Hydrostatic force on a vertical gate

Water stands 3 m deep against a vertical gate 2 m wide, with the free surface at the top of the gate. Taking the specific weight of water as 9.81 kN/m³, find the resultant force on the gate and its line of action.

Given

Specific weight of water
Depth of water
Gate width

Solution

  1. 1.Resultant of the triangular pressure distribution
  2. 2.It acts at the centroid of the pressure triangle, above the bottom

Answer

F_R = 88.29 kN, acting 1 m above the bottom of the gate (2 m below the surface).

Worked in ProveCalc

The fluid pressure load in the free body diagram applies the same γ·depth pressure to the face and solves the gate's supports with it, so the resultant is checked against the hinge reactions.

The results above were evaluated by ProveCalc's compute engine (SymPy and Pint), the same engine the desktop app runs on your machine.

Civil engineeringMechanical engineering

Related examples

Buy once, own it forever

$200 one time. No subscription, no renewal, and the version you bought keeps working.

No connection needed

Works offline. The only network use is checking for updates and a one-time activation check.

AI-native, never required

The assistant drafts on the same worksheet you work on. You can do everything without it, and it never does the math: the engine does, with units, and checks it.

Try it in the browser$200 once, yours forever
Hydrostatic Force on a Vertical Gate: Resultant and Center of Pressure | ProveCalc