(a)As shown in Figure 2.1, an architect with an artistic flair designs a gateABC to trap liquid of density pin a canal. The gate is hinged at A and is ofunit width into the plane of the page. Section AB of the gate correspondsto a circular quadrant of radius R centred at O. Section BC of the gate isvertical with a height of 2R. The height of the liquid in the canal is R.Neglect the weight of the gate and friction in the hinge. Some geometricproperties of a rectangle and a circular quadrant are provided in Figure2.2, where the symbols have their usual meanings.(i) Determine the magnitude and direction of the horizontal componentof the hydrostatic pressure force exerted on the gate by the liquid inthe canal.(ii)(iii)Determine the magnitude and direction of the vertical component ofthe hydrostatic pressure force exerted on the gate by the liquid inthe canal.Determine the minimum force F applied at B to prevent the gatefrom opening (i.e. turning anticlockwise about the hinge A).2RBAir(a) RectangleсGateRa A = ba4:381xx.c=Figure 2.1AirLiquid p-Hinge1 ba³12 yy,c= -ab³Figure 2.2TR²4xxc=y.c=0.05488 R¹A =(b) Quadrant

Answered: Image /qna-images/answer/4b9fe442-863a-47fd-aa16-be2286c78668.jpg

(a) As shown in Figure 2.1, an architect with an artistic flair designs a gate ABC to trap liquid of density pin a canal. The gate is hinged at A and is of unit width into the plane of the page. Section AB of the gate corresponds to a circular quadrant of radius R centred at O. Section BC of the gate is vertical with a height of 2R. The height of the liquid in the canal is R. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle and a circular quadrant are provided in Figure 2.2, where the symbols have their usual meanings. (i) (ii) Determine the magnitude and direction of the horizontal component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. Determine the magnitude and direction of the vertical component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. (iii) Determine the minimum force F applied at B to prevent the gate from opening (i.e. turning anticlockwise about the hinge A). 2R Air (a) Rectangle с Gate B OX R A = ba 14:48 Figure 2.1 Air Liquid p -Hinge !xx,c= -ba³ ¹yy.c= -ab³ Figure 2.2 xc=y.c=0.05488 R4 (b) Quadrant

(a) As shown in Figure 2.1, an architect with an artistic flair designs a gate ABC to trap liquid of density pin a canal. The gate is hinged at A and is of unit width into the plane of the page. Section AB of the gate corresponds to a circular quadrant of radius R centred at O. Section BC of the gate is vertical with a height of 2R. The height of the liquid in the canal is R. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle and a circular quadrant are provided in Figure 2.2, where the symbols have their usual meanings. (i) (ii) Determine the magnitude and direction of the horizontal component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. Determine the magnitude and direction of the vertical component of the hydrostatic pressure force exerted on the gate by the liquid in the canal. (iii) Determine the minimum force F applied at B to prevent the gate from opening (i.e. turning anticlockwise about the hinge A). 2R Air (a) Rectangle с Gate B OX R A = ba 14:48 Figure 2.1 Air Liquid p -Hinge !xx,c= -ba³ ¹yy.c= -ab³ Figure 2.2 xc=y.c=0.05488 R4 (b) Quadrant

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.113P: Calculate the resultant force caused by the water acting on the parabolic arch dam. The water levels...

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