Statics_III_2022_Part_4_Notes

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Oct 30, 2023

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Class Objectives Fluid Statics III: Hydrostatic) Force on a Curved Surface Projection Method Applications
(Part 4) Hydrostatic Force on a Curved Surface Given Fluid Property Surface Characteristics ( curve )+ shape Find (i) Resultant Forces (ii) Line of Action Projection Method F H on A V F V on A H Weight of Liquid Pressure Prism Formula Force & Moment curved A V A H Horizontal direction Vertical direction (Text Chapter 3-5 to 3-6)
water = (3 m)(2 m)(1 m) g + p /4(2 m) 2 (1 m) g Forces on a Circular Curved Surfaces Find resultant force and location on a circular arc with a width of b = 1m F V = F H = 2 m 2 m 3 m W 1 W 2 W 1 + W 2 = 89.7 kN = g (4 m)(2 m x1 m) = 78.5 kN y x h c =4m b a 3 12 xc ba I = x R F V = 2 1 3 ) 2 ( 4 ) 1 ( W m W m p + 4 3 R p x R = 0.948 m x R Projection Method = ?. 𝟎𝟖?? c V h A g xc R c c I y y y A = + R y 3 1 2 /12 4 4(2 4. 8 ) 1) 0 3( m = + = F H F V = 0.948 m
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(78.5kN)(1.083m) - (89.7kN)(0.948m) = ___ 0 0.948 m 4.083-3= 1.083 m F V =89.7kN F H = 78.5kN Notes & Comments Do all hydrostatic forces pass through point C Does the hydrostatic force exert moment at point C? Does the resultant force F R pass through point C ? No Yes C Yes Only F H on the place surface creates the moment at point C Circular Curved Surfac H F
(78.5kN)(1.083m) - (89.7kN)(0.948m) = ___ 0 0.948 m 4.083-3= 1.083 m F V =89.7kN F H = 78.5kN Notes & Comments Do all hydrostatic forces pass through point C Does the hydrostatic force exert moment at point C? Does the resultant force F R pass through point C ? No Yes C Yes Only F H on the place surface creates the moment at point C Circular Curved Surfac H F
Dad, I wonder if the people that designed this know the projection method . Babe/Son, of course! I, graduated from CEE/GLE UW-Madison , designed this. Go Badger!!!
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Buoyancy (F H ) L = (F H ) R (F H ) L (F H ) R (F V ) bottom The weight of fluid displaced by the body What is buoyant force? Archimedes’ Principle - (F V ) upper = F B (F V ) bottom (F V ) upper Horizontal: Vertical: bottom g upper g g = ∀(?𝒐???𝒆)
w s S g W w s S g Hydrometer ( ) w o Ah W S g  + = A h o s o Ah =  + weight Buoyance W = A device to measure density ( specific weight ) Therefore, we can obtain
Summary of Hydrostatic Forces Buoyant Force (1) Pressure Prism Method Plane Surface Curved Surface (2) Formula Method (3) Force/Moment Balance Method (4) Projection Method
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