FLOOD03637 - Laserfiche WebLink

Home Browse Search

.. 1680 .. OCTOBER 1973 ENERGV:'l:EAM POWER, AND UNIT STREAM POWER HY10 Gilbert (6), among others, hypothesized that the potential energy loss between two stations was used up in overcoming the flow friction and transporting sediment between these two stations. Thus, it was concluded that a clear stream flow would have a larger energy slope and therefore. according to the Chczy formula. a faster velocity than a comparable one carrying sediment. Examples cited by Yanoni and Nomicos (34) provided both positive and negative evidence that Gilbert's hypothesis could be accepted. This contradictory evidence indicates that energy may not be a good parameter for the study of sediment transport. Stream power, defined as the time rate of potential energy expenditure per unit bed area, was used by Bagnold (1) [or the calculation of sediment discharge, Although Bagnold's approach is still subject to criticism (7), his study clearly demonstrates that a stream's ability to transport sediment depends on its available power not on its available energy. Through his studies in stream morphology (24.37.38.39). Yang (40) concluded that the unit stream power, defined as the time rate of potential energy expenditure per unit weight of water in an alluvial channel, is the dominant factor in determining total sediment concentration or vice versa. The relationship between unit stream power and total sediment concentration can be expressed by f log C, = a + i3 log (VS - V"S) . . . . . . . . . . . . . . . . . . . . . . . . (I) in which C/ == total sediment concentration; VS = unit stream power; VcrS = critical unit stream p,O)wer required at the incipient motion; VS - VcrS = effective unit stream power; and ex, j3 = parameters. Eq. 1 was verified by 1,225 sets of laboratory data and 50 sets of field data. Most of these data showed a correlation coefficient of 0.98 or higher, and a standard error of estimate of O. t or less with the computed results from Eq. 1. There are two major drawbacks in Eq. I. First, V crS is not related to sediment and flow characteristics. but is determined by regression analysis which gives the least deviation of the calculated results from measurements. Secondly, Eq. I is not dimensionally homogeneous, Le., Cf is dimensionless, yet VS has the dimension of power per weight. The present paper aims to improve these two drawbacks. and to explore further the concept of unit stream power. INCIPIENT MOTION The determination of incipient motion is important not only to the study of sediment transport but also to the design of a stable channel and other hydraulic engineering work. Most engineers use either critical shear stress, or critical average velocity as a criterion for incipient motion. Using the modem concept of boundary layer theory and fluid mechanics, Shields (22) published his famous diagram for critical shear stress. Although most people (20) prefer Shields diagram to other criteria, considerable dissatisfaction with this shear stress criterion can be found in literature (2,11,14). The writer would like to point out the following facts for consideration. I. The justification for selecting shear stress instead of average velocity is based on the existence of the universal velocity distribution law which facilitates - computation of the shear stress from shear velocity and fluid de'-. Theoretically, water depth does not appear to be related directly to the shear stress calculation while the mean velocity is a function of water depth. However, in common practice. the shear stress is replaced by the average shear stress or tractive force,. = 'Y DS, in which 'Y = specific weight of water; D = water depth; and S = energy slope. In this case, the average shear stress is not independent of the water depth. 2. Although by assuming the existence of a universal velocity distribution law, the shear velocity or shear stress is a measure of the intensity of turbulent fluctuations (2 I), our present knowledge of turbulence is limited mainly to laboratory studies. 3. Shields derived his criterion of incipient motion by w~ing the concept of laminar sublayer. According to that theory, the laminar sublayer should not have any effect on the velocity distribution when the shear velocity Reynolds number is greater than 70. However, the Shields diagram clearly indicates that his dimensionless critical shear stress still varies with shear velocity Reynolds number when the latter is greater than 70. 4. Shields extends his curve to a straight line when the shear velocity Reynolds number is less than 3. As shown by Uu (14). this means that when the sediment particle is very small. the critical tractive force is independent of the sediment size. However. White (35) has shown that for a small shear velocity Reynolds number, the critical tractive force is proportional to the sediment size. 5. It is not appropriate to use both shear stress,. and shear velocity U. in Shields diagram as dependent and independent variables, because they are interchangeable by U. ~ v;;P in which p = density of fluid. Consequently. the critical shear stress cannot be determined directly from Shields diagram; it must be determined through trial and error. 6. Shields simplifies the problem by neglecting the lift force and considers the tangential force only. The lift force cannot be neglected especially at a high value of shear velocity Reynolds number. 7. Because the rate of sediment transport cannot be uniquely determined by shear stress (3,40), it is questionable whether critical shear stress should be used as the criterion for incipient motion for the study of sediment transport. INCIPIENT MOTION o -' .j ; ~ d 1 ; ~ Ii 11 1 In view of the preceding facts. the writer doubts that the Shields diagram is the best criterion for incipient motion. The forces acting on a spherical sediment particle at the bottom of an open channel are shown in Fig. 1. For most natural streams, the channel slopes are small enough so that the component of gravitational force in the direction of flow can be neglected as compared with other forces acting on a spherical sediment particle. The drag force can be expressed by 1Td2 P FD= CD--V~ 4 2 . . . . . . . (2) in which CD = drag coefficient at velocity Vd; d = particle diameter; p = density of water; and V d = local velocity at a distance, d, above the bed. The terminal fall velocity of a spherical particle is reached when there is a balance between drag force and submerged weight of the particle, i.e., when ~,;