, and is almost exclusively used.

An interminable amount of detail and discussion is involved in this subject
and it is difficult if not impossible to put it in a concise and perfectly digested
form for a general work on Engineering, and the reader must be referred to
such works as Fanning's Water-supply Engineering, Latham^s Sanitary En-
gineering, Staley and Pierson's Separate Sewers, Flynn's Irrigation Canals, etc.,
Stephenson^s Canals and Rivers, etc., for full discussions under their appropriate
titles.

APPUCATION OF KUTTER'S FORMULA TO THE FLOW OF WATER IN OPEN CHAXXELS.

The author has not considered it necessary to introduce in this volume ei-
tended tables of the coefficient of discharge c, or of the square roots of the
hydraulic radius r, or of the square roots of the slope i, to be used in the solution
of problems of flow by Kutter's formula. Such tables are of great value to m
engineer when working a number of problems, and can be found in such works
as Flynn on Irrigation Canals and Works, also Wilson on the same, and to i
limited extent in Merriman's Hydraulics and Trautwine's Engineer's Pocket-
Book.

Th is article will be limited to the working out a few examples in full. Ftob
a clear understanding of these the reader will have little trouble in working oet
similar problems under other conditions as to roughness of bed and side surfaces,
slope of bed, and hydraulic radius. In order to obtain very accurate results, all
terms should be carried out to five or six places of decimals ; for less important
problems two places of decimals are sufficient. In Article IX is found a genenj
discussion of the flow of water in open channels, and the formulsB of D'Arcy and
Kutter are given, with the values of the coefficient of roughness n and a taWe
containing a few of the coefficients of discharge. As will be noticed, D'Arcy'^
formula, eq. (40), depends upon and varies with the hydraulic radius rand slope/,
while Kutter's depends upon and varies not only with r and t, but also with tie
condition of surface of the channel as represented in the coefficient n. There are
a large number of formulae in use, all of which have constant coefficients, except
the four following, Kutter, Baziu, Molesworth, and Gauchler. Only the first two
will be considered in this place. D*Arcy^8 formula will be referred to under the
head of the flow of water in pipes.



Digitized by



Google



FLOW OF WATER IK OPEN CHANNELS. 1537



BAZIN'S FOBMULiE.



For very even surfaces, such as planed planks, smoothly plastered sides and
beds, and other surfaces in the same or similar condition,



V ;



= yi -+-0.0000045[l0.16 + -) X Vrf.
For surfaces of cut stone, brickwork, ordinary mortar, sawn plank, etc.,

V = yi + 0.000018[4.854 + M x |/ri.
For rubble masonry and similar surfaces,



r = |/l + 0.00006^1.219 + t) X V''*-
For uneven surfaces, such as earth,

V = |/l -+- 0.00086^0.2438 + M ^ '♦^^•

In these formulsB it is to be noted that the coefficients of 4/ri depend upon
and vary with the character of the surface over which the water flows and also
upon the hydraulic radius r, but are independent of the inclination or slope of
the bed of the channel.

Mr. Flynn says that Bazin's formula for given channels agrees very nearly
with Kutter, n = 0.0275 up to 8 feet in depth, and with Kutter, n = 0.025 from 8
to 5 feet in depth. It is also shown that Bazin's formula is almost a mean be-
tween Kutter with n = 0.025 and 7* = 0.0275; that is, that it almost suits canals
and rivers in earth 0/ tolerably uniform cross-section, slope and direction, m
moderately good average order and regimen and free from stones and weeds,.
and also canals and rivers in earth below the avei-age in order and regimen.
The results again show that it gives too low a velocity for canals in earth above
the average in order and regimen with n = 0.0225 or a smaller value of n, whil&
it gives a too high velocity for canals and rivers in earth, in rather bad order
and regimen, luiving stones and weeds occasionally^ and obstructed by ditritns,
for which n = 0.(^. With these remarks no further notice will be taken of
Bazin's formulae, as the practical application of them can be readily made after
understanding the examples worked out with Kutter's formula :

The following is Kutter's formula :



t> =



l:8il^4i.e + ?:????l



1 +



(„...2-S).^



X ^ri = c Vri ;



in which, as in other formulae, n is the coefficient of roughness of the surface of
the channel, and, as given in Art. IX, varies from 0.009 to 0.05, the smaller values^
from 0.009 to 0.02 applying to the smoother surfaces and from 0.0225 to 0.05 ap-
plying to the rougher surfaces, as more specifically described in Art. IX. The
coefficient e, seemingly complex, depends upon the roughness of the surface a&



Digitized by



Google



1538



SUPPLEMENT.



represented by w, the hydraulic radius r, and the slope of the bed i. Witli the
smoothest pipe it would be hardly advisable to use a value of n less than 0.013
in order to provide for increase of resistance from use ; and it will rarely be
justifiable to use a value greater than n = 0.03. It will serve the present pur-
poses to determine the vidues of c for values of n between the limits of 0.017 aDd
0.026. The slopes will be taken at 1 in 1000, 1 in 10,000, and 1 in 30,000. Tbe
hydraulic radius will depend upon the area of the cross-section and the surface
wetted by the water, or wetted perimeter, as it is called.

Example 1.— Given the bed width, depth, and grade of a chapnel, to find tlj€
velocity and discharge. We will assume that the nature of the surface falls
under the one or the other of the following conditions: Rubble in cemetit; coam
rubble of all hinds; also coarse gravel carefully laid and rammed, or rmg^
rubble where the interstices have become filled with silt, (See Art. IX, par. 75, f®

area
which n = 0.02.) Since r = netted perimeter ' ^® ^^" assume the width of the

channel = 125 feet, and its depth 12.5 feet, with side slopes 1 to 1. (Here itmaj
be noted that when the bed width is over from 60 to 70 feet the side slopes haw
very little effect on the velocity.) The urea will be (125 + 12.5) x 12.5 = 1718.75
aqu are feet; the wetted perimeter will bet]&5 + 2 x 12.5 x sec 45*, or 125 +

2 -/i2^« + 1275' == 125 + 85.4 = 160.4; then. the hydraulic radius =f =

1718 75

-j^5^-= 10.71 and the Vr = 3.27. The slope i will be taken 1 in 10,000 =

0.0001, 4/i =r — = 0.01. We have now the values of n = ©02; ^^7= a37;
Vi = 0.01. Substituting these values in the coeflacient in Kutter's formnb,



there results



\



« = ^ri = -



1.811 . .- ^ . 0.00281
0.02 "^ ^^'^ **■ 0.0001



1 +



/,, o 0.00281\ 0.02

[^''' ■" oTo-ooi) ^ 07



\



X Vri.



Reducing,



1.811 ,, ^ 0.00281
+ 41.6 +



=



0.02



0.0001



fA< o 0.00281\ 0.02 "" 1.

^ + r-«+ o:ooorj^8:27



1 60.25
4258



= 112.43.



Then



Online LibraryWilliam Macfarland PattonA treatise on civil engineering → online text (page 130 of 145)