Problem 1: Vertical Rectangular Gate

A vertical rectangular gate is $2\text{ m}$ wide and $3\text{ m}$ high. Its top edge is $1\text{ m}$ below the water surface. Determine the hydrostatic force and center-of-pressure depth.

Problem 2: Inclined Circular Gate

A circular gate has diameter $1.5\text{ m}$ and is inclined $60^\circ$ above horizontal. Its top edge is $2.0\text{ m}$ below the water surface. Determine the force and center of pressure.

Problem 3: Vertical Triangular Plate

A triangular plate has a horizontal base $2\text{ m}$ wide at the water surface and a downward-pointing height of $3\text{ m}$. Find the hydrostatic force and center of pressure.

Problem 4: Horizontal Inspection Hatch

A horizontal rectangular hatch measures $1.2\text{ m}$ by $0.8\text{ m}$ and lies $4.5\text{ m}$ below a water surface. Determine the hydrostatic force and its point of application.

Problem 5: Inclined Rectangular Gate

A $2\text{ m}$ by $3\text{ m}$ rectangular gate is inclined $60^\circ$ above horizontal. The top edge is $1\text{ m}$ below the water surface. Find the force and center of pressure.

Problem 6: Quarter-Cylindrical Curved Gate

Water lies above a quarter-cylindrical gate of radius $2\text{ m}$ and width $1\text{ m}$. The water surface passes through the top of the gate. Find the horizontal, vertical, and resultant forces.

Problem 7: Vertical Trapezoidal Gate

A vertical trapezoidal gate extends from the water surface to a depth of $4\text{ m}$. Its width increases linearly from $1\text{ m}$ at the top to $3\text{ m}$ at the bottom. Determine the force and center of pressure.

Problem 8: Cable Force on a Top-Hinged Gate

A vertical gate is $2\text{ m}$ wide and $2\text{ m}$ high, with its top hinge at the water surface. A horizontal cable attached at the bottom holds it closed. Neglect gate weight and determine the cable tension.