Library of Congress Cataloging in Publication Data Measurement and computation of streamflow. Geological Survey Water-Supply Paper 2175) Includes bibliographies. Coefficients of discharge for full-width, broad-crested weirs with downstream slops s.1: 1 and various upstream slopes 152. Stage-discharge relation and significant depth-discharge re- lations for l-ft trapezoidal supercritical-flow flume _ _ _ 162.
Stage-discharge relation and significant depth-discharge re- lations for 8-ft trapezoidal supercritical-flow flume. High-flow extrapolation by use of conveyance-slope method-Klamath River at Somes Bar, Calif. Rating curve for hypothetical rectangular thin-plate weir, with shift curves for scour and fill in the weir pool.
Schematic representation of family of stage-discharge curves, each for a constant but different value of fall.
OF STREAMFLOW
VOLUME 2. COMPUTATION OF DISCHARGE
CHAPTER IO.-DISCHARGE RATINGS USING SIMPLE STAGE-DISCHARGE RELATIONS
Even where a single cross section of the channel is the control for all stages, a sharp break in the. The surface of the weir over which the water flows is the crest of the weir. A logarithmic plot of the rating (not shown here) indicates that the equation for all but the very small values of head is.
The tailwater elevation is measured downstream from the turbulence that occurs in the immediate vicinity of the downstream face of the weir. Because we have raised the value of e, the low-water end of the curve will be concave downward. Again, the precise values of the constants in the dis- charge equation are dependent on the geometry of the installation.
The precise values of the constants in the equation will vary with conditions for each installation. The shape of the crest above a stage of 0.7 ft is essentially a flat Vee for which the theoretical exponent of head is 2.5 in the discharge equation.
QII’
The exponent N and the gage height of effective zero flow are influenced, as described above, by the transverse profile of the streambed at the control cross section. Conversely, if the high end of the curve is made a tangent, the low- water end of the curve becomes concave upward. Because the value of e for the upper end of the rating is something less than 2.2 feet, the high end becomes concave downward.
If the high end of the curve is made a tangent, the effec- tive value of e is found to be 0.0 ft. This being too low a value of e for the lower end of the curve, the low end becomes concave upward. If the rating for a section control (low end of the curve) is a tangent, the value of the exponent N is expected to be greater than 2.0.
Inspection of the second difference column shows the second differences to be increasing at the low-water end (section control, N > 21 and decreasing at the high- water end (channel control, N < 2). The conveyance-slope method assumes first that the geometry of the cross-section used for discharge measurements is fairly representa-.
69) where
The discharge under those conditions is a function of both stage and slope of the energy gradient. The length of the reach should be such that ordinary errors that occur in the deter-. The form of the relation depends primarily on the channel features that control the stage-discharge relation.
It is not uncommon for variable backwater to be effective for only part of the time. The discharge under variable backwater conditions may be computed as the product of (a) the discharge Qr from the base rating and (b) the. Compute and tabulate the percentage departures of the plotted QV discharges from the Q, rating curve.
The line of initial submergence shown crossing the lower part of the stage-fall relation has the theoretical position and slope discussed above. Because the river stage rises faster than the stage of the detention pool, fall decreases with stage at the base gage, as shown by the rating-fall curve. That part of the rating that is affected by variable backwater is analyzed as though no section control existed.
If the base gage has a section control, determine the position of the line of initial submergence on the plot of stage versus measured fall. On the basis of the scatter of the plotted points about the curve in step 7, adjust the Q,. On the basis of the scatter of the plotted points about the curve in step 15, adjust the QV and F,.
After having obtained acceptable Q,., F,., and fall-ratio curves, plot adjusted values of the discharge measurements on the Q,. Where the rating-fall curve (stage versus fall) is so well defined, the first estimate of the Q,. Because the stage was rising, the unadjusted discharge would plot to the right of the rating curve.
The use of an unattended standard current meter, securely an- chored in a fixed position in the stream below the minimum expected stage, is attractive because of the simplicity of the device. The deflection meter has a submerged vane that is deflected by the force of the current. The amount of deflection, which is roughly pro- portional to the velocity of the current impinging on the vane, is transmitted either mechanically or electrically to a recorder.
Values of the mean velocity of the stream are determined from discharge measurements, and mean velocity is then related to deflection and stage. The force of the current acting on a vertical-axis vane turns the vertical shaft and the motion is transmitted to a graphic or digital. In addition, removal of the vane for service and repair is difficult because of the weight involved.
Furthermore, the projection of the vane assembly above the water surface makes it susceptible to damage by ice. This type is designed to overcome many of the difficul- ties mentioned in connection with the vertical-axis vane. The force of the current acting on the horizontal-axis vane causes it to deflect.
The velocity curve shows the relation of deflection units to measured mean veloc- ity in the channel; stage was not a factor in the relation because of the limited range (2 ft) in stage. The deflection meter at the station is of the vertical-axis type and is equipped with vane A (fig. 202) to measure deflection at a. Acoustic velocity meters operate on the principle that the velocity of sound propagation through a fluid in motion is the alge- braic sum of the fluid velocity and the acoustic propagation rate through the fluid.
Measurement of the water velocity is possible because the velocity of a sound pulse in moving water is the algebraic sum of the acoustic propagation rate’and the component of velocity parallel to the acous- tic path. Reference is made to figure 211 in the following derivation of the mathematical relations of the system. In the continuing discussion of “Theory”, equation 96 will be used with the understanding that C, = 1.00 in some of the acoustic- velocity meter systems.
The effect of path orientation will now be examined for one of the AVM systems used in the U.S.A. In the installation of an AVM system, consideration must be given to the factors that affect the propagation of the acoustic signal through the water. When the acoustic path is located near the water surface or near the streambed, part of the acoustic signal will be reflected from the boundary (air-water interface or streambed).
The degree of attenuation of signal strength caused by the reflec- tion and scatter of the acoustic signals from sediment particles sus- pended in the stream has not been fully documented. The effect of aquatic weeds in the acoustic path is variable, depend- ing on the location and density of the weed growth. Weed-covered sites and sites where air bubbles are entrained in the water should be avoided in selecting an acoustic path because of the likelihood of signal attenuation.
For a given field strength the magnitude of the induced voltage is proportional to the velocity of the conductor. The discharge of the river could not be related to stage or to stage and slope. The electromagnetic probe is mounted on a structure attached to the upstream end of a bridge pier in the center of the stream.
In accordance with Fara- day’s law of electromagnetic induction, the equation relating the length of the conductor moving in the magnetic field to the emf that is generated, is. V is average velocity of the river water, in meters per second, and b is river width, in meters. The trench in which the coil is laid roughly follows the contours of the bed and banks to minimize the effect of variation in the velocity profile.
The probes are used to detect the electromotive force induced in the mov- ing water and to define precisely the cross section of the measurement area. Such materials as aquatic vegetation and bed and bank sediments streamward from the probes are included in the size of the. The principles underlying the computation of discharge have been discussed in the subsection on theory of the integrated-velocity index.
CHAPTER IS-DISCHARGE RATINGS FOR TIDAL STREAMS
