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(pools and riffles). The boundary shear stress, z, is the force per unit bed area acting in the direction of flow, 2=pgRSe (3) where p is the density of water, g is the gravitational acceleration, R is the hydraulic radius, and Se is the slope of the energy grade line, also termed the friction slope. In channels with a high width-depth ratio, R is approximately equal to the mean flow depth, h, hence these variables are often used in place of each other. Assuming p and g are constant, (3) shows that r varies with the product of R and Se . Both R and Se may vary with discharge, however, not necessarily in the same direction. As discharge increases, R generally increases; however, SQ may increase, decrease, or stay the same, depending on the topography of the channel reach. Undulations in the bed caused by pools and riffles force the water to accelerate (or decelerate), producing a net fluid force in addition to the weight of the water moving downstream. The effects of these flow accelerations are accounted for in the one dimensional equation for gradually varied flow, which can be written as follows, 2 Se=-a =-d z + h + g (4) dx ? where Se is the energy gradient (also called the friction slope), H is the total energy, z is the average bed elevation, h is the average flow depth (approximately equal to R), and u2/2g is the velocity head. The first term on the right hand size of (4), dz/dx, is the bed slope, which may be either positive or negative. The second term, dh/dx, is the water surface slope, which also can be positive or negative. These two terms are typically of the same magnitude, thus they are both important, but they can be of opposite sign, in which case their effects on the friction slope and shear stress can offset each other. Together, the first two terms, dz /dx and dh /dx, represent the streamwise gradient in gravitational potential energy. The third term, d(u2/2g)1dx, represents the 21