and depth, and if the stream bottom is smooth, 

 no interchange should occur. If gradient, 

 permeability, or bed depth vary in the direc- 

 tion of intragravel flow, however, interchange 

 should occur. Each of the three variables may 

 cause a change in total intragravel flow inde- 

 pendently of the others. 



D'Arcy's law of flow related fluid flow 

 velocity in a porous gravel bed to permeability 

 and the energy change within the bed, viz.. 



V = 



k (Ah) 



(1) 



where V is the average flow velocity, k the 

 gravel permeability and Ah the loss in specific 

 energy through the bed length L (Scheidegger, 

 1957; King and Brater, 1954). To describe the 

 flow of water within a streambed, the energy 

 change and bed length may be combined, giv- 

 ing. 



V = - k sin e 



(2) 



where e is the angle of the energy line, that 

 is, the rate at which energy is lost in the 

 direction of flow (American Society of Civil 

 Engineers, 1949). 



In the discussion that follows it will be as- 

 sumed that the energy line and stream surface 

 profile or hydraulic gradient are approxi- 

 mately equal, that is, they have the same 

 slope and curvature. In extreme cases, for 

 instance hydraulic jump, slopes of the energy 

 line and stream profile differ greatly; how- 

 ever, cases to be considered here are as- 



sumed to have nearly uniform flow. Hence, 9 

 will be the slope of the stream surface pro- 

 file in the direction of intragravel flow. Per- 

 meability, defined by equation (1), is the 

 property of gravel permitting fluid flow and 

 is affected by gravel particle size, size dis- 

 tribution, porosity, organic content, and par- 

 ticle shape. 



Consider the intragravel channel of unit 

 width and depth, the upper face of which is 

 the gravel surface and the bottom face and 

 sides of which are impermeable boundaries. 

 Axial flow within this channel follows the con- 

 tinuity equation (Lapple, 1951). 



W = Ap V 



(3) 



where W is the mass flow rate (weight of 

 water flowing per unit time), A the channel 

 cross-section area, p the water density, and 

 V the average intragravel velocity. By sub- 

 stitution of equation (2) in (3) 



W = - k Ap sin e 



(4) 



Since the channel cross-section area is as- 

 sumed to be constant, any increase in mass 

 flow rate must enter the channel by inter- 

 change across the gravel surface. 



Interchange may be measured by the vari- 

 able, I, the flow rate of stream water entering 

 the gravel per unit area of gravel surface. 

 The interchange flow into the intragravel 

 channel must equal the change of axial intra- 

 gravel flow, W. Considering flow along an 

 increment of length, A L (fig. 3), (intragravel 



Stream bottom *%, ^ ^ 



V. "c^r^ 



Interchange 



Figure 3. --Interchange and intragravel flow to a channel section. 



4 



