II
ILLINOI
S
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
PRODUCTION NOTE
University of Illinois at
Urbana-Champaign Library
Large-scale Digitization Project, 2007.
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THE EFFECT OF MOUTHPIEES ON
THE FLOW OF WATER THROUGH
A SUYBMERGED SHORI' PIPE
BY
FRED t. 2SEELY
'::.^ls ~ .^:^ -·. ·:;'? ^ ^ '-*yEW I^ ,^ '*.^<% 1' '
·,**-- *. ;i ^r-Je;J/ ^ ~ a ~ f ^*--^-*"',„ ^ ? ."-,';: <
'A, AT O 0f> -f. t0 -T l0 - -s
- 0;
*^ OO CD OO; OiO i O i
^ 0 10 10 0c 0- 0 - -^ -
10 dl 0 S - t f
4 0 dl . . - .) - .0
0 0 0 10 A4 01 .4 -4 rf> 0
w t o 0 1 0 . w
-C -, - 7,; -, w 7 w Z to Z 57 7 " 7
J 0 0i 0 1101,060
- - - - - - - - -
Entrance
Degrees
Discharge
Degrees
go-
Coefficient of Discharge
from Experiment
Based on Area of Pipe
Same as Col. 3 Except
Based on Outer Area
of Mouthpiece
Contraction
Suppressed
Contraction
not
Suppressed
@?1
o a.
Sml
(s 0 *1
s °
15 ..'
10
0
Coefficient of Loss Based on
Velocity Head in Pipe
"Equivalent Head" or Head
on Straight Pipe to Give
Same Discharge
Ha= (e 2
That Part of Equivalent
Head Due to Discharge
Mouthpiece
H'D = HE
HE
Increase in Equivalent Head
for Discharge Mouthpiece
Due to Entrance Mouth-
piece
H'D -HD
Coefficient of Discharge Cal-
culated from Data for
Mouthpieces When Tested
Separately
c'=.785X-4 HEXHD
Coefficient of Loss Based on
c' but on Velocity Head
in Pipe
I (aQQ)l
DO
--
ILLINOIS ENGINEERING EXPERIMENT STATION
cases, the coefficient of discharge decreases more or less rapidly as
the velocity decreases from 1 or 2 ft. per sec.
Tables 5, 6, and 7 give the values of the coefficients of discharge
and the corresponding values of the coefficients of loss for the short
pipe with the various mouthpieces for velocities of from 2 to 5 ft.
per see. as taken from the curves in Figs. 6, 7, 8, and 9, together
with certain other data used in the discussion which follows. Figs.
12 and 14 show the influence upon the action of discharge mouth-
pieces of attaching an entrance mouthpiece to the short pipe. The
entrance mouthpiece suppresses the contraction at entrance to the
pipe and allows the discharge mouthpiece to receive the water in a
smoother state of flow than when the entrance end of the pipe is
simply inward projecting. The influence of smooth flow is shown in
Figs. 12 and 14 which are obtained by plotting the gain in rate of
discharge and gain in velocity head recovered (expressed in per cent)
as ordinates and the angle of discharge mouthpieces as abscissas.
8. Inward-Projecting and Flush Entrance.-The values of the
coefficients of discharge for the short pipe with inward-projecting
entrance (no mouthpiece attached) were determined with special
care since the effect of attaching a mouthpiece could not otherwise
be found. It will be noted from Fig. 6 and Tables 5 and 6 that the
value of the coefficient of discharge and the coefficient of loss are
respectively c = 0.785 and m = 0.62 while the values generally given
in texts for an inward-projecting pipe are c = 0.72 and m = 0.93.
That is, the head lost at the entrance to an inward projecting pipe is
v2 V2
0.62 of the velocity head in the pipe (0.62 -) instead of 0.93
2g 2g
It would hardly be expected that all inward-projecting pipes would
give the same coefficient of discharge, for such factors as the condi-
tion of the edge at entrance to the pipe, the diameter of the pipe or
perhaps the ratio of the thickness of the pipe to the diameter, the
degree of wetness of the material (effect of oil, etc.), the temperature
and velocity of the water, the form and size of tank together with the
location and form of piezometer orifice, and the conditions of dis-
charge (submerged or into air) might easily influence the flow.
In order to get further data on this form of entrance another
short pipe, 3.11 in. in diameter by 12 in. long, was tested in the same
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 31
MEAN VELOCITY IN PIPE-- FT. PER SEC.
FIG. 6. RELATION BETWEEN COEFFICIENT OF DISCHARGE FOR THE SHORT PIPE
WITH MOUTHPIECES AND THE MEAN VELOCITY IN PIPE
32 ILLINOIS ENGINEERING EXPERIMENT STATION
.9 0
0 U =
45 (1 TO 3) E TRANCE
.9
S0 20 1 TO 4) EN FRANCE
100 15 l TO 3) EN3RANCE
Id
I
O
0
1-
0
IL
O
z
U
MEAN VELOCITY IN PIPE--FT. PER SEC.
FIG. 7. RELATION BETWEEN COEFFICIENT OF DISCHARGE FOR THE SHORT PIPE
WITH MOUTHPIECES AND THE MEAN VELOCITY IN PIPE (CONTINUED)
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 33
1.05 - - -
1.00 -5-(1 O 2) DISh --- --- --- -- CHARGE-- D 0--
5°(1 TO 2) DISCHARGE ) O
U V I O
SO
0 -
S K °-- o 10°( TO 2) DISCHARGE
C e 15'°(1 TO 2) DISCHARGE
0.90 -
00
o - I o (1 T 2) DISC IARGE
U ·
8 *
.80 L -
OO 00 0 " 0 30'(1 TO 2) DISCHARGE
.75
.70' -__ _ _ _ _ ___ _ _ _ _ _ _ _ _ _ _ ____ _ _ _ __ _ -_-_- -_-
5 <.0 15 2.0 2.5 50 n5 40 0**0
MEAN VELOCITY IN PIPE- FT. PER SEC.
FIG. 8. RELATION BETWEEN COEFFICIENT OF DISCHARGE FOR THE SHORT PIPE
WITH MOUTHPIECES AND THE MEAN VELOCITY IN PIPE (CONTINUED)
1.4 -
20°(1 TO 2) ENTRANCE
5'(1 0 2) DISCHARGE---- , S:0 0
20°(1 ro 3) ENTRANCE
1.3_1 T 2) DISCHARGE
2D
O 20°(1 TO 2) E TRANCE 10°(1 TO 3) DISCHARGE
.2 0 •
20-(1 TO 2) ENTRANCE 10°(1 TO ) DISCHARGE 86.80
20° 1 TO 2) ENTRANCE 15°(1 TO 3) DISC ARGE
[I.10 4-P 5I lOTO2)~)ENTRA1NCE15°(l TO 2) DI CHARGE
S--- 20'(1 TO 2) ENTRANC
S-- 2 TO 4) I SCHARG E
* 2 '5l TO 3 ENTRA NCE 20"(1 TO 2) DISCHARGE
.0 -2 °11 TO 2 ENTRANCE 20 (I TO 3) DICHARGE
3 o
30 (1 TO 2) ENTR.ANCE 30 (1 TO 2) DISCHARGE 48
.9 c ) -(1 TO- T - 5.02
B. 1 - 45 TO 2) ENTRNCE 45( TO 2) OISCHARC E 71
.80
1.5 2.0 2.5 3.0 3.5
MEAN VELOCITY IN PIPE -FT. PER SEC.
FIG. 9. RELATION BETWEEN COEFFICIENT' OP DISCHARGE FOE THE SHORT PIPE
WITH MOUTHPIECES AND THE MEAN VELOCITY IN PIPE (CONTINUED)
0 5C
1.0
4.0 4.5
ILLINOIS ENGINEERING EXPERIMENT STATION
tank, the maximum velocity being slightly greater than 5 ft. per sec.
The values of the coefficient of discharge varied but little, ranging
from 0.783 to 0.788. The ratio of the thickness of the pipe at entrance
to the diameter for the 6-in. pipe was 0.05 and for the 3-in. pipe
this ratio was 0.054. The entering edge of the 3-in. pipe was some-
what sharper than that of the 6-in. pipe.
The value for the lost head at entrance to an inward-projecting
pipe as usually given seems to be based on rather meager data
obtained chiefly from experiments with discharge into air at rather
high velocities through tubes of small diameters. The value c = 0.72
for the coefficient of discharge seems to have been handed down from
Weisbach. Bidone* reported a value of c = 0.767 and Bilton* a value
of c = 0.75 for a 21/-in. pipe, increasing to 0.79 for a 1-in. pipe
and to 0.93 for a ½/-in. pipe, the length in each case being 21/2
diameters.
The values of the coefficient of discharge and the coefficient of
loss for a flush entrance (corresponding in these experiments to a
90-degree entrance mouthpiece having an area ratio of 1 to 3) also
fail to check closely the values so generally given in texts and so
generally used, namely, c = 0.82 and m 0.49. As shown in Fig. 6
and Table 6, the values found in these experiments are c = 0.80 and
m = 0.56. That is, the lost head at entrance to a short pipe having
v2
a flush entrance is 0.56 -. A 90-degree mouthpiece with an area
2g
ratio of 1 to 3 is ample to give the same conditions of flow as a reser-
voir wall which is flush with end of the pipe and hence it should give
the same rate of discharge.
More experimental data on short pipes having flush entrances
are available, and they cover a wider range of sizes and conditions
than do those for inward-projecting pipes, the value of the coefficient
of discharge ranging from 0.785 to 0.84 with the majority of the
values lying below 0.82.*
The lost head at the entrance to a pipe can probably be deter-
mined better from a submerged tube than from one discharging into
air. It would seem, therefore, that the value of the lost head at the
entrance to an inward-projecting pipe is not so different from that
*See Appendix for references.
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 35
for a pipe having a flush entrance as is usually believed, and that
the common text book values need revision to apply to conditions
commonly met in hydraulics.
9. Entrance Mouthpieces.-From Tables 5 and 6 and the curves
in Figs. 7 and 8, it will be seen that entrance mouthpieces having
angles of from 10 degrees to 30 degrees (20 degrees to 60 degrees
total angle of convergence) give practically the same discharge, while
all the entrance mouthpieces having angles of from 5 degrees to 60
degrees (10 degrees to 120 degrees total angle) give only about 5
per cent range in the rate of discharge. In other words, the lost head
at the entrance to an inward-projecting short pipe may be reduced
from 0.62 of the velocity head in the pipe to 0.18 of the velocity
head by a conical mouthpiece having an angle ranging from 10 degrees
to 30 degrees. Also, the lost head will vary but little from 0.20 of
the velocity head in the pipe for all entrance mouthpieces having
angles between 10 degrees and 45 degrees (20 degrees and 90 degrees
total angle). It should be stated, however, that conditions surround-
ing the entrance to the mouthpiece may have some effect, such as the
accumulation of dirt in a passage or any other obstruction. Further-
more, it is clear from a comparison of Figs. 7 and 8 that no advantage
results from increasing the length of the entrance mouthpiece beyond
that corresponding to an area ratio of 1 to 2. The lost head at the
entrance to a mouthpiece is sometimes considered the same as would
occur at the entrance to an inward projecting pipe of the same area
as that of the mouthpiece; that is, the lost head is found by multiply-
ing the velocity head at entrance to the mouthpiece by the coefficient
of loss for an inward projecting pipe. There seems to be little
reason to justify such a method, since an entrance mouthpiece having
an area ratio of 1 to 3 gives almost the same lost head as one with an
area ratio of 1 to 2 while the velocity head at entrance to the former
mouthpiece would be, of course, only one ninth of that of the latter.
It is not clear just what effect a straight throat or pipe has when
added to an entrance mouthpiece. The discharge through the mouth-
pieces alone was not determined in these experiments. It would seem
that if the mouthpiece suppressed the contraction very completely,
the pipe would cause added resistance only, and hence decrease the
discharge, while if the suppression was rather incomplete, the pipe
might recover some of the velocity head during the expansion in it.
ILLINOIS ENGINEERING EXPERIMENT STATION
If this was in excess of the head lost during the expansion, the net
results might be an increase in the discharge. Further, the sup-
pression of the contraction by an entrance mouthpiece not only de-
creases the entrance loss but also reduces the turbulence of the sub-
sequent flow in the pipe, thereby increasing the effect of a discharge
mouthpiece. This will be discussed later under the heading of Com-
binations of Mouthpieces and Effect of Smooth Flow.
10. Earlier Experiments with Entrance Mouthpieces.-The
results of other experimenters on entrance mouthpieces are not en-
tirely consistent but give data of considerable importance. Table 3
gives in condensed form the results of the more important experi-
ments. From this table it will be seen that adding a straight pipe to
the mouthpiece used by Balch increased the discharge while in the
experiments by Stewart the discharge was decreased. Futhermore,
the coefficient of discharge increased with the velocity in the experi-
ments by Balch and also in those by Davis and Balch but decreased
in the experiments by Ellis, while Stewart found the coefficient to
decrease at first and then to increase (not shown in Table 3). In the
experiments recorded in this bulletin, the coefficient remained nearly
constant. It will be observed that the mouthpieces used by the last
four experimenters named in Table 3 have a throat diameter less than
11/4 in.; in fact in only one case is the throat diameter above 0.6 in.
These mouthpieces give somewhat higher values for c than do mouth-
pieces of larger throat diameters. Perhaps the higher values for
the coefficients of discharge for these small mouthpieces may be due
to a lesser amount of turbulence; that is, it may be that the water
flowing through a small mouthpiece is affected, or controlled more by
the sides than in the case of a large mouthpiece, at least when the
water enters or is received by the mouthpiece in a somewhat disturbed
state of flow.
11. Discharge Mouthpieces.-As might be expected, the angle
of the discharge mouthpieces influences the flow in a very different
way from that of the entrance mouthpieces. Tables 5 and 6 and the
curves of Figs. 7 and 8 show that when there is no mouthpiece on
the entrance end of the short pipe, the coefficient of discharge for a
discharge mouthpiece (attached to the pipe) diminishes rather rap-
idly as the angle of the mouthpiece increases, dropping somewhat
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 37
abruptly to practically no effect for an angle slightly greater than 20
degrees (40 degrees total angle).
It will be noted also by a comparison of Figs. 10 and 11 that
increasing the length of the discharge mouthpiece beyond that corre-
sponding to an area ratio of 1 to 2 has comparatively little effect on
the rate of discharge. It may be, however, that an increase in length
would show a greater effect for smaller angles than were used in
these experiments, that is, for angles less than 5 degrees for an area
ratio of 1 to 2 or less than 10 degrees for an area ratio of 1 to 3. But,
it will appear (see article 12) that the size of the pipe, or the smallest
area of the mouthpiece, is a much more important factor in the flow
through a discharge mouthpiece than it is for an entrance mouth-
piece. In other words, a discharge mouthpiece with a throat diameter
of 1/2 in. may give quite different results from that of a discharge
mouthpiece having the same area ratio and the same angle of diver-
gence but with a throat diameter of 6 in., at least when the water
is received by the mouthpiece in a turbulent state of flow. The dis-
charge mouthpiece with the small throat diameter (having a rela-
tively large ratio of circumference to cross-sectional area) seems to
be able to affect a greater percentage of the water flowing and thus
regain more energy per pound of water discharged. Furthermore,
the chances of having the water approach the discharge mouthpiece
with smooth flow is greater in the case of the small pipe, hence per-
haps the two causes work together, and for any given case they would
be difficult to separate. For these reasons a comparison with earlier
experiments on discharge mouthpieces for the purpose of extending
the present experiments is apt to be misleading.
It is clear from Figs. 10 and 11 that the governing factor in the
recovering of velocity head by means of a discharge mouthpiece
attached to a short pipe, having a diameter of several inches or more,
is the angle at which expansion begins-rate of expansion at the
start-at least when the total angle of divergence is not less than 10
degrees and the area ratio not less than 1 to 2.
12. Earlier Experiments with Discharge Mouthpieces.-Table 4
gives, in condensed form, the results of the more important earlier
experiments with discharge mouthpieces. These experiments seem
to show the influence of the size of throat area as discussed above.
The increase in the coefficient of discharge, c, with an increase in
ILLINOIS ENGINEERING EXPERIMENT STATION
ANGLE OF MOUTHPIECE - DEGREES
FIG. 10. RELATION BETWEEN COEFFICIENT OF DISCHARGE FOR THE SHORT PIPE
WITH MOUTHPIECES AND ANGLE OF MOUTHPIECE FOR AREA RATIO OF 1 TO 2
w
I
U
0
I-
Z
U
LL
0
U
ANGLE OF MOUTHPIECE- DEGREES
FIG. 11. RELATION BETWEEN COEFFICIENT OF DISCHARGE FOR THE SHORT PIPE
WITH MOUTHPIECES AND ANGLE OF MOUTHPIECE FOR AREA RATIO OF 1 TO 3
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE
the length of the discharge mouthpieces having small throat diame-
ters is probably somewhat larger than would be obtained with mouth-
pieces having large throat diameters but with the same angles of
divergence. As already noted in the experiments herein recorded the
value of c increased very little for an increase in length correspond-
ing to an increase in area ratio from 1 to 2 to 1 to 3 when the total
angle of divergence was 20 degrees or more. It is clear from Table 4
that for discharge mouthpieces having small throat diameters and
with the water in a state of smooth flow as it approaches the mouth-
piece (entrance mouthpiece attached), an increase in length has a
marked effect on the discharge. It will be noted that the greatest
increase in c in the experiments reported by Francis occurred when
the area ratio was increased from 1 to 2 to 1 to 5. It is probable
that the increase in length would have been more noticeable in the
present experiments for smaller angles of divergence, particularly for
the smoother conditions of flow.
13. Combinations of Mouthpieces and Effect of Smooth Flow.-
In order to get some measure of the influence of smooth flow upon the
rate of discharge and the amount of velocity head recovered by a
discharge mouthpiece, experiments were made using combinations of
an entrance and a discharge mouthpiece when attached to the short
pipe. The results are given in Table 7. It will be seen from this
table that a discharge mouthpiece acts more effectively in recovering
velocity head when a mouthpiece is attached to the entrance end.
The following example will show this in the case of the 5-degree (1 to
2) discharge mouthpiece. This mouthpiece gave a coefficient of dis-
charge of 0.99 (Table 5) when no mouthpiece was attached to the
entrance end of the short pipe. From Table 7 it will be seen that
the short pipe with a combination of the 5-degree (1 to 2) discharge
mouthpiece and the 20-degree (1 to 2) entrance mouthpiece gave a
coefficient of discharge of 1.34. This means that the 5-degree mouth-
piece has a coefficient of discharge of 1.137 when used in combina-
tion with the 20-degree entrance mouthpiece. This value is obtained
from the following steps: Attaching a 5-degree (1 to 2) discharge
mouthpiece to the short pipe when no entrance mouthpiece is used
is equivalent to raising the head on the inward projecting pipe from
h to 1.59h as obtained by equating the rates of discharge,
ILLINOIS ENGINEERING EXPERIMENT STATION
0.99 a V\2gh = 0.785 a. V2gHD, from which HD = 1.59h.
In like manner it is found that attaching a 20-degree (1 to 2) mouth-
piece to the entrance end of the pipe when no mouthpiece is attached
to the disharge end is equivalent to raising the head on the inward
projecting pipe from h to 1.39h (HE = 1.39h).
Now if both of these mouthpieces were attached to the short pipe,
it might be expected that the head on the inward projecting pipe
required to give the same discharge (equivalent head) would be
1.39h times 1.59 or 2.21h and that the coefficient of discharge for the
combination, c, would be found from,
c, aVý2gh = 0.785 a/2g (2.21h) or, c. = 1.17* . (7)
As already noted, however, the coefficient of discharge for this com-
bination as found from experiment is 1.34 (Table 7) which cor-
responds to an equivalent head of 2.92k. If all of this increase is
attributed to the more efficient action of the discharge mouthpiece
due to the fact that it receives the water in more nearly parallel stream-
lines (smooth flow), the result is an equivalent head for the 5-degree
(1 to 2) discharge mouthpiece of 2.10h (Col. 7, Table 7) instead of
1.59h, an increase of 0.51h due to smooth flow. Hence, the coefficient
of discharge for the short pipe with the 5-degree (1 to 2) discharge
mouthpiece, assuming smooth flow as the water approaches the mouth-
piece, would be found from
Cd a/2gh -= 0.785 aV2g (2.10h), or Cd = 1.137t . (8)
as compared with 0.99. In other words, this particular mouthpiece
gives an increase, due to smooth flow, of 14.9 per cent in the rate of
discharge.
Tables 5 and 6 give the values of the coefficient of discharge for
the short pipe with the various discharge mouthpieces attached when
the water flowed through an entrance mouthpiece on its way to the
discharge mouthpiece. These values are represented by the dash lines
in Figs. 10 and 11. Even though the entrance mouthpiece used gives
stream lines that are far from parallel, it is thought that a less turbu-
lent condition of flow would seldom be found at least in a 6-in. pipe,
and for velocities above 2 ft. per sec. Hence, the values of the
*See Table 7.
tSee Col. 9, Table 5.
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 41
coefficient of discharge given by the dash lines are about the maxi-
mum to be expected. In each combination the entrance mouthpiece
used was one giving about the minimum contraction.
Tables 7 and 8 also give the percentage gain in the coefficient of
30
25
L
o
0
I-
z
£ 10
0
U
z
5
0
hi
5
0
ANGLE OF MOUTHPIECE-DEGREES
FIG. 12. RELATION BETWEEN PER CENT GAIN IN COEFFICIENT OF DISCHARGE FOR
DISCHARGE MOUTHPIECES DUE TO ENTRANCE MOUTHPIECE, AND
ANGLE OF DISCHARGE MOUTHPIECES
discharge for the various discharge mouthpieces due to the entrance
mouthpiece. The relation of this gain to the angle of the discharge
mouthpiece is shown in Fig. 12 for both series of mouthpieces. It
will be noted that as the angle of the discharge mouthpiece increases
ILLINOIS ENGINEERING EXPERJMENT STATION
from 5 degrees (10 degrees total angle) the gain in the coefficient
decreases rather rapidly, reaching zero for both series of mouth-
pieces at an angle of about 20 degrees (40 degrees total angle of
divergence). Furthermore, this is the same angle at which a dis-
charge mouthpiece rather abruptly ceases to regain any velocity head
when no mouthpiece is used on the entrance end (see Figs. 10 and
11). It would seem, therefore, that a 20-degree discharge mouthpiece
(total angle of divergence of 40 degrees), or one with a greater angle,
allows such a turbulent condition of the water to develop that it is
unable to recover any velocity head no matter how smooth the flow
may be as the water approaches the mouthpiece. It is worth noting
also that a comparison of the results in Table 5, Col. 10, and Table 6,
Col. 10, indicates that the length of a discharge mouthpiece has a
somewhat larger influence on the discharge when smooth flow exists
than when the flow is more turbulent, and it is probable that
this effect would have been more noticeable for smaller angles of
divergence.
Attention has been called to the fact that the theoretical amount
of velocity head which is possible of recovery by discharge mouth-
pieces having area ratios of 1 to 2, 1 to 3, and 1 to 4 is respectively
75, 88, and 94 per cent of the velocity head in the pipe. The effect
of smooth flow may also be measured in terms of the increase in the
amount of velocity head recovered by the discharge mouthpieces.
For example, the coefficient of loss for the particular combination
discussed above is 0.232 (Col. 5, Table 7) and the coefficient of loss
for the pipe with the 20-degree (1 to 2) entrance mouthpiece only,
is 0.165. Hence the loss of head in the discharge mouthpiece alone
is 0.067 times the velocity head in the pipe. But 0.75 of the velocity
head is the maximum amount possible of recovery, and since the
mouthpiece lost 0.067 velocity heads, the amount recovered is 0.683
velocity heads which is 91 per cent of the maximum amount possible
of recovery (Table 7, Col. 11). By a similar analysis it is shown that
these same mouthpieces would have regained 58 per cent of the
theoretical amount possible of recovery if the 5-degree (1 to 2) dis-
charge mouthpiece had given the same action when in combination as
it did when it was the only mouthpiece attached. That is, smooth
flow allows a 5-degree (1 to 2) discharge mouthpiece to recover 33
per cent more velocity head than when the water approaches this
mouthpiece in a turbulent state of flow (Table 5, Col. 11). The
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 43
relation between the increase in the velocity head recovered by the
discharge mouthpieces due to an entrance mouthpiece, expressed in
per cent of the maximum theoretical amount possible of recovery, and
the angle of the discharge mouthpieces is shown in Fig. 11. It is prob-
able that the two curves should have the same ordinate for a 15-
degree mouthpiece. At least, the curve for the mouthpieces having
an area ratio of 1 to 3 should not be above the other curve. If the
same entrance mouthpiece had been used in each case, the difference
would probably have been negligible. The curves, therefore, are
drawn to give the same ordinate for the 15-degree mouthpiece.
In the foregoing discussion it has been assumed that adding a dis-
charge mouthpiece to the short pipe will not change the state of flow
in the pipe. This is probably true if the pipe has an entrance mouth-
piece attached, suppressing the contraction. If, however, there is
no mouthpiece on the entrance end, it appears that the influence of
the discharge mouthpiece extends back into the pipe, producing, in
effect, a mouthpiece whose smallest cross-sectional area is somewhat
less than the area of the pipe and perhaps allowing the expansion of
the stream in the pipe to be continuous with that in the mouthpiece.
For example, the short pipe with a 10-degree (1 to 2, 20-degree total
angle) discharge mouthpiece gave a coefficient, of loss of 0.872 (Table
5), and since the short pipe without any mouthpiece attached gives
a coefficient of loss of 0.62, the mouthpiece alone should give a loss
of 0.252 times the velocity head in the pipe. But from Table 7 it
will be seen that this same mouthpiece gives in combination with a
20-degree (1 to 2) entrance mouthpiece a coefficient of loss of 0.468,
and after deducting 0.165, which is the loss for the short pipe with
the 20-degree entrance mouthpiece, 0.303 is left as the coefficient of
loss for the discharge mouthpiece alone. This is inconsistent with
the value, 0.252, already established. A similar effect occurs with
all the mouthpieces except the 5-degree. The explanation, as already
suggested, seems to be that the coefficient of loss for the short pipe
is less than 0.62 when a discharge mouthpiece is attached; that the
influence of the mouthpiece is felt back into the pipe. This also helps
to explain why the coefficients of discharge for mouthpieces with
small throat diameters and connected by a short throat are relatively
large.
Fig. 13 shows the relation between the coefficient of loss for the
short pipe with entrance mouthpiece attached and the angle of mouth-
ILLINOIS ENGINEERING EXPERIMENT STATION
piece. It also shows the relation for the discharge mouthpieces alone
as obtained by deducting the loss up to the mouthpiece. The values
for the discharge mouthpieces alone are the larger ones as indicated
in the example given. The values are given in Table 5. The number
of velocity heads in the pipe recovered by any discharge mouthpiece
would be the value obtained by subtracting the ordinate to the curve
in Fig. 11 from 0.75 for an area ratio of 1 to 2 and from 0.88 for an
area ratio of 1 to 3.
14. Experimental Difficulties Encountered.-During the early
part of the investigation great difficulty was experienced in getting
ANGLE AT MOUTHPIECE - DEGREES
FIG. 13. RELATION BETWEEN COEFFICIENT OF LOSS AND ANGLE OF MOUTHPIECE
consistent results at the higher velocities, especially with mouthpieces
having small angles of divergence. The head would fluctuate at times
for apparently no good cause, and the value of the coefficient of dis-
charge would vary considerably in successive experiments. It was
noticed finally that vortices sometimes formed in the upstream com-
partment causing a "suck hole" as large as 11/2 in. in diameter at
the water surface and tapering to a fine point some 10 or 12 in.
below the surface. It was observed also that this vortex motion was
more active and persistent when the unsteady conditions prevailed,
but in no case did it appear to allow air to enter the pipe. In order to
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 45
prevent the formation of the vortex a float was made fitting closely
in the upstream compartment. Grill work on the under part of the
float extended deep enough to suppress the vortex before it could
fully form. Results were more consistent after the float was used,
and it was kept in use for the remainder of the experiments. It was
at once noticed, however, that the coefficient of discharge for the
longer discharge mouthpieces was lowered by the use of the float
and considerable time was spent in attempting to measure the effect
35 -i5- - -- - - - {
0 5 10 15 20
I - P - - P· - - - P
ANGLE OF DISCHARGE MOUTHPIECE-DEGREES
FIG. 14. RELATION BETWEEN GAIN IN VELOCITY HEAD RECOVERED BY DISCHARGE
MOUTHPIECES DUE TO ENTRANCE MOUTHPIECE, EXPRESSED IN PER CENT
OF THEORETICAL AMOUNT POSSIBLE OF RECOVERY, AND
ANGLE OF DISCHARGE MOUTHPIECE
of the vortex. The experimental results clearly indicated that the
vortex motion may increase the discharge by at least 2 per cent in the
case of the discharge mouthpieces with the smaller angles. If air had
entered the pipe, the discharge would, of course, have been decreased.
It would appear, therefore, that the whirling motion of the water
allowed it to enter the pipe with less contraction. With a 15-degree
discharge mouthpiece, the vortex seemed to show no effect although
I HUI1iiI
1-1.-I 1-4 l l
I AREA RATIO I TO
I. I
AREA RATIO I TO 3
10-----
0S w
I I I\ I I I I I I I I 1 _I
·
·
\
\
35
ILLINOIS ENGINEERING EXPERIMENT STATION
the vortex was not so large nor active as for the 5 and 10-degree
mouthpiece. This suggests that perhaps the increase due to the
vortex is caused more by the smoother flow of the water as it ap-
proaches the discharge mouthpiece, resulting in more efficient action
by the mouthpiece (as already discussed), than by reduction in the
entrance loss.
Another troublesome factor met with during the experiments
was that of temperature changes of the water in the 2-in. pipes used
as still basins for the hook gauges. The zero readings of the gauges
were taken frequently during the experiments and were found to
remain constant until the summer months when results became very
erratic. After considerable time it was discovered that the trouble
was due to the fact that the sun shone only on the pipe attached to the
downstream compartment early in the afternoon, later shifting so as
to shine only on the pipe attached to thWe upstream compartment.
After correcting for the difference in temperature thus caused in the
two still-basin pipes, consistent results were obtained. It was found,
however, that the whole trouble could be avoided by frequently taking
water from the tank and pouring it down the pipes.
15. Conclusions.-The preceding discussion has shown that the
losses accompanying the flow of water depend largely upon the state
of its motion which in turn is influenced by many factors, the effects
of which in many cases can be but roughly estimated. While the
results of these experiments tend to define the range of such effects
for certain conditions of flow, additional experiments would be neces-
sary to establish all the inferences which have been suggested. The
following conclusions, however, seem justified:
a. As applying to conditions likely to be met in engineer-
ing practice, the value for the head lost at the entrance to an
inward-projecting pipe (i. e. without entrance mouthpiece and
not flush with wall of the reservoir) is 0.62 of the velocity head
V2 V2
in the pipe (0.62-) instead of 0.93-, as usually assumed. To
2g 2g
put it in another form, the coefficient of discharge for a sub-
merged short pipe with an inward-projecting entrance is 0.785
instead of 0.72 as given in nearly all books on hydraulics. Fur-
ther, the lost head at the entrance to a pipe having a flush or
square entrance is 0.56 of the velocity head in the pipe (0.56-)
2g
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 47
V2
instead of 0.49 - as usually assumed. In other words, the
2g
coefficient of discharge for a submerged short pipe with a flush
entrance is 0.80 instead of 0.82 as given by nearly all authorities.
b. The loss of head resulting from the flow of water
through a submerged short pipe when a conical mouthpiece is
attached to the entrance end, may be as low as 0.165 of the
v2
velocity head in the pipe (0.165 -) if the mouthpiece has a
2g
total angle of convergence between 30 and 60 degrees and an
area of ratio of end sections between 1 to 2 and 1 to 4 or some-
what greater. In other words, the coefficient of discharge for
a submerged short pipe with an entrance mouthpiece as specified
above is 0.915.
c. The loss of head which occurs when water flows through
a submerged short pipe having an entrance mouthpiece varies
but little with the angle of the mouthpiece if the total angle of
convergence is between 20 and 90 degrees and if the area ratio
is between 1 to 2 and 1 to 4 or somewhat more. The loss of head
for any mouthpiece within this range would be approximately
v2
0.20 of the velocity head in the pipe (0.20 -). There is, there-
2g
fore, little advantage to be gained by making an entrance mouth-
piece longer than that corresponding to an area ratio of 1 to 2.
Thus, an entrance mouthpiece with a total angle of convergence
of 90 degrees and the length of which is only 0.2 of the diameter
v2
of the pipe gives approximately 0.20 - for the loss of head.
2g
d. The amount of velocity head recovered by a conical
mouthpiece when attached to the discharge end of a submerged
short pipe depends largely upon the angle of divergence of the
mouthpiece, but comparatively little upon the length of the
mouthpiece. This is true for lengths greater than that cor-
responding to an area ratio of 1 to 2 and for total angles of
divergence of 10 degrees or more. The amount of velocity head
recovered decreases rather rapidly as the angle of divergence
increases from a total angle of 10 to 40 degrees. At or near 40
degrees the amount of velocity head recovered rather abruptly
falls to approximately zero.
ILLINOIS ENGINEERING EXPERIMENT STATION
e. A conical discharge mouthpiece having a total angle of
divergence of 10 degrees and an area ratio of 1 to 2, when
attached to a submerged short pipe, will recover 0.435 of the
velocity head in the pipe, which is 58 per cent of the theoretical
amount possible of recovery.
f. The amount of velocity head recovered by a diverging
or discharge mouthpiece when attached to a submerged short
pipe is considerably more when a converging or entrance mouth-
piece is also attached than it is when the entrance end of the
short pipe is simply inward-projecting (no mouthpiece at-
tached). This excess in the velocity head recovered diminishes
rather rapidly as the angle of the discharge mouthpiece in-
creases, and it becomes zero for a discharge mouthpiece having
a total angle of divergence of approximately 40 degrees. This
increase in the velocity head recovered is probably due to the
effect of smooth flow in the pipe as the water approaches the
discharge mouthpiece. The smooth flow allows the mouthpiece
to recover more of the velocity head in the pipe than when a
more turbulent flow exists; this increase amounts to as much
as 33 per cent in the case of the discharge mouthpiece having a
total angle of divergence of 10 degrees and an area ratio of
1 to 2.
While these conclusions are drawn from experiments on the
flow of water through a particular short pipe having various entrance
and discharge conditions, it is felt that the results of the experiments
are applicable in a general way to a large variety of cases in engineer-
ing practice where the contraction and expansion of a stream of water
occurs. A number of such cases are suggested in the introduction.
EFFECT OF MOUTHPIECES ON FLOW THROUGH SUBMERGED PIPE 49
APPENDIX
BIBLIOGRAPHY
1. Short Pipe with Inward Projecting Entrance.
H. Smith, Jr. Hydraulics, p. 344. Results of Bidone's Experiments.
J. Weisbach. Mechanics of Engineering (Coxe's Translation), p. 855.
H. J. I. Bilton. Victorian Institute of Engineers, Vol. 9, 1908. Coefficients
of Discharge for Circular Orifices.
2. Short Pipe with Flush Entrance.
H. Smith, Jr. Hydraulics, p. 205. Table taken from D'Aubisson's "Traite
a Hydraulique," giving Results of Various Authorities. Also on p. 204,
Results of Bossut's Experiments.
J. Weisbach. Mechanics of Engineering (Coxe's Translation), p. 854.
C. B. Stewart. Bulletin No. 216, University of Wisconsin. Experiments
with Submerged Tubes 4 Feet Square.
3. Entrance Mouthpieces.
J. B. Francis. Lowell Hydraulic Experiments, pp. 212 to 225.
T. G. Ellis. Transactions American Society of Civil Engineers, Vol. V.
Experiments with Large Apertures.
Jas. Brownlee. Institution of Engineers and Ship Builders in Scotland, Vol.
XIX, 1875-76. On the Action of Water and Frictional Resistance or Loss
of Energy when Flowing at Various Velocities through a Nozzle with a
Converging Entrance and Diverging Outlet.
L. R. Balch. Bulletin No. 700, University of Wisconsin. Investigation
of Flow through 4-inch Orifices and Tubes.
G. J. Davis and L. R. Balch. Bulletin No. 629, University of Wisconsin.
Experiments with Submerged Draft Tubes.
4. Discharge Mouthpieces and Compound Tubes.
J. B. Francis. Lowell Hydraulic Experiments, pp. 212 to 225.
Jas. Brownlee. Institution of Engineers and Ship Builders in Scotland, Vol.
XIX, 1875-76. On the Action of Water and Frictional Resistance or Loss
of Energy when Flowing at Various Velocities through a Nozzle with a
Converging Entrance and Diverging Outlet.
G. J. Davis and L. R. Balch. Bulletin No. 629, University of Wisconsin.
Experiments with Submerged Draft Tubes.
J. Weisbach. Mechanics of Engineering (Coxe's Translation), p. 861.
Divergent Mouthpiece, p. 862. Divergent Mouthpiece Used by Eytelwein.
K. Andres. "Versuche iiber die Umsetzung von Wassergeschwindigkeit in
Durch," in "Zeitschrift der Vereines Deutscher Ingenieure," Sept. 17
and 24, 1910.*
*This reference was not found until after this bulletin had been written. The
sizes of the mouthpieces and their angles of divergence are so small (about 0.6 in.
throat diameter and 4 to 12 degrees total angle of divergence) and the velocity is so
high (32 to 131 ft. per sec. throat velocity) that the results are not directly comparable
with the results given in this bulletin. The article contains, however, much valuable
information, emphasizing in particular the decrease in lost head when the water is
caused to whirl or rotate about the axis of the tube as it enters the tube. The above
article also refers to experiments of Banninger, published in "Zeitschrift ftir das
Gesamte Turbinenwesen," 1906, page 12. The results of these experiments have not
been available for examination.
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:V 7 , . -"; i : ,: " : ' " i. ;4* -4-:ri, • ; - --,
a:, > .
SEDMUND J. JAMis, Ph. D., IL. D., President
-4-
THE UNIVERSITY INCLUDES THE FOLLOWING DEPARTMENTS.
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