Specific Force and Momentum

 

Conservation of linear momentum provides a third principle, in addition to continuity of mass and conservation of energy, that is used to solve open channel flow problems.

The momentum principle states that all forces acting on a system result in a change of momentum in the system. For fluid flow those forces include; pressure in the downstream direction, weight in the downstream direction, pressure in the upstream direction, and friction in the upstream direction. The momentum at a cross section can be defined as the product of mass flow rate and the velocity.

Momentum = (Mass flow rate) x (Velocity)

The expression of momentum is a function made up of two terms: The momentum of flow passing through a channel section per unit time per unit weight of water and the second is the force per unit weight of water. The sum is known as Specific Force:

Where

M = specific force,

Q = flow rate,

A = cross sectional area of flow,

zbar  = distance from the water surface to the centroid of the cross sectional area of flow

 

Momentum principles can be applied to situations that deal with a high loss of internal energy, like hydraulic jumps, which cannot be evaluated with the energy principles alone.