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Show that the resultant of the hydrostatic forces acting on a submerged plane area A is a force P perpendicular to the area and of magnitude
Fig. P9.66
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Vector Mechanics for Engineers: Statics
- A swimming pool has a width of 12 ft and a side profile as shown. Determine the eccentricity e of the resultant force the pressure of the water exerts on bottom BC. Inclined BC makes an of 14.478° with the horizontal, D. 3 ft 8 ft 20 ft O 7.28 ft O 6.06 ft O 4.71 ft O 5.34 ftarrow_forwardThe parabolic end-plate of the trough shown here is subjected to a fluid pressure that varies linearly from 0 at its top to 100 lb/ft? at its bottom B, that is, p(y) = 100 -25y. Determine the magnitude of the resultant force on the end-plate. 2 ft 2 ft y = x² 4 ft B O 501 Ib O 271 Ib O 314 Ib O 427 Ib O 623 Ibarrow_forwardA circular plate with radius r = 0.785 m lies next to a rectangular plate with base br = 0.948 m and height hr = 0.770 m which lies next to a triangular, plate with base bt = 1.41 m and height ht = 0.712 m. Determine the center of gravity of the rectangular plate in the y-direction if its surface density varies in the x and y-direction according to σr = 4.84·x·ykg / m2.arrow_forward
- Determine the pressure difference between points C and D. Take the specific weights to be Benzene: 8640 N/m³, Mercury:133100 N/m³ Kerosene: 7885 N/m³, Water: 9790 N/m³, Air: 12 N/m³. Water Air Benzene 50 cm 19 cm 30 cm $18 cm 24 cm Mercury- Kerosinearrow_forwardA circular plate 1.2 m diameter is placed vertically In water so that centre of the plate Is 2m below the free surface. Determine the depth of centre of pressure. X=2 m CG• СР +d= 1.2 marrow_forwardThe curved and flat plates of width 6-m are connected at A, B and C. They are submerged in water at the depth h=7-m. The distance d =4-m and the radius R= 2-m. Find the resultant force [kN] in the hinge at B. h В R A darrow_forward
- The semicircular drainage pipe is filled with water. Determine the resultant horizontal and vertical force components that the water exerts on the side AB of the pipe per foot of pipe length; w(water) = 9.81 lb/ft3. Take r =2m Determine the resultant vertical component of force that the water exerts on the side AB of the pipe per foot of pipe length. Determine the resultant horizontal component of force that the water exerts on the side AB of the pipe per foot of pipe length. Thank you!arrow_forwardThe Figure below shows a dam 30.5 m long that retains 8 m of fresh water and is inclined at an angle of 30°. Calculate the magnitude of the location of the center of pressure. W2 ve Center of pressure /3 L/3arrow_forward3 - Obtain the center of gravity of the surface area of the constant thickness plane plate in the figure in the (x, y) set given. Dimensions a = 13 m, b = 17 m and r = 1 m, the center of the circle is at the point (2a, 1/2 b). Which of the following is the correct coordinates of the center of gravity of the triangle on the plate?A) (36.67; 7.67)B) (43.33; 5.67)C) (43.33; 7.67)D) (40; 7.67)E) (36.67; 5.67)arrow_forward
- Given the curve y = x + 2 and density δ(x, y) = 3x + 2y, find the centroid ofthe region within x ∈ [0, 1]arrow_forwardan oil tank is in the shape of a right circular cylinder with a radius of r meters and its axis is horizontal. if the tank is half full of oil having mass density 750 kg per cubic meter, find r if the total force on one end of the tank due to liquid pressure is 8000 Narrow_forward11 - Obtain the center of gravity of the surface area of the constant thickness plane plate in the figure in the (x, y) set given. Dimensions a = 12 m, b = 23 m and r = 3 m, the center of the circle is at the point (2a, 1/2 b). Which of the following is the correct coordinates of the center of gravity of the circle on the plate?A) (24; 12)B) (24; 11.5)C) (12; 11.5)D) (12; 23)E) (24; 23)arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L