The term dH/dx is the slope of the energy grade line. It is always a negative quantity because the total head reduces in the direction of the flow, or Sf=-dH/dx. Similarly, the term dz/dx is the slope of the channel bed. It is negative when the elevation of the channel bed reduces in the direction of the flow; it is positive when the elevation of the channel bed increases in the direction of the flow. In general, we may write S0=-dz/dx. Rearranging the equation gives:
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