To determine The horizontal force P required keeping gate in equilibrium. Explanation Given information: S . G . of oil = 0 .83 density of oil ( ρ ) = 830 kg/m 3 D e p t h of top surface of plate from free surface (X 1 ) = 3 m Depth of bottom surface of plate from free surface (X 2 ) = 5 m Angle of inclination of gate ( θ ) = 50 o B a s e of gate (b) = 1 m Weight of gate (W) = 1500 N L e n g t h of gate (h) = X 2 − X 1 Sin θ = 5 − 3 Sin 50 = 2.61 m Depth of Center of gravity from its base (point A) (X 3 ) = h 3 = 2.61 3 = 0.87 m Depth of Center of gravity from free surface ( X ¯ ) = X 1 + ( X 3 Sin θ ) = 3 + ( 0.87 * Sin 50 ) = 3.67 m Area of plate (A) = ( 1 2 ) * b * h = ( 1 2 ) * 1 * 2.61 = 1.305 m 2 Calculation: N o w we know that hydrostatic force is given by F = ρ gA X ¯ = 830 * 9

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 2, Problem 2.68P

To determine

The horizontal force P required keeping gate in equilibrium.

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