AMERICAN JOURNAL OF SCIENCE VOL 251 AUQUST1953 PP 606 6241 DOWNSTREAM CHANGE O F VELOCITY IN RIVERS LUNA B LEOPOLD ABSTRACT Because river slope generally decreases in a downstream direction it is generally supposed that velocity of flow also decreases downstream Analysis of some of the large number of velocity measurements made at stream gaging stations demonstrates that mean velocity generally tends to increase downstream Although there are many reaches in nearly all rivers where mean velocity decreases downstream the general tendency for conservation or for downstream increase was found in all data studied Computations of bed velocity indicate that this parameter also tends to increase downstream Near the streambed shear in the vertical profile of velocity rate of decrease of velocity with depth tends to decrease downstream This downvalley decrease of shear implies decreasing competence downstream GENERALSTATEMENT ECAUSE rivers tend t o be steep in their headwaters and flow at flat gradients near their mouths it appears logical to suppose that the stream velocities are great in the headwaters and decrease downstream Yet the engineer who actually measures stream velocities for purposes of computing the water discharge uses the same current meter for a measurement in a small brook as in the Mississippi River T h e velocities t h a t he measures a r e not sufficiently different in small headwaters and downstream reaches to furnish any obvious indication of a definite pattern of organization in the data The purpose of the present paper is t o organize some of the large amount of available data on river velocities so t h a t the downstream change may be evaluated B DATA O N RIVER V E L O C I T Y There are more than 6000 gaging stations in the United States Records on many streams are more than 50 years in length A t each station periodic measurements of discharge are made by use of a current meter T h e discharge on other days is determined indirectly from the recording chart o r daily readings of stage water surface elevation 606 Downstream Change of Velocily in Rivers 607 When a river measurement is made by current meter the water speed is measured at about 20 to 30 verticals across the section and usually a t t w o depths in each vertical From these direct measurements the form of the river cross section may be plotted as well as an approximate pattern of the vertical and horizontal distribution of velocity I n stream gaging practice the mean velocity is not a simple average of the velocity measurements made at various positions across the stream T h e current meter placed in a given position in the cross section measures the downstream movement of the water in a given interval of time T h e metering thereby defines a prism of water whose width and depth are known and whose downstream dimension is represented by the measured movement T h e volume of the prism that passed the meter during the measured time interval represents the discharge in units of volume per unit time as denoted by the identity Q aV where Q is discharge in cubic feet per second a is cross sectional area in square feet and V is velocity in feet per second T h e total discharge past the cross section is the sum of the discharges represented b y the individual prisms T h e total discharge having been obtained in this way the mean velocity used in hydraulic practice is an expression of the velocity of a single rectangular prism having the same crosssectional area as the stream This mean velocity is defined as the quotient of the discharge in the cross section divided by the cross sectional area of flowing water Arithmetically the mean velocity so defined is equivalent to a weighted mean in which the velocities of the individual prisms are weighted by the cross sectional area of the respective prisms Owing t o the distribution of the velocity with depth the mean velocity is closely equal t o t h a t existing a t a position 0 6 of the distance from the water surface t o the streambed It is recognized Rubey 1938 p 129 t h a t the mean velocity in the cross section is not the most meaningful velocity with respect t o sediment transport Direct measurements of the bed velocity however it may be defined are not possible at present On the other hand a large fund of measurements of mean velocity exists It appears instructive t o examine the downstream change of t h a t velocity parameter for which meas 608 Luna B Leopold urements exist recognizing that the parameter mean velocity is not ideal f o r discussing geomorphic progresses I n a later section downstream changes of a computed bed velocity will be presented As indicated previously velocity in a stream is a conservative quantity Even the maximum point velocity maximum at any point in the cross section does not ordinarily greatly exceed the mean velocity f o r the cross section An unpublished study by the Geological Survey of 2950 measurements of maximum point velocity values from a variety of rivers showed a median value of 4 11 f t per sec mean of 4 84 f t per sec and less than one per cent of the total exceeded 13 f t per sec The largest value of maximum point velocity in a natural river channel ever measured by stream gaging personnel of the U S Geological Survey was about 22 f t per sec Approximately this value was measured on several occasions Brazos River at Waco Texas Sept 27 1936 Canadian River near Newcastle Okla May 4 1941 New River at Caperton W Va Aug 1940 Potomac River a t Washington D C May 14 1932 F L O W DURATION A N D FLOOD F R E Q U E N C Y I n order t o compare the mean velocity in a small headwater tributary with t h a t in a large trunk stream it is necessary t o establish a basis of comparability It would be meaningless t o compare the velocity during a flood flow a t one point on a river with that of a low flow at some other point T h e two points t o be compared must both be experiencing flood flow or must both be experiencing low flow T h e relative magnitude of flow is discussed in hydrologic practice by the use of the flood frequency concept If the mean flow for each day of record a t a station is tallied in categories of size the number of days on which each category of size is equaled or exceeded may be counted The number of days in each category may be accumulated from the largest category to the smallest and divided by the total number of days T h e resulting quotients represent the percentage of the total days each given discharge is