Vízügyi Közlemények, 1970 (52. évfolyam)

4. füzet - Rövidebb közlemények és beszámolók

that f

c for —- = const, values, is a hyperbolical function of the y2lo g

—1/3 relative roughness D/d. Furthermore as will be perceived from Eq. (8) the resistance coefficient fc depends also on the slope S in a manner that for = const. ^,2/3 g—1/3 values, the relationship between f

c and S is a parabolical one. It should be noted in this connection that for the boundary condition of dune formation a three-variable family of curves, similar to the relationships expressed by Eqs. (7) and (8), can be plotted. The relationships mentioned above apply only to a sediment having a specific gravity y\ = 2,65 p/cm

3, since the experimental results available have been obtained using a similar sediment. As a results of further investigations the critical mean velocity could also be expressed in terms of the relative roughness D/d, and of the value . With D denoting the water depth and o' — — —, the V

21

3 g m ' • Q

w numerical form of these relationships, expressed with the help of dimensionless numbers is v

c YgÔQ' — tc2 = 1,7 ff)-* 405 (9) V id I

0'

3

4 c ~*

е

2 = 0,085 — — (10) YgDQ> ' U

2/

3r Since all experiments were run using a sediment with a specific gravity y\ = 2,65 p/cm

3, or in the vicinity thereof, the validity of Eqs. (9) and (10) is also limited to a specific gravity of 2,65. An additional drawback of these two expressions is that for a given sediment material and water depth the critical value of the slope at which the critical mean velocity v

c defined by these relationships results, must be determined by successive approximation. By introducing the shear velocity U

, — gDS the critical mean velocity is defined also by the three-variable numerical relationship (- d rpr (11) U

2/

3g1/

3J UJ As indicated by the above expression, for ^ = const, values vJU, ^,2/3 g—1/3 is in a parabolical relationship with the relative roughness D/d. — = 0,000044 u, 16