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Publication Number: FHWA-HRT-07-036
Date: March 2007

Junction Loss Experiments: Laboratory Report

4. RESULTS

SCALING EFFECTS

The first set of tests was designed to verify the effect of scale on the access hole (junction) loss experiments. A subset of the base runs (one inflow and one outflow pipe) was used to analyze scaling issues. The dimensions of the apparatus for the base runs were scaled down by a scaling ratio factor of 1 to 4, and total energy loss across the access hole was measured. Figure 11 shows that scaling had little effect on relative energy loss; that is, a change in dimensions was matched by a proportionate change in energy loss.

Figure 11. Graph. Effects of scaling. This is a graph with linear Cartesian coordinates. The vertical axis is the total energy loss in old model scale and is in millimeters, ranging from 0 to 25. The horizontal axis is the total energy loss in new model scale and is in millimeters, ranging from 0 to 25. Data points are tightly scattered along a straight line. The equation for the line is delta E subscript old equals 0.8819 times delta E subscript new, and the R squared value is 0.9344.

Figure 11. Graph. Effects of scaling.

VALIDATION OF Ki AND Ko

The next set of tests was designed to validate the loss coefficients for the inflow pipe (an exit loss) and the outflow pipe (an entrance loss). The first idea for calculating these losses involved measuring the kinetic energy distribution across the access hole. This idea, however, did not work well because the flow in the access hole was too turbulent and chaotic to characterize. The final idea was to measure the outflow energy loss and then infer the inflow energy loss using two basic steps.

The first step was to design a miniculvert apparatus with scaled conditions similar to the access hole apparatus. The miniculvert apparatus was used to isolate the entrance loss for the outlet pipe by measuring the velocity along the outflow pipe (using PIV) and the HGL (using standpipes and CIS) along the outflow pipe and in the headbox of the miniculvert apparatus. The EGL was calculated by summing the measured HGL and the velocity head. The difference in the EGLs projected to the headwall yielded the energy loss in the outflow pipe (a contraction entrance loss). The main idea of the first step was then to determine if there is a direct correlation between the measured energy loss and the area of maximum contraction in the outflow pipe, often referred to as the vena contracta, as suggested by Morris.(8) Conceptually, the vena contracta is a reduced flow area that conveys most of the through-flow downstream of a contraction. In reality, though, with experimental measurements, the area and the location of the vena contracta is not readily apparent, and the area is highly subjective. The location was determined by taking velocity measurements at several sections, as illustrated in figure 8, to determine where the maximum local velocities occur. Researchers tried several techniques for defining the contracted area and ultimately selected a repeatable technique that measures the area containing a prescribed percentage of the maximum velocities in each cross section.

Figure 12 is an example of a shaded contour plot of the velocity profile at a location along the outflow pipe. The lightest shade of gray in this figure represents all of the velocities that are less than 86.6 percent of the highest velocity in the profile. The three contours near the center, in order from light to dark, represent the velocities greater than 86.6, 90.0, and 92.5 percent of the maximum velocity in the cross section, respectively. Appendix A has an example of the velocity profile at each location along the outflow pipe.

Figure 12. Image. Selected contours of velocity magnitude in the outflow pipe. This computer image is a cross-sectional view of an outlet pipe that shows an area of higher velocity near the center and areas of lower velocity closer to the perimeter.

Figure 12. Image. Selected contours of velocity magnitude in the outflow pipe.

Now consider the following definitions.

Ao

is the cross-sectional area of the outlet pipe (m2).

Ak

is the cross-sectional area associated with a contour of velocity (m2).

K

is the subscript denoting a contour of velocity where V is greater than 86.6, 90, or 92.5 percent.

Eoc

is the energy loss in the outflow pipe (a contraction entrance loss (m)).

Do

is the diameter of the outlet pipe (m).

The relative area, Ak over Ao, enclosed by these three contours was then correlated with the ratio of the outflow energy loss, ∆Eoc, over the diameter of the pipe, Do (equation 17).

Equation 17. The quotient of delta E subscript o c divided by D subscript o equals a function of the quotient of A subscript k divided by A subscript o. (17)

Table 2 shows the distance along the outflow pipe from the culvert (see figure 8) where Ak was used in the calibration, which again was selected based on where the integrated velocity was the largest (i.e., the point closest to the maximum contraction in the pipe). Appendix B shows the contours of maximum velocity that were measured at these locations in each miniculvert run.

Table 2. Distance along the culvert outflow pipe where Ak was measured.

Ak Measured

Miniculvert Experiment

Q/Ao = 42 cm/s

Q/Ao = 57 cm/s

Q/Ao = 69 cm/s

A86.6

0 mm

5 mm

0 mm

A90

0 mm

5 mm

0 mm

A92.5

0 mm

5 mm

0 mm

Figures 13 to 15 show that there is a strong correlation between the contraction energy loss and the contracted-area ratio regardless of which velocity contour was selected for the contracted area. The regression equations shown in figures 13 to 15 can be used to estimate the entrance energy loss for the outlet pipes in the access hole experiments (i.e., using measurements of these areas of maximum velocity).

Figure 13. Graph. Correlation of delta E subscript o c and A subscript 86.6. This is a graph with linear Cartesian coordinates. The vertical axis is delta E subscript o c divided by D subscript o and is dimensionless, ranging from 0 to 0.6. The horizontal axis is A subscript 86.6 divided by A subscript o and is dimensionless, ranging from 0.2 to 0.45. Three data points are shown scattered close to an upwardly curved line. The equation for the line is y equals 16.425 times x superscript 4.0672, and the R squared value is 0.9855.

Figure 13. Graph. Correlation of ∆Eoc and A86.6.

Figure 14. Graph. Correlation of delta E subscript o c and A subscript 90. This is a graph with linear Cartesian coordinates. The vertical axis is delta E subscript o c divided by D subscript o and is dimensionless, ranging from 0 to 0.4. The horizontal axis is A subscript 90 divided by A subscript o and is dimensionless, ranging from 0.1 to 0.45. Three data points are shown scattered close to an upward line. The equation for the line is y equals the product of 1.2026 times x superscript 1.0, all minus 0.1087. The R squared value is 0.9923.

Figure 14. Graph. Correlation of ∆Eoc and A90.

Figure 15. Graph. Correlation of delta E subscript o c versus A subscript 92.5. This is a graph with linear Cartesian coordinates. The vertical axis is labeled delta E subscript o c divided by D subscript o and is dimensionless, ranging from 0 to 0.4. The horizontal axis is A subscript 92.5 divided by A subscript o and is dimensionless, ranging from 0 to 0.3. Three data points are shown scattered close to an upward line. The equation for the line is y equals 1.1868 times x superscript 0.9287. The R squared value is l.

Figure 15. Graph. Correlation of ∆Eoc and A92.5.

The second step in validating the inflow and outflow pipe loss coefficients used the access hole setup to run experiments with scaled conditions similar to four of the original junction loss experiments-labeled JCT114 through JCT117 in Appendix B of the report by Chang et al.(1) When these experiments were rerun using the scaled model, the HGL was measured using standpipes and CIS, and velocity profiles were measured using PIV. The total energy loss across the access hole was measured by summing the measured HGL and the velocity head. Table 3 shows the total energy loss across the access hole in each experiment.

Table 3. Total energy loss across the access hole.

Q/Ao = 43 cm/s

Q/Ao = 57 cm/s

Q/Ao = 64 cm/s

Q/Ao = 75 cm/s

4.1 mm

9.3 mm

14.2 mm

16.3 mm

Similarly, table 4 shows the distance along the outflow pipe (from the access hole) where the maximum contraction and Ak were measured. Appendix C shows contours of maximum velocity that were measured at these locations in each access hole run.

Table 4. Distance along the access hole outflow pipe where Ak was measured.

Ak Measured

Access Hole Experiment

Q/Ao = 43 cm/s

Q/Ao = 57 cm/s

Q/Ao = 64 cm/s

Q/Ao = 75 cm/s

A86.6

5 mm

0 mm

0 mm

0 mm

A90

5 mm

0 mm

0 mm

0 mm

A92.5

5 mm

0 mm

0 mm

0 mm

The energy loss in the outflow pipe (an entrance loss) was then computed using the measured area of maximum velocity and the relationships from figures 13 to 15. Figure 16 shows that the relationship between the computed outflow energy loss and the velocity head is fairly strong. Recalling equation 4, the slope of the line in this figure shows that the outflow (entrance) loss coefficient, Ko, is approximately 0.16, which is remarkably close to Kilgore's estimate of 0.2.

Figure 16. Graph. Outflow (entrance) loss versus velocity head. This is a graph with linear Cartesian coordinates. The vertical axis is Outflow (Entrance) Loss, delta E subscript o c and is in meters, ranging from 0 to 0.01. The horizontal axis is the quotient of the squared quotient of Q divided by A subscript o, divided by the product of 2 times g, and is in meters, ranging from 0 to 0.035. There are twelve data points generally scattered around an upward line. The equation for the line is delta E subscript o c equals the product of 0.1583 times the quotient of the squared quotient of Q divided by A subscript o, divided by the product of 2 times g. The R squared value is 0.4247. The four upper points are labeled 92.5 percent, the four middle points are labeled 90 percent, and the four lowest points are labeled 86.6 percent. This formula is meant to highlight that the slope of the fitted line equals 0.1583.

Figure 16. Graph. Outflow (entrance) loss versus velocity head.

The inflow (exit) loss (∆Ei) was then calculated from the total energy loss (∆Etotal) and the outflow (entrance) loss (∆Eoc) (equation 18).

Equation 18. Delta E subscript i equals delta E script total minus delta E subscript o c.(18)

Figure 17 shows that the relationship between the computed inflow energy loss and the inflow velocity head is strong. Recalling equation 16, the slope of the line in this figure shows that the inflow (exit) loss coefficient, Ki, is approximately 0.43, which is very close to Kilgore's estimate of 0.4.

Figure 17. Graph. Inflow (exit) loss versus velocity head. This is a graph with linear Cartesian coordinates. The vertical axis is Inflow (Exit) Loss, delta E subscript i and is meters, ranging from 0 to 0.015. The horizontal axis is the quotient of the squared quotient of Q divided by A subscript i, divided by the product of 2 times g, and is in meters, ranging from 0 to 0.035. There are twelve data points generally scattered around an upward line. The equation for the line is delta E subscript i equals 0.4319 times the quotient of the squared quotient of Q divided by A subscript i, divided by the product of 2 times g. The R squared value is 0.7733. The four upper points are labeled 86.6 percent, the four middle points are labeled 90 percent, and the four lowest points are labeled 92.5. This formula is meant to highlight that the slope of the fitted line equals 0.4319.

Figure 17. Graph. Inflow (exit) loss versus velocity head.

BASE RUNS

Next in the current lab study, 15 runs in the access hole setup were conducted to test the total energy loss predicted by the new junction loss method. These experiments all had a level outflow pipe, and an inflow pipe oriented at 180°. Table 5 shows the discharge intensities and access hole depths that were maintained in each run. The measured total energy loss across the access hole was then plotted versus the discharge intensity and compared to the total energy predicted by the new junction loss method using Ki equal to 0.43 and Ko equal to 0.16. Figure 18 shows that the new method matches the new lab data very well.

Table 5. Parameters for the 15 base runs.

Run

DI

Average Access Hole Depth (cm)

1

0.71

4

2

0.94

4.45

3

1.05

7.02

4

1.22

10.02

5

1.22

11.05

6

1.03

6.4

7

0.23

7.46

8

0.44

7.51

9

0.44

11.08

10

0.66

5.6

11

0.66

11.01

12

0.89

9.61

13

0.67

7.45

14

0.67

11.2

15

1.09

7.7

Figure 18. Graph. Validation of total energy loss calculations. This is a graph with linear Cartesian coordinates. The vertical axis is Total Energy Loss and is in meters, ranging from 0 to 0.025. The horizontal axis is Discharge Intensity D subscript i equals the quotient of Q subscript o divided by the product of A subscript o times 0.5 power of the product of g times D subscript o; the term is dimensionless, ranging from 0 to 1.6. There are two data series plotted: one is computed from Kilgore's proposed methodology and the other is measured. Each series is represented by an upwardly curved line passing through its data points. The two lines lie almost atop each other.

Figure 18. Graph. Validation of total energy loss calculations.

SUPERCRITICAL OUTFLOW AND ANGLED INFLOW

One of the major limitations of the existing FHWA methodologies is a failure to apply to some steep terrain conditions. The proposed new procedure addresses the problem with steep outflow pipes by defaulting to inlet control equations 7 and 8 to compute the base flow depth in the access hole. Eighteen runs were conducted with supercritical flow in the outflow pipe as part of this lab study to test the applicability of the proposed procedure for steep pipes. These experiments also included three different inflow pipe configurations (i.e., angled inflow). Supercritical flow was assured by using a 3 percent slope for the outflow pipe. Recall also that Ki equals 0.43, and Ko equals 0.16. One surprising result of these tests was an almost constant depth in the center of the access hole for a fairly wide range of discharge intensities. Figures 19 to 21 generally show that the new junction loss methodology does a good job of estimating the EGL elevations in the inflow pipes for supercritical flow situations. The only exception, which Kilgore anticipated, appears to be when one inflow pipe is oriented at 180° with high discharge intensity into a supercritical outflow pipe. Kilgore anticipated that water shooting directly across an access hole in a jet into a supercritical outflow pipe may not expand and contract again in the way that this method predicts.

Figure 19. Graph. Validation of E G L with a 180 degree inflow pipe and supercritical outflow. This is a graph with linear Cartesian coordinates. The vertical axis is E G L elevation of the 180 degree inflow pipe and is in meters, ranging from 0 to 0.16. The horizontal axis is Discharge Intensity, D subscript i equals the quotient of Q subscript o divided by the product of A subscript o times 0.5 power of the product of g times D subscript o; the term is dimensionless, ranging from 0 to 2.There are two data series plotted: one is computed from Kilgore's proposed methodology and the other is measured. Each series is represented by an upwardly curved line passing through its data points. The two lines begin on the left virtually atop each other at low values but diverge slightly with increasing values of discharge intensity. The curve for measured data is slightly lower than the curve for computed values from Kilgore's proposed methodology.

Figure 19. Graph. Validation of EGL with a 180° inflow pipe and supercritical outflow.

Figure 20. Graph. Validation of E G L with a 90-degree inflow pipe and supercritical outflow. This is a graph with linear Cartesian coordinates. The vertical axis is E G L elevation in the 90-degree inflow pipe and is in meters, ranging from 0 to 0.25. The horizontal axis is Discharge Intensity, D subscript i equals the quotient of Q subscript o divided by the product of A subscript o times 0.5 power of the product of g times D subscript o; term is dimensionless, ranging from 0 to 2. There are two data series plotted: one is computed from Kilgore's proposed methodology and the other is measured. Each series is represented by an upwardly curved line passing through its data points. The two lines lie almost atop each other.

Figure 20. Graph. Validation of EGL with a 90° inflow pipe and supercritical outflow.

Figure 21. Graph. Validation of E G L with two inflow pipes and supercritical outflow. This is a graph with linear Cartesian coordinates. The vertical axis is E G L elevation in the two inflow pipes and is in meters, ranging from 0 to 0.2. The horizontal axis is Discharge Intensity, D subscript i equals the quotient of Q subscript o divided by the product of A subscript o times 0.5 power of the product of g times D subscript o; term is dimensionless, ranging from 0 to2. There are two data series plotted: one is computed from Kilgore's proposed methodology and the other is measured. Each series is represented by an upwardly curved line passing through its data points. The two lines lie almost atop each other.

Figure 21. Graph. Validation of EGL with two inflow pipes and supercritical outflow.

PLUNGING INFLOW

The last runs 18 runs tested the method's prediction of energy loss with plunging inflow conditions. The drop in elevation for the inlet, with respect to the base of the outlet pipe, in these runs varied between 3 to 10 times the outflow pipe diameter, and two different access hole depths were maintained (i.e., 1.5Do versus 3.0Do). Recall also that Ki equals 0.43, and Ko equals 0.16. Figure 22 shows that the new junction loss method predicts the EGL in the inflow pipe very well. This figure shows that the measured grade line is about 7 percent greater than what the existing junction loss method predicts.

Figure 22. Graph. Validation of the total energy loss with plunging inflow. This is a graph with linear Cartesian coordinates. The vertical axis is Measured E G L subscript i and is in meters, ranging from 0 to 0.14. The horizontal axis is Computed E G L subscript i and is in meters, ranging from 0 to 0.14. The data is shown as a scatter plot in generally two groups: one centered near x equals 0.06 and y equals 0.06, and the second centered at x equals 0.105 and y equals 0.105. There is a one-to-one line plotted, and the second group of points is slightly above that line indicating that those measured values were slightly higher than the computed values. The Mean Squared Error is 0.0000214 meters.

Figure 22. Graph. Validation of the total energy loss with plunging inflow.

Figures 23 and 24 show that the new junction loss method predicts the EGL in the nonplunging inflow pipe remarkably well over a variety of plunging inflow rates, plunging inlet elevations, and access hole water depths.

Figure 23. Graph. E G L in the inflow pipe versus plunging inflow rate for E subscript a equals 1.5 D subscript o. This is a graph with linear Cartesian coordinates. The vertical axis is E G L elevation in the 180-degree inflow pipe and is in meters, ranging from 0 to 0.08. The horizontal axis is Q subscript k divided by Q subscript o and is dimensionless, ranging from 0.2 to 0.8. Six data series are plotted. Three of the series represent measured data, and three of the series represent data that were computed using Kilgore's proposed method. The three pairs of measured and computed data represent three different values for the dimensionless value Z subscript k divided by D subscript o: 3, 5 and 10. In each series, a point is plotted for x equals 0.25, 0.5, and 0.75. The scatter in the data-up to 0.02 meters-is highest at x equals 0.5. Regression lines for measured versus computed values are atop each other at x equals 0.25 and gradually diverge; at x equals 0.75, the measured regression line is almost 0.01 meters greater than the computed regression line. The regression lines have small upward slopes, and most of the data falls between the y values of 0.05 and 0.07 meters.

Figure 23. Graph. EGL in the inflow pipe versus plunging inflow rate for Ea = 1.5Do.

Figure 24. Graph. Energy grade line in the inflow pipe versus plunging inflow rate for E subscript a equals 3.0 D subscript o. This is a graph with linear Cartesian coordinates. The vertical axis is E G L elevation in the 180-degree inflow pipe and is in meters, ranging from 0 to 0.14. The horizontal axis is Q subscript k divided by Q subscript o and is dimensionless, ranging from 0.2 to 0.8. Six data series are plotted. Three of the series represent measured data, and three of the series represent data that were computed using Kilgore's proposed method. The three pairs of measured and computed data represent three different values for the dimensionless quantity Z subscript k divided by D subscript o: 3, 5 and 10. In each series, a point is plotted for x equals 0.25, 0.5, and 0.75. The scatter in the data-up to 0.02 meters-is highest at x equals 0.5. Regression lines for measured versus computed values are atop each other at x equals 0.25 and gradually diverge; at x equals 0.75, the measured regression line is almost 0.008 meters greater than the computed regression line. The computed regression lines decreases slightly with increasing x value, while the measured regression line has a small upward slope. Most of the data falls between the y values of 0.09 and 0.12.

Figure 24. Graph. EGL in the inflow pipe versus plunging inflow rate for Ea = 3.0Do.

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The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). The hydraulics and hydrology research program at the TFHRC Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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