Explanation Given information: The weight of the rectangular gate is 280 kg , the width of the rectangular gate is 6 m , the angle made by the floor with the gate is 45 ° . Write the expression for the length of the line A B . sin θ = B E A B A B = B E sin θ ...... (I) Here, the distance from point B to E is B E . The figure below shows the forces acting on the gate. Figure-(1) Write the expression for the length of the line B D . sin θ = B C B D B D = B C sin θ ...... (II) Write the expression for surface area of the gate exposed to water. A = L × w = A B × w ...... (III) Here, the width of the plate is w . Write the expression for distance of the centroid of the plate from the water surface. H = ( B D + A B / 2 ) sin θ ...... (IV) Write the expression for the resultant force acting on the surface of the gate exposed to water. F R = ρ g H A ...... (V) Here, the density of the water is ρ , the acceleration due to gravity is g , the distance of the centroid of the plate from the water surface is H and the area of the plate is A . Write the expression to obtain the position of F R along the gate plane to point D . y p = B D + ( A B / 2 ) + w b 3 12 [ B D + A B / 2 + P o / ( ρ g sin θ ) ] w b ...... (VI) Here, pressure is P o . Write the expression for taking moment at point B . ∑ M B = 0 F R ( y p − B D ) − F ( A B 2 ) = 0 F = 2 F R ( y p − B D ) A B ...... (VII) Calculation: Substitute 3 m for B E and 45 ° for θ in Equation (I). A B = 3 m sin 45 ° = 4.2426 m Substitute 0.8 m for B C and 45 ° for θ in Equation (II). B D = 0.8 m sin 45 ° = 1.131 m Substitute 6 m for w and 4.2426 m for A B in Equation (III). A = 6 m × 4.2426 m = 25.4556 m 2 Substitute 1.131 m for B D and 4.2426 m for A B in Equation (IV). H = ( 1.131 m + ( 4.2426 m 2 ) ) sin 45 ° = ( 1

Fluid Mechanics Fundamentals And Applications

3rd Edition

ISBN: 9780073380322

Author: Yunus Cengel, John Cimbala

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 3, Problem 173P

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The minimum force required for opening the gate.

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Chapter 3, Problem 172P

Chapter 3, Problem 174P

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The minimum force required for opening the gate.

Solution Summary: The figure below shows the forces acting on the gate.

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The minimum force required for opening the gate.

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