Specific force
Specific force is the horizontal force of flowing water per unit weight of water. It is derived from the momentum equation. A specific force curve looks similar to the specific energy curve. The critical depth occurs both at the minimum energy for a given discharge and also at the minimum specific force for a given discharge. This similarity shows how energy concepts and force or momentum concepts can be employed similarly in many hydraulic analyses, often with nearly identical results.
The designer should know what circumstances would cause the two approaches to diverge, however. Specific force concepts are applied over short horizontal reaches of channel, where the difference in external friction forces and force due to the weight of water are negligible. Examples are the flow over a broad-crested weir through a hydraulic jump or at junctions. One way to conceptualize why a momentum-based method, rather than an energy-based method, might be more applicable would be to energy changes in a hydraulic jump. Much energy is lost through turbulence caused by moving mass colliding with other mass that is not accounted for by energy principles alone.
An equation for specific force may be derived from the momentum equation. If the practitioner wishes to apply this equation to short sections of channel such as a weir or hydraulic jump, the frictional resistance forces, Ffr can be neglected. With a flat channel of low slope, θ approaches 0, then the last two terms in equation 12 can be dropped. As a result, equation 11 becomes:
Assume also that the Boussinesq coefficient (β) is 1. From the fact that the pressure increases with depth to the maximum of ρgy at the channel bottom (y being depth, b being channel width, and ρ being fluid density), the overall pressure on the vertical flow area may be expressed as 1/2ρgby2. The velocities may be expressed as Q/A. For a rectangular channel:
that becomes:
For a channel section of any other shape, the resultant pressure may be taken at the centroid of the flow area, at a depth, z, from the surface. Then the momentum formulation is:
Either side of this equation is the definition of specific force, and the specific force is constant over a short stretch of channel such as a hydraulic jump. The first term represents change in momentum over time, and the second term the force of the water mass. As Chow (1959) explains, specific force is sometimes called force plus momentum or momentum flux.