page_title: Momentum–depth relationship in a rectangular channel
section_title: Application of the momentum function equation to evaluate the thrust force on a sluice gate
hierarchical_section_title: Momentum–depth relationship in a rectangular channel / Application of the momentum function equation to evaluate the thrust force on a sluice gate
caption_attribution_description: English: dynamic force acting on a sluice gate
context_page_description: 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 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 principle of conservation of momentum in open channel flow is applied in terms of specific force, or the momentum function; which has units of length cubed for any cross sectional shape, or can be treated as length squared in the case of rectangular channels. Although not being technically correct, the term momentum will be used to replace the concept of the momentum function. The conjugate depth equation, which describes the depths on either side of a hydraulic jump, can be derived from the conservation of momentum in rectangular channels, based upon the relationship between momentum and depth of flow.
context_section_description: The momentum equation can be applied to determine the force exerted by water on a sluice gate (Figure 7). Contrary to the conservation of fluid energy when a flow encounters a sluice gate, the momentum upstream and downstream of the gate is not conserved. The thrust force exerted by water on a gate placed in a rectangular channel can be obtained from the following equation, which can be derived in the same way as the conservation of momentum equation for rectangular channels:
  Where:
  Fthrust-gate = force exerted by water on the sluice gate (ML/t²)
  γ  = specific weight of water (M/L²t²)
  ΔMᵤₙᵢₜ = difference in momentum per unit width between the upstream and downstream sides of the sluice gate (L²).
caption: Figure 7: Force on a Sluice Gate (simplified version)
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