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MISCELLANEOUS PAPER ~-68-3

HEAD LOSSES IN SUBCRITICAL FLOW CHANNEL TRANSITIONS by

•

Y. 1-t Chu

l

September 1968

Sponsored by

Office, Chief of Engineers U. S. Army Conducted by

U. S. Army Engineer Waterways Experiment Station CORPS OF ENGINEERS Vicksburg, Mississippi

T~IS DOCUMENT ~AS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED

LIBRARY US ARMY ENGINEER WATERWAYS EXPERIMENT STATIOI'l VICKSBURG, MISSISSIPPI

MISCELLANEOUS PAPER H-68-3

HEAD LOSSES IN SUBCRITICAL FLOW CHANNEL TRANSITIONS by

Y.

~.

Chu

September 1968

Sponsored by

Office, Chief of Engineers U. S. Army

Conducted by

U. S. Army Engineer Waterways Experiment Station CORPS OF ENGINEERS Vicksburg, Mississippi THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED

H'/ ------------------------------------------------~

LU'a.~~

N o l-1- lo ~ - ~ PREFACE The s tudy described in this paper was performed at the Wat~rways

Engineer

u. s.

Army

Experiment Station, Vicksburg, Mississippi, during

the • period May-October 1967.

The study was made to provide data for

' .~ : use in revising Engineer Manual, Engineering and Design, Hydraulic Design •

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·~r

Flood Control Channels, EM 1110-2-1601, dated 30 October 1967, for the •

Offic.e, Chief of Engineers. •

..

It was supported by FY 1967 and 1968 Engineer-

ing Studies funds allotted under ES 804, Development of Hydraulic Design -Criteria.

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The basic tests were made and the data analyzed by PFC Joseph Canton,

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...

E4, under the supervision of Mr. Y. H. Chu, Hydraulic Research Engineer,

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· . Analysis Section, Hydraulic Analysis Branch, Hydraulics Division.

This

report was prepared by Mr. Chu under ·the supervision of Mr. R. G. Cox, Chief, Analysis Section •

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Director of the Waterways Experiment Station during the study was Col. J.

s.

Oswalt, Jr.

Mr. J. B. Tiffany was Technical Director.

of the Hydraulics Division was Mr. E. P. Fortson, Jr.

Chief

Mr. F. B. Campbell •

was Chief of the Hydraulic Analysis Branch. ,, /

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69389

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HEAD LOSSES IN SUBCRITICAL •' .

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FLOW CHANNEL TH.ANS IT IONS

The purpose of the study was the investigatioh of the head losses for subcritical flows pnssing channel transitions. It was also desired to · provide additional information for Figure 3, MP 2-818 relative to depth correction factors for use in the momentum procedure developed therein. 1.

2. A plywood transition was buil~ for the purpose of the investigations. It consisted of a transition and two rectangular channel reaches. The divergent or convergent angle of the transition reach was 12.5 degrees as recommended by Hind< 1 >*. The rectangular channels, one 28 3/4 in. wide ru1d the other 6 in. wide, were connected to their respective ends of the transition reach. Detail geometric construction can be discerned from Plate 1. The study was accomplished by inserting the plywood channels in the existing steel flume of Hydraulic Research Facility. The channels were positioned in the flume first to operate as a contraction and then as an expansion (see Plate 1). By the use of triangular fillet blocks, the wide rectangular channel and the transition reach were transformed, respectively, into a trapezoidal-shaped channel and a broken-back-type transition. The slope of the fillet block in the uniform channel was 1 on 2. The height of channels was six inches. 3. Discharge was measured using a 6- x 3-inch venturi tube equipped with .a U-tube water nanometer. Previous flume investigations indicated that this method of discharge measurement is reasonably accurate. Watersurface elevations relative to the rail of the steel flume were measured with a standard point gage . 4. The head losses in channel transitions, generally, are classified as outlet losses for expansions and inlet losses for contractions. The loss coefficients C0 and Ci are usually defined< 2 as: . AZ = (1 - C0 ) AhV

(outlet loss coefficient)

AZ - (1 + Ci) AhV

(inlet loss coefficient)

.. where AZ and Ahv are , respectively, the change of surface elevation and ve locity head from upstream to downstream of the transition. Stations located approximately 0.5 times the transition length upstream and downstream from the transition reach were considered to approximate unifprm

•

*Raised figures are reference numbers at end of text. •

flow and were selected for computation purposes. When the surface fluctuations become pronounced as a result of increasing the Froude number, the mean water-surface elevations were carefully determined by averaging repetative point gage readings. In addition, the surface profile for eack test run was recorded. Because of the relatively smooth bo~ndary involved, the friction losses were small compared with the turbulence loss, and therefore were considered as part.of the transition geometric loss. 5. Test results are summarized as shown in Table 1. The code'of each run is designated, as for example, RIT5-3 which means the third run on a rectangular (R) to trapezoidal (T) transition with an expansion of 1 to 5. Water surface profiles for each run are attached (Plates 2-10) . . These profiles reflect any unstable surface fluctuations at the measuring stations; and the plotted data, therefore, may not necessarily correlate exactly with the depth data of Table 1. Plate 11 shows the loss coefficients plotted against the Froude numbers. For the expanding transitions, the coefficient C0 was plotted as a function of the Froude number of the upstream flow (F1 ). The value of loss coefficient C0 varied between 0.8 and 1.0 for the simple rectangular expansion (Plate lla). No correlation between C0 and F1 was observed. The loss coefficient for the broken-back-type transition expansions was found to vary from 1.0 to 0.4 as F1 increased from 0.2 to 0.6 (Plate llb). Such a (~jnd of variation also has been reported by Soliman(3) and Simmons . Additional tests are needed to permit more firm conclusions to be made.

•

For the contracting transition, the downstream Froude number (F2 was used in plots. As can be discerned in Plate llc and d, the loss Ci is in the neighborhood of 0.3. The results seem to indicate that for higher F2 the Ci value has a slight tendency to decrease for the simple rectangular transitions. The average Ci for the broken-back-type contraction is about 0.32 which is slightly higher than that for simple rectangular ones.

)

6. It was noticed that the expansion loss (C 0 ) is appreciably greater than the contract ion loss (Ci) even though the expansion and contraction angles are the same. With 12 . 5 degrees expansions, the flow is not completely expanded along the side wall. Photograph 1 shows the side eddy resulting from flow separation. The eddy formed on either side of the expansion, and with any minor disturbance in the flow could be moved to the opposite side. The high degree of turbulence induc~d by this eddy contributes to the large energy dissipation for expanding transition.

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TABLE 1

BASIC OBSERVED AND COMPUTED RESULTS

Run

Q

v:a

Ya

cfs

ft

fps

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Contractions

R5R1-1 R5R1-2 R5R1-3 R5R1-4 R5R1-5 R5Rl-6 R5R1-7

0.257 0. 184 0.184 0.184 o. 184 0.182 0.183

0.377 0.368 0.312 0.264 0.279 0.276 0.371

0.323 0.343 0.280 0. 197 0.230 0.227 0.348

0.2727 0.200 0.236 0.279 0.264 0.264 0.197

1.567 1. 073 1.314 1.868 1.559 1.604 1.052

0.078 0.058 0.074 0.096 0.088 0.088 0.057

T5R1-1 T5Rl-2 T5Rl-3 T5R1-4 T5R1-5 T5Rl-6 T5R1-7

0.170 0.232 0.273 0.212 0.187 0.167 0.206

0.3535 0.352 0.341 0.315 0.314 0.345 0.319

0.332 0.303 0.239 0.261 0.279 0.325 0.2745

0.2719 0. 3732 0.4591 0.3755 0.3524 0.2763 0.3799

1.024 1. 531 2.284 1.624 1.341 1.028 1.501

0. 081 0.11 o. 14 0.12 0.11 0.083 0.12

Run

Q

•

0.48 0.32 0.44 0.74 0.57 0.59 0.31

0. 30 0.40 0.20 0.25 0.15 0.24 0.34

0.31 0.49 0.82 0.56 0.44 0.32 0.50

0.35 0.39 0.27 0.34 0.27 0.26 0.34

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Expansions R1T5-1 R1T5-2 R1T5-3 RlT5-4 R1T5-5 R1T5-6 R1T5-7 R1T5-8* R1T5-9* R1T5-10*

0.215 0.215 0.145 0.145 0.156 0.148 0.147 0.155 0.157 0.155

0.345 0.308 0.3505 0.336 0.3755 0.357 0.348 0.267 0.191 0.210

0.362 0.325 0.367 0.349 0.388 0.368 0.360 0.336 0.294 0.311

1. 2463 1.3961 0.8276 0.8630 0.8311 0.8291 0.8448 1.161 1.644 1.476

0.3324 0.3863 0.2199 0.2360 0.1675 0.2236 0.2291 0.2659 0.317 0.3252

0.26 0.31 0.17 0.18 0.17 0.17 o. 18 0.40 0.66 0.57

R1R5-1 R1R5-2 R1R5-3 R1R5-4* R1R5-5*

0.168 0.168 0.240 0.218 0.218

0.378 0.277 0.390 0.319 0.295

0.3905 0.286 0.403 0.382 0.375

0.889 1.213 1. 231 1.364 1.478

0.1912 0. 2473 0.2508 0.2397 0.2448

0.25 0.41 0.35 0.43 0.48

/

*Data obtained from sloping channel •

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0.097 0.12 0.064 0.070 0.047 0.065 0.067 0.081 0.103 0.103

0.73 0.79 0.44 0.81 0.85 1. 00 0.926 0.60 0. 41 0.38

0.054 o. 081 0.070 0.068 0.071

o. 87 1.14 0.91 0.86 1.03

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7. In general, quantitative results are comparable with those from the recent research. Simmons< 4 > reported a value of 0.65 (varied from · 0.6 to 0.7) f?r the outlet loss (C 0 ) for broken back, open-channel transitions discharging from pipe into canals an~ ~ value of 0.45 (varied from 0.4 to 0.5) for the inlet loss (C 1 ). Chow 2 recommended 0.3 for Ci and 0.5 for C0 for straight-line type transition and 0.3 for Ci and 0.75 for C0 for the square-ended type one. Compared with data in other references · listed at the end of this memorandum, the present results seem slightly high. It is worthwhile to point out that Formica(5), Smith and Yu(6) computed their head losses by using the differences of specific energy. Although, their test flume had a relatively flat bed, it is believed that a small deviation from the level will cause large effects on energy loss computation, especially for subcritical transitions. Because the geometric conditions for the tested channels used in the references are not the same, a general comparison was not drawn. It should be emphasized here that the energy loss for subcritical flow transitions is quite small compared with the specific energy of the incoming flow. The analysis is based on onedimensional approach, and does not include a velocity correction coefficient. The resulting coefficients are based on assumed velocity distribution both ver~ically and horizontally. 8.

The test data have also been analyzed in a manner permitting a comp~rison to be made with Figure 3 of MP 2-848< 9 >. The results are indicated as WES data shown in Plate 12. Generally, results are in good agreement with other data shown for expanding channels. For converging channels, the depth ratio obtained (y2 /y1 ) is limited to 1.03. Higher ratios would have resulted in supercritical flow downstream from the transition. The "Correction Factors" computed according to equation 14 of MP 2-848 for diverging flow are close to unity. The computed WES data are summarized below. TABLE 2

Depth Correction Factor Kp •

Run R5Rl-l RSRl-2 R5Rl-3 R5Rl-4 R5Rl-5 RSRl-6 R5Rl-7 RlR5-l RlRS-2 RlR5-3

Y2 1Y1

B2 /}\

0.973 0.929 0.897 0.746 0.846 0.823 0.938 1.033 1.033 1.033

0.21 0.21 0.21 0.21 0.21 0.21 0.21 4.79 4.79 4.79

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K

p

0.960 1. 050 1.069 1.245 1.113 1.144 1.042 0.985 1.012 0.999

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References

1. Hinds, J • H., " The Hydraulic Design of Flume and Siphon Transitions," Paper ~o. 1689 and discussions. Trans. of ASCE, Vol. 92, 1928. 2. Chow, V. T., "Open Channel Hydr.aulics," page 310, McGraw-Hill Book Co., 1959. 3. Soliman, M. M. , Discussion on "Use of Baffles in Open Channel Expansions," by c. D. Smith and James N. G. Yu. Journal of the Hydraulics Division, ASCE, Vol. 92, No. HY 5, Sept. 1966. 4. Simmons, W. P., "Transitions for Canals and CUlverts,'' Journal of Hydraulics Division, ASCE, May 1964. 5. Formica, G., "Expenenge preliminari sulle predite di caric o nei canadi, devute a cambi amenti di sezione," page 554, L'Energia Elettrica, 1955.

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6 ., Sm1.' th , C D and Yu , James N G , "Use of Baffles 1.' n Open Chan- ,~1 Expansions," Journal of the Hydraulics Division, ASCE, Vol. 92, No. ~ . ~ , March 1966. I

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"De sign Standards No. 3 - Canals and Related Structures " paragraP.h 2•25B, USBR, 1963 • .

7<

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8. Powell, S • B., No. 640, WESHP. .

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Expansion and Contraction Coefficients,

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Patterson, J. W., "A MP 2-848, WES.

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