Momentum–depth relationship in a rectangular channel Momentum–depth relationship in a rectangular channel In classical physics, momentum is the product of mass and velocity and is a vector quantity, but in fluid mechanics it is treated as a longitudinal quantity (i.e. one dimension) evaluated in the direction of flow. Additionally, it is evaluated as momentum per unit time, corresponding to the product of mass flow rate and velocity, and therefore it has units of force. The momentum forces considered in open channel flow are dynamic force – dependent of depth and flow rate – and static force – dependent of depth – both affected by gravity. The
Mass flow rate product is as follows. The only mass flowing "through" the cross-section is the amount normal to the area, i.e. parallel to the unit normal. This amount is: where "θ" is the angle between the unit normal formula_4 and the velocity of mass elements. The amount passing through the cross-section is reduced by the factor formula_5, as "θ" increases less mass passes through. All mass which passes in tangential directions to the area, that is perpendicular to the unit normal, "doesn't" actually pass "through" the area, so the mass passing through the area is zero. This occurs when "θ" = "π"/2: