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6/01 c/CIRC/DateDue.p65-p. 15

 

 
 

 

 

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i UPON... -
THE CALIBRATION OF 4 MEASCRIMG TAM:
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~~-o9--- A THESIS UPON ~--o---

THE CALIBRATION OF A MEASURING TANK.

The measuring of large quantities of water without

wcolghing is a matter that has for some time been under dis-

cussicn. Various methods have been employed by different

persons and for various purposes. ‘The weir hae given good

results where great accuracy was not required. Some methods
of measuring by discharge through orifices have been em
ployed with varying success.

The ex-ecrimcrnts upon ywnich this thesis is based were
of the last type, 2nd were carried on ror the purpose of
determining the amount of water that vould flow through
each of ten different sized orifices under any head be-
tween 1 foot and 5 1/2 fecte

A general view of the apparatus employed is given on

the first page. ‘The tank there represented is of boiler

iron; sides 1/4 inch in thickness, bottom 3/8 inch. It is

6 fect high by 4 feet in diameter, and has screwed into the
bottom, ten nozzles like that represented in Plate I. fhe
holes in the nozzles are parallel, as nearly as may be, and

are of the following diameters:

3/4", 7/e", 1", 1 1/8", 1 9/64", 1 31/64", 1 5/8", 1 3/4
THES!S
\24
(o 30

THHS
(2)

and 1 7/8". On the side of the tank is a glass guage

run-ins, the whole height of the tank by means of which the

head of water in thc tank may be read. The wholcs thing is

elevated upon a platform sufficiently high to allow a pair
of seales and a small tank to be placed underneath it.

During the experimenting the holes in the bottom were stop-
ped with wooden plugs which could be dravn out from beneath

the platform. The water ror conducting the experimcnt was

conveyed to the tznk from a fire hydrant through several

lengths of fire hose. A vaive was placed in the end of the
EB

hose by means of which the water flowin~ into the tank

could =e regulatcd to any desircd amount up to the capacity

of the hose (2 1/2 in. ) under about 30 pounds pressure. An
iron pipe l 1/4 inenes in caciametcr also brought water to
surfi-

the tenk under the s_me pressure, but this was foun:

cient only rer exverime:.ting with tne smallor holes and

at the lower heads. The method ci conducting the ex-

perimcnts was somcinat as follows: Water was run into the

tank until tne glass guage showed some desired head. the

103918

 
(3)

plug was then drarm from the hole to be tested and the

water allowed to flow off through a piece of tin pipe toa
drain. The water flowing into the tark was then regulated

so as to Keep the required head constant, that is having

arrived at the desired head the same amoun: of water was

allowed to flow into as flowed out of the tank. When this

had been resulatcd so tnat the level of the water was con-
stant at the nead desired the seceles below were balanced
uy with this small tank uron them, and 600 of extra weight

put uron the seale beam. A stov-watehn in hend the stream

of water from the large tenk was turned into the small

tank and at the same instant the waten set in motion. ‘The

watch was stopred just at the time when the water in the
sm ll tank balanced the 600% of extra weight on the scale
beam. ‘The time registered by the wateh would then be the
time required for GOO of water to flow through the orifice
at the nead at which it wa: tested.

In this way eacn orifice was carefully tested at four

adiffcrent heads. The direct results of these experiments
are given in Table I. - to get the results into more con-
venient form for comparison the amount of flow of water

per second was computed and arranged to make Table II. -

To further assist in comparisons and deductions the theo—
(4)

retical discharge was calculated from V — \2 GH ( in which
V is the velocity of flow in fect per second, Gis the ac-
celeration of gravity in feet per second, and H is the head

in feet, ) and the ratio of the actual discharge to the

theoretical discharge obtained. These results were compiled
in Table Iil.

Hoy; to apeiy these results so as to rind the amount of

flow through a hole for any nead between those ror which it

is tested, we employ a sraphical metnod. We refer the four

results cbtained from eacn oririce to a system of coordi-

of waver is the ordinate, ana the

nates in wnich tne head
amount of water Slowing through tne orifice is the abcissa

It is evident that the rcsulting curve wiil thcoretically

2
be a@ parovala from V” =~2GH, sinee the amount of water
=_—aw 3

‘
—_-

Flowing through the orifice is proportional to the velocity

or the stream. The actual curve approaches somerhat closely

to the parabola. ‘The graphical represcntation of flow for

all the holes are shovn in Plate III. The only curve there

represented th:t docs not pass turough the points Cound py

actual experiments is tne one for the 7/8 * hole. frhis

curve is dravm in red irk and the points as found by exper- $

_—-
(5)

iments are marked by a small circle of red ink surrounding

them.

-t deductions may be made from an exami-

nation and ccmparison or the tables and plotted curves. In

t

the first tliace we observe that cxcept in one or two cases

the results show a very feir degree of univormity: which

>cem to indicatc a corr.:sponding accuracy in the ex-

)

wotid s

perimentation and in the results ovtained. The orifice

showing the most marked variations is the 7/8 inch one

previously mcontioned.

A littic later we Will notice some of the things that

gscem to enter in to effcet thc results obtained. Perhaps’

one cf the first things we vould notice from the study of

the tebles is tne ract that most of the crifices give a
nearly constant ratio ror the theoretical and actual dis-

charge. ‘the same thing is seen in the near approach of the

curve to the parabola. There incy at rirst tnought be some

question abcut the curve being a paravola even with the

ratio of actual discharge to theoretical discharge constant,

unless tne ratio be unity. Let us see, ve may represent
(6)

the theoretical flow by V—- 2GH, or Ve=YV2GH. Ssup-
pose such conditions entcring into thet V', the actual flow
—Kv. then x v—12 K2 G Hor vi-V2 K- GH or v'2 —2 KZ
GH , which is still the equation of a parabola.In the most
uniform results however this ratio is highest at the lowest
head, and decreased slightly as the nead increases, so that
the actuel eurve is not actually a parawoola, but approaches
a direction parallel to the axis @ little faster than the
parapola viould do.

Another fact tnat the tables scem to indicate is thet
the small hoies sive ae greater ratio of actual to thceoreti-
cal discharge tnan tne liarger holes do. This is just con-
trary to wnat miisht be exvected. it would scem as though
the smailer orifice would present more friction in propor=
tion to the area of cross-section, and would thus cut dow

the actual flow in greater vrovortion. But this idea is
&

-

not carried out by the results from experiments, and I am

convinced that at least for these yarticular orifices and

with the condition under which the tests were made the re-

sults obtained are practically correct.
(7)

With reference to the conditicns that might cnter into
and altcr the results obtained the two following seem to me
to be the most potent. First the amount by which the axis
of the ocrifice inclincs from the vertical, and second the
amount by which the axis of the orifice inelines froma
prependicular to the bottom of the tack. ‘The most uniform
results wiil be obtained with tne axis or the orifice ver-
ticle cnd also perrendicuiar to tie bottom of the tank.

Yhen in actual use tne tank is to set in some perma-
nent position where the water whien flows through it can
run directly into a drain. The holes are to ve stop ed by
plugs like that represented in Plate II. to each plug will
be attacned a chain and ring which can oe reacned from the
top of the tank. If we desirc to measure the rate of flow
of water rrom any scurce we may convey the water to the
tank, drayv out one or the zlugs and let the water run until
it maintains a constant head. Note this head and by the
use of.the curve plotted for the orifice the amount of water
flowing through the tank per second may be determined.

Again, suppose we have < large quantity of water to

measuree Let it be conducted to the tank in some way so
(8)

that the rate at which it flows into the tank can be regu-
lated by 2 valve or some other means. Fiii the tank to
any desired head from some other source. Nov draw one
of the plugs and at the samc time open end regulate the
valve allowing the water which it is desired to measure
to flow into the tank sufficiently fast to maintain the
head constant. Take tne time rcquircd to run ali of the
water into the tank, multiply this time expressed in seconds
by the rate of flow of the orifice employed at the head used
and the result gives tne amount ov water.

Of course this last method is more or less inaccurate
in starting and stoprving, and snould oniy ve employed for
large quintities of water, and wnerce great accuracy is not
required. By usin. considercesvle care, however, very zood
results may ve obtained, and for the purpose of getting
rates of flow I belicve it wiil give even more accurate

results then are ordinarly ontaincd by weighing, and with

much less trouble and inconvenience.
%

(9)

HEAD.

1.4 feet

2.8

448

54

1.4

504

1.4

228

4.2

‘

if

i?

v

Minutes.

4

37

25

50

29

55

O09

55

49

16

29

45

17

58

54

06

51

27

60

48

TIME REQUIRED TO RUN 600¥¢

Secords.

1/2

3/4

1/2

1/2
1/2
3/4
1/2

1/4
3/4
1/4
1/2
3/4

1/4

 
(10)

~> TABLE 1. :-
DIAMETER OF HOLE HEAD. TIME REQUIRED TO RUN 600#

Minites. seconds.
17/8 Inch 5.4 fect. 0 42 3/4
I 31/64 " 1.4 2 12 1/4
1 31/64 * 2.8 " I 35 1/4
I 31/64 " 4.2 1 I 15 1/4
I 31/64 * 5.4 I o7 1/4
Tifa I.4 # 3 48 1/2
Ti/fe 8 2.8 ” 2 43 1/4
Ii/e 8 4.2" 2 14 1/2
Ii/fa 5.0 " 2 02 8/4
7/8 * 1.4 " 6 00 1/4
7/8 * 2.8 * 3 18 1/2
7/8 ® 4.2 " 3 32 1/2

7/8 * 5.0 ” 2 31
Is5/a * 1.4 * I 50 1/4

I 5/8 " 2.8 ” I 19
15/8 " 4.2 * I 05 1/4

15/e * 5.0 # 0 60
DIAMETER OF HOLE.

1 23/64 Inch

I 23/64
I 23/64

I 23/64

(11)

ZABLE Le :-

HEAD.

1.4 Feet.

2-8 0

Minutes.

2

I

TIME REQUIRED TO RUN 600 #

seconds.
35 1/2
51
31 3/4

24 1/2
DIAMETER OF HOLE.

I

I

Inch.

3/4 8

3/4"

9/64"
9/64"
9/64"
9/64"
7/8 *
7/8"

7/8"

(12)
ZABLE Ii.
HEAD.

1.4 FORT.

2.8 "
4.2 "
5e4 "
1.4 "
2.7 u
4.35 "
5-35 "
4
2-8 "
4.2 "
5e4 "
1.4 "
£8 "
4.2 "
54 "
1.4 "
2.8 "
4.2 o

POUNDS RUN PER SECOND.

2-116

£29287

6.400

8.6335

10.909

12.121

I.594

20nd

22684

52046

2-749

5877

4.752

5.581

6.858

10.000

12.4355
DIAMETER OF HOLE.

I

IT

I

7/8
31/64
31/64
31/64
31/64
1/8
1/8
1/8
1/8
7/8
7/8

7/8

7/8
5/8
5/8
5/8 |
5/8
23/64
23 /64
23/64

23/64

Inch.

tf

(15)

SABLE Il. :-
HEAD. POUNDS
5.4 feet.
1.4 *
2.8 "
4.2 "
5-4 4
1.4 "
28 "
4.2 u
5.0 "
1.4 "
2.8 %
462 "
5.0 "
I.4 "
2.8 "
462 "
5.0 =”
1.4 "
2-8 "
4.2 "
5.0 "

RUN PER SECOND.

13.956

4.2556

6.454

7.973

8.922

2-626

3.676

4.461

4.888

1.665

2 6.022

£2825

5.074

5.858

5.405

6.540

7.100
9/64
9/65
9/64
9/64
7/8
7/8
7/8
7/8

DIAMETER.OF HOLE.

Inch.

iW

"

tt

(14)

TABLE Jil. :-

Head.

164 feet.

28

462

54

1.4

—~=5.4

1.4

2.8

1.4

£8

4.2

5e4

u

wv

it

w

tf

RATIO OF ACTUAL DISCHARGE

TO THEORETICAL DISCHARGE.

2elT

22935

10.91

+ 3.19

efe
e
e
j
Cc

Ie
ON
e
Oo
Oo

I.
bh
®

t
©

ole
~]
e

to
Lon)

©
e

tO
qa

u

tt

tt

il

i

u

648

063

0832

o631

878

~654

0654

0504

0624

0654

627
(15)

| -~: ABLE III. :~

|

| DIAMETER OF HOLE. HEAD. RATIO OF ACTUAL DISCHARGE
TO T)EORETICAL DISCHARGE.
I 31/64 Inch 1.4 FEET. 4.544 7.1 = .639
I 31/64 * 2.8 " 6.45 + 10.04 " .64
I 51/64 " 4.2 " 7.97 412.3 " .645
I 31/64 * 5.4 8.928 + 15.94 " .64
I 1/8 " 1.4 " 2.63 + 4.07 " .646
I 1/8 , 2.8 * 3,68 + 5.76 " .639
I 1/8 " 4.2 " 4.46 + 7.05 " .633
I 1/8 i 5.0 " 4.89 + 7.69" .636
7/8 " 1.4 ” 1.67 + 2.46 " .679
7/8 " 2.8 " 3.08 + 5.48 " .868
7/8 : 4.2 " 2.82 + 4.26 " .662
7/8 " 5.0” 3.97 + 4.65 " .854
1 5/8 " 1.4 * 5.44 + 8.5 " .64
1 5/8 " 2.8 " 7.6 4+ 12.02 " .632
I 5/8 " 4.2 " 9.2 £14.72 " .625
1 5/8 " 5.0 10.00 + 16.06 " .623
1 23/64 * 1.4 * 3.86 + 5.95 " .649
L 23/64 * 2.8 * 5.41 + 8.41 " .643
123/64 * 4.2 * 6.54 + 10.3% " .634
I 23/64 * 5.0 * 7.1 + 11.25 " .631

' si
  

 

 

 

 

 

 

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NOZZLE gow ORIFICES.

& Vorrves Kov ne Di(Kervent Nozzles
Acc ordi Xo Vive Orifice Desvred.

Ful\ Scole.
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