Consider a dam of width D and a water body of a depth of H, as shown in the figure below. Determine the net force acting on the dam. H
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Q: -1 = 5 m D=4 m
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- The hemispherical glass bowl is filled with water. Find the location y of the center of gravity of the filled bowl. Approximate the bowl as a thin shell of radius R=6.15in. Use 1=162lb/ft3 for glass and 2=62.4lb/ft3 for water.The 12-ft wide quarter-circular gate AB is hinged at A. Determine the contact force between the gate and the smooth surface at B due to water pressure acting on the gate. Use =62.4lb/ft3 for water.One side of the container has a 03-m square door that is hinged at its top edge. If the container is filled with water, determine the smallest force F that must be applied to the bottom edge of the door to keep it closed.
- 1. Consider a conic reservoir of unit depth that is initially filled with water at the height of h = 200 mm. A rigid cuboid block, with dimensions of 10 cm x 5 cm x 3 cm, is then dropped into the water. When the equilibrium state is reached, the block floats on the water's surface, as shown in the figure. If the specific gravity of the block is 0.5, determine the change in the free surface position of the water, i.e., Ah, in mm. %3D Hint: You can calculate the volume of liquid inside the conic reservoir with a unit depth in terms of the liquid height as V = th³/3. Ah block water waterA semicircular gate with a radius R = 7 ft is hinged along B and held by a horizontal force FA applied at A. The picture on the right shows the gate if you were looking in the direction of the arrow beneath FA. The liquid to the left of the gate has a specific weight of y-64.8 lbf/ft° and a depth of H-26 ft. Calculate the force of the liquid on the gate in Ibf. FA A Gate: side view R ВA B с OIL WATER 1.0M 0.5m In the tank open to the atm. shown in the figure below, there is on oil layer 1 meter high on a 0.5 meter high water layer. Since pont & is in the Middle of paints A and C. calculate the pressures at points A, B, C, D in Kla. (Density of water 1000 kg/m³, density of oil 800 kg/m³)
- The figure below shows a container filled with a liquid of density p up to a height of 4R. The container is of unit width into the plane of the screen and AB is half a parabola with a height of kR and a base of R. Determine the magnitude and direction of the horizontal component F# of the hydrostatic force acting on the curved surface AB if k= 3, R = 0.5 m, p = 1000 kg/m³ and the gravitational acceleration g = 9.81 m/s². Note that F is positive if it acts towards the right and is negative if it acts towards the left. Geometric properties of a half-parabola are also given below. FH 1. [17.8419375, 18.9455625 kN. 4R h m/00 b Liquid Р X Half-Parabola BR 9 A KR A = bh |xc=bh³ yy,chb³ = 15A factory's pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 ft. and whose length is 40 ft. The tank is a vertical cylinder surmounted by a cone, and it has a hemispherical base. If the alti-tudes of the cylinder and the cone are respectively 6 ft. and 3 ft. and if all three parts of the tank have an inside diameter of 6 ft., find the volume of water in the tank and pipe when full.A tank contains oil (s = 0.80), gasoline (s = 0.90) and sea water (s = 1.03). If the depth of the liquids are 0.5 m, 0.8 m and 1 m for oil, gasoline and sea water respectively. Find the pressure at the interface of oil and gasoline and bottom of the tank.
- The figure below shows a container filled with a liquid of density p up to a height of 4R. The container is of unit width into the plane of the screen and AB is half a parabola with a height of kR and a base of R. Determine the magnitude and direction of the vertical component Fy of the hydrostatic force acting on the curved surface AB if k = 2, R = 0.5 m, p = 1000 kg/m³ and the gravitational acceleration g = 9.81 m/s². Note that Fy is positive if it acts upwards and is negative if it acts downwards. Geometric properties of a half-parabola are also given below. Fy= 1. [-6.7362, -6.3438 kN. 4R h ထမ 35 b Liquid Р X Half-Parabola BR KR A = 3bh 1xc=²bh³ |yxc=hb³ |yy,c=²7/531 2 h632. The gage pressure of the air in the Oil tank is measured to be 65 kPa. Find SG = 0.72 the differential height (h) of the 75 cm column. Specific gravities (SG) of Air -Water the manometer fluids are given in 30 cm -Mercury SG = 13.6 h the figure. Assume that the density of water is 1000 kg/m³.The uniform 5-m-long round wooden rod is tied to the bottom by a string. find the tension in the string. The fluid specific gravity S=0.2. D= 8 cm- Fluid 4 m - String