Problem 3.77

# Problem 3.77 - Problem 3.77 [Difficulty: 3] w = 35 m Given:...

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Problem 3.77 [Difficulty: 3] Given: Tainter gate as shown w3 5 m = Find: Force of the water acting on the gate Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards from free surface) dF p dA = (Hydrostatic Force) Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts at free surface of water and on outside of gate Integrating the hydrostatic pressure equation: p ρ g h = ρ g R sin θ () = Resolving the hydrostatic force into horizontal and vertical components: dF H dF cos θ = pdA cos θ = ρ g R sin θ w R d θ cos θ = since dA w R d θ = Integrating this expression: F H 0 θ 1 θ ρ g R 2 w sin θ cos θ d = where θ 1 asin 10 m 20 m = 30 deg = F H ρ g R 2 w 0 30 deg θ sin θ ( ) cos θ d = ρ g R 2 w sin 30 deg 2 2 = ρ g R 2

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## This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 3.77 - Problem 3.77 [Difficulty: 3] w = 35 m Given:...

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