This walkthrough shows how to use FlowStudio ’s sluice gate (rectangular channel) worksheet: upstream pool depth from specific energy, downstream gradually varied flow, and—when the case allows— hydraulic jump placement plus an empirical jump length (SI units). Open FlowStudio → https://flow.syncster.dev What you are solving A bottom sluice in a wide rectangular channel passes a discharge Q . The worksheet assumes a contracted depth at the vena contracta, y 2 = C c a , where a is gate opening and C c is a contraction coefficient (often near 0.6–0.65). From specific energy matching between the upstream pool and the contracta—together with a check against uniform normal depth y n for the approach channel—the sheet finds upstream pool depth y 1 . Downstream, it integrates Manning-based gradually varied flow from the gate. If the contracta is supercritical and you set a subcritical tailwater y t (or...
This walkthrough shows how to find normal depth in a trapezoidal open channel when you know discharge , geometry , Manning’s n , and bed slope —using FlowStudio ’s trapezoidal open-channel worksheet (uniform flow, SI units). Open FlowStudio → https://flow.syncster.dev What you are solving In uniform flow , depth and velocity stay constant along a long prismatic reach. Manning’s equation links discharge to geometry and resistance. For a trapezoid with bottom width b and side slope z (horizontal to vertical, H:V), flow area and wetted perimeter depend on water depth y . If Q , b , z , n , and S are given, there is a unique normal depth y that satisfies Manning for that discharge (within physical limits). FlowStudio uses the standard relations: area A = y ( b + zy ), wetted perimeter P = b + 2 y √(1 + z ²), hydraulic radius R = A / P , then V = (1/ n ) R 2/3 S 1/2 and Q = VA . It also reports t...