Vertical hydrostatic force acting upwards on a curved surface?

theBEAST · Feb 2, 2013

Homework Statement

I am only confused about F_y.

Schematic of a water tank with a 5 m water depth and a 0.8 m height marked near the bottom, a circular gate of radius R = 0.8 m hinged at point A with the curved wall of length s = 4.2 m, and a free-body diagram of the fluid beneath the cylinder showing forces F_x, F_y, F_R, F_H, F_V and W.

Worked solution from a fluids textbook, Example 3-9, on a gravity-controlled cylindrical gate, showing horizontal force F_H = 36.1 kN and vertical force F_y = 39.2 kN calculations with equations in plain text.

The Attempt at a Solution

I don't understand why in the equation F_y = ρgh_cA, the h_c is 5m. Why do they take the centroid distance to be the very bottom?

haruspex · Feb 3, 2013

They're analysing the forces on a particular region of the water, treated as a block. It's the region lying 'under' the cylinder, i.e. it's bounded by a vertical line through point A, the floor of the chamber, and a quadrant of the cylinder. Fy is the vertically upward force on this block from the floor of the chamber. It must be equal and opposite to the force the block exerts on the floor. The pressure there is the pressure at 5m depth.

Vertical hydrostatic force acting upwards on a curved surface?

Homework Statement

The Attempt at a Solution

Discussion

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