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Publication Number: FHWA-RD-06-138
Date: October 2006
Effects of Inlet Geometry on Hydraulic Performance of Box Culverts
CHAPTER 4. DATA ACQUISITION AND DATA ANALYSIS PROCEDURES
This chapter describes the data acquisition system used for the culvert study and explains the data analysis procedures.
DATA ACQUISITION FOR CULVERT SETUP
The pressure sensors installed to measure the hydraulic grade line (HGL), the flow meters to gauge discharge, and the tailgate control for the culvert setup were linked to a National Instruments FieldPoint® system, a modular distributed input/output system. FieldPoint is designed for measurement, control, and data logging applications that require reliable, rugged systems involving diverse sensors and actuators located centrally or spread over large distances. FieldPoint also provides the flexibility to choose an open, standard networking technology such as Ethernet, serial, or wireless that best suits an application. At the FHWA Hydraulics Laboratory, wireless networking technology is used to integrate Fieldpoint into the lab data acquisition system. National Instruments’ LabVIEW® graphical development software provides the tools to create measurement and control applications for FieldPoint.
The pressure sensors were Baumer Sensopress Type PCRD D015.14C.B110. The maximum pressure that can be applied to the sensor is 10 kPa (100 millibars or a 39-inch water column). For inlet control tests, only the tailbox pressure sensor readings were analyzed. For outlet control tests the pressure sensor readings in head, barrels, and tailbox were evaluated. To verify the pressure sensor data in the barrels, four standpipes per barrel were installed. Pressure sensors were mounted on the bottom of the standpipes. In addition to the pressure sensors, a scale attached to a side of the standpipes was used for manual readings of the water column in the standpipes. Scales were also mounted in the head and tailbox to validate the electronic readings.
Data management and data analysis were performed using the LabVIEW graphical programming technique for building applications such as testing and measurement, data acquisition, instrument control, data logging, measurement analysis, and report generation. LabVIEW programs are called virtual instruments (VIs) because their appearance and operation imitate physical instruments such as oscilloscopes and multimeters. Every VI uses functions that manipulate input from the user interface or other sources and displays that information or moves it to other files or other computers.
Figure 21 shows the calculation procedure used to obtain inlet performance curves, inlet coefficients, and outlet coefficients.
Figure 21. Diagram. Data management flow chart.
DATA ANALYSIS FOR INLET CONTROL TESTS
Using the equation in figure 14 in the preceding chapter as a regression equation, inlet control coefficients K and M for unsubmerged flow conditions were derived directly from performance curve data. For submerged flow, the terms c and Y were derived using the equation in figure 15 as a regression equation.
When a full sequence of trial data was collected (ideally five unsubmerged and five submerged trials), the regression analysis was done using the nonlinear Levenberg-Marquardt fit algorithm in LabVIEW to determine the set of coefficients that minimized the chi-squared quantity (figure 22).
Figure 22. Equation. Regression analysis, chi-squared.
In this equation, xi and yi are the input data points, f(xi; a1,…aM) is the nonlinear function, and a1,…aM are coefficients. If the measurement errors are independent and normally distributed with a constant standard deviation σi = σ, the equation gives the least square estimation.
In addition to the proposed inlet coefficients (K, M, c, Y), fifth-order polynomials for inclusion in future updates to HDS-5 were derived to fit the unsubmerged and submerged data points (figure 23).
Figure 23. Equation. Fifth-order polynomial for HW⁄D.
The coefficients a through f are the polynomial coefficients. The other terms have been previously defined.
The best-fit coefficients were calculated using LabVIEW’s general polynomial fit virtual instrument, which is based on the least squares procedure to estimate the best fit.
DATA ANALYSIS FOR OUTLET CONTROL TESTS
Outlet control entrance loss is just one component that is added to friction and outlet losses to relate headwater elevations to tailwater (TW) elevations. Data from outlet loss experiments require careful scrutiny to avoid reporting unreasonable results. The entrance loss coefficient, Ke, for outlet control was computed from the relationship in figure 19 in the preceding chapter. Figure 19 is rearranged in figure 24.
Figure 24. Equation. Entrance loss coefficient.
HLe is the entrance loss component that is usually computed for the design situation but is measured in the lab to compute Ke.
The technique used to measure HLe illustrated in figure 25 involved extrapolating energy grade lines (EGLs) in the headbox and in the culvert barrel to a common plane and taking the difference in the EGLs at that common plane. Standard practice is to report an average design value of Ke that is a function of the inlet type only.
For higher discharge intensities, when the culvert barrel was at or near full, the computed Ke values were reasonably constant to warrant reporting an average value for design purposes. For the lower discharge intensities, when the culvert barrel was partly full throughout, the Ke values scattered considerably. This scatter was the result of the velocity head being very small and approaching zero for the very low discharges. In addition, HLe was sensitive to the extrapolation process and to the flow distribution in the multiple barrels that pushed the resolution limits of the pressure transducers (figure 26). The difficulties of the extrapolation process for low flows justified splitting Ke into an unsubmerged and a submerged coefficient.
Figure 25. Diagram. Technique to determine HLe.
Figure 26. Graph. Typical behavior of Ke versus discharge intensity.