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Department of Civil Engineering, The University of the West Indies CVNG 1001—Fluid Mechanics; CHNG 1006—Transport Phenomena 1 Hydrostatic Forces-Curved surfaces April 2005 A 4-metre wide gate having a 2-metre radius quadrant circular cross-section is hinged at its bottom axis and is used to contain water as shown below in the figure. A tie-line attached to the top at an angle of 30° to the horizontal is used to keep the gate closed. Determine the tension, T, in the tie-line required to keep the gate closed. T 30° O Water 2m hinge gate April 2004 A sluice gate AB, 1.0 m wide and having a circular cross-section of radius 1.0 m, is hinged at one edge B to a vertical plate as shown in the figure. If the depth of water, h, to the bottom of the sluice gate is 2.0 m, determine the horizontal and vertical components of the resultant hydrostatic force acting on the sluice gate. Hence determine the resultant hydrostatic force, its line of action, and its direction from the horizontal. If the gate is now held closed at its lower end, A, by a horizontal force determine the magnitude of this force. (Note the 2nd Moment of area of a rectangle of width b and depth d is given by: water 2.0 m bd 3 12 ) B 1.0 m A Hydraulic curved gate hinged at B to a vertical plate. July 1998 #1 The figure below shows the cross-section of a water tank of width 2 m (perpendicular to the plane of the diagram). AB is vertical and BC is a quadrant of a circle of radius 0.8 m. Determine the magnitude and line of the hydrostatic thrust on the side ABC of the tank when the depth of water in the tank is 1.2 m. (21385 N acting 48.8˚ below the horizontal.) Page 1 of 2 July 1997 The side width of the water tank is in the form of a quadrant of a circle of radius 1 m and width 2 m as shown in the tutorial. Determine the magnitude and direction of the hydrostatic thrust on the sidewall when the water depth in the tank is 0.8 m. (6537.99 N at –16.78˚) Find the moment of this thrust about an axis through edge A of the tank. (1896 N m) July 1996 #1 A gate one metre wide, retaining water, comprises a circular quadrant of radius 0.8 m made up of two parts as shown in the tutorial. The top section, AB, subtends an angle of 30˚ at the centre O, and the lower section, BC, subtends an angle of 60˚. AO is horizontal and OC is vertical. Determine the magnitude and line of action of the hydrostatic thrust on section BC if the water level is at the top of the gate. (5.188 kN acting 63 to horizontal and passing through O.) Page 2 of 2