Solved Problems

Example

Problem: A rectangular gate 2 m wide and 3 m high is vertical and submerged. Its top edge is 1 m below the water surface. Find the total hydrostatic force and the location of the center of pressure.

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Example

Problem: A circular gate of diameter 1.5 m is inclined at 6060^\circ to the horizontal. The top edge of the gate is 2 m below the water surface. Calculate the hydrostatic force and the center of pressure.

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Example

Problem: A curved surface is in the shape of a quarter cylinder with radius R=2R = 2 m. The length of the gate (into the screen) is 1 m. Water stands to the top of the gate. Find the horizontal and vertical components of the force.

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Example

Problem 4: Force on an Inclined Rectangular Gate A rectangular gate 2 m2 \text{ m} wide and 3 m3 \text{ m} high is submerged in water at an angle of 3030^\circ to the vertical. The top edge is 1 m1 \text{ m} below the water surface. Calculate the total force acting on the gate and the location of the center of pressure.

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Example

Problem 5: Force on a Submerged Triangular Plate A triangular plate with base 2 m2 \text{ m} and height 3 m3 \text{ m} is submerged vertically in water with its base at the water surface. Calculate the total hydrostatic force and the center of pressure.

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Case Study 1: Tainter Gates in Spillways

Context: Tainter gates (radial gates) are commonly used in dam spillways to control water flow.
Application: A Tainter gate is a segment of a cylinder. The hydrostatic force acts normally to the curved surface at all points. Because all these normal forces pass through the center of curvature of the gate, the resultant hydrostatic force produces zero moment about the pivot point (trunnion). This ingenious design means the only force required to open or close the gate is that needed to overcome the gate's weight and trunnion friction, making it highly efficient for controlling large volumes of water.

Case Study 2: Sluice Gates and Flow Control

Context: Vertical or inclined sluice gates are critical for regulating flow in irrigation channels and sewers.
Application: The design of a sluice gate must account for the immense horizontal hydrostatic force pushing against it, which translates to high frictional forces in its guide slots. To lift the gate, the lifting mechanism must overcome both the dead weight of the gate and this frictional resistance. Engineers often incorporate rollers or use low-friction materials to manage these forces, ensuring the gate can be operated reliably during varying flow conditions.