Sheet 3 - Forces on Submerged Surfaces - Answer PDF

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Cairo University Faculty of Engineering Chemical Engineering Department

Fluid Mechanics Fall 2020 Sheet ()

Problem (1): A vertical gate is 5 m wide and has water at a depth of 7.5 m on one side and to a depth of 3 m on the other side. Find the resultant horizontal force on the dock gate and the position of its line of action. To what position does this line tend as the depth of water (Ans. 1.16*106 N, 2.78 m)

on the shallow side rises to 7.5 m?

[1]

Problem (2): The 2m diameter gate AB in Fig. swings about a horizontal pivot C located 100mm below the center of gravity. At what depth h the gate won’t swing? (Ans. 1.5 m)

[2]

Problem (): A circular plate 125cm in diameter is immersed in water so that the vertical distances measured from the liquid surface to the plate ends varies from 60cm to 150cm. Find the total force due to the water acting on one side of the plate and the vertical distance of the center of pressure below the surface. 1.098m)

center of mass = ((150-60)/2)+60 = 1.05 area = (1/4)*pi*D^2 = 1.227 Force = density*g*area*centerOfMass Force = 1*9.81*1.227*1.05 Force = 12.639KN

[3]

(Ans.

12.64

kN,

Problem (4): A horizontal cylindrical tank made of stainless steel is used to store a liquid chemical with a specific gravity of 1.2. The tank has a volume of 30 m3, and its diameter is one half its total length, both ends of the tank are flat circle plates. When the tank is completely full, calculate: a. The maximum and minimum gage pressures inside it, and determine their positions.

(0 on the top, 1.47 kPa on the bottom)

b. Force magnitude and direction acting on the half bottom of the tank. (5.16 kN) c. The force magnitude acting on one end of the tank.

[4]

(88 kN)

Problem (5): As shown, a round viewing window of diameter D = 0.8 m is situated in a large tank of seawater (S = 1.03). The top of the window is 1.2 m below the water surface, and the window is angled at 60° with respect to the horizontal. Find the hydrostatic force acting on the window and locate the corresponding CP. below L.S. (Liquid Surface))

[5]

(Ans. 7.85 kN, 1.57m

Problem (6): (Done in Lecture) Surface AB is a circular arc with a radius of 2 m and a width of 1 m into the paper. The distance EB is 4 m. The fluid above surface AB is water, and atmospheric pressure prevails on the free surface of the water and on the bottom side of surface AB. Find the magnitude and line of action of the hydrostatic force acting on surface AB. (Ans. 146.9 kN, 48° with the horizontal)

[6]

Problem (7) - Problem 2.61, Munson: A homogeneous, 4-ft-wide, 8-ft-long rectangular gate weighing 800 lb is held in place by a horizontal flexible cable as shown in Fig. Water acts against the gate, which is hinged at point A. Friction in the hinge is negligible. Determine the tension in the cable. (Ans. 150 lbf)

[7]

Problem (8) - Problem 2.70, Munson: (Done in Lecture) An open tank has a vertical partition and on one side contains gasoline with a density ρ=700 kg/m3 at a depth of 4 m, as shown in Fig. A rectangular gate that is 4 m high and 2 m wide and hinged at one end is located in the partition. Water is slowly added to the empty side of the tank. At what depth, h, will the gate start to open? (Ans. .55 m)

[8]...