As shown, a round viewing window of diameter D = 0.8 m is situated in a large tank of seawater (specific gravity 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 center of pressure (CP).
This question is based on the concepts hydrostatic force and center of pressure.
Hydrostatic Force: A fluid always exerts a pressure on the submerged bodies. This pressure causes a force on the submerged bodies known as hydrostatic force.
Center of pressure: On a submerged body pressure force acts through a point, this particular point is known as the center of pressure.
Specific gravity: Specific gravity of a fluid is defined as the ratio of the density of fluid to density of the reference fluid. Most of the times water is considered as the reference fluid.
Calculate the vertical distance of the centroid of the window from the free surface. Use the expression for the hydrostatic force applied on a submerged object in order to calculate the value of hydrostatic force on the window.
Calculate the second area moment of inertia of the window about the axis passing through the centroid of the window. Use the expression for the center of pressure in order to calculate the distance of center of pressure of the window.
The expression of hydrostatic force is,
Here, is the hydrostatic force that acts on the object , is the fluid, is the acceleration due to gravity and is the center of gravity of window.
The expression of the center of pressure of an object is written as,
Here, is the center of pressure, is the moment of inertia of object about center of gravity, and is the inclination angle.
The expression of moment of inertia of circular section about center of gravity is written as,
Here, is the diameter of the window.
The area of circular section is expressed as,
Here, is an area of the window.
The density of seawater is written as,
Here, is the density of water and is density of the sea water.
Calculate the area of the window.
Substitute for .
Write the expression for the vertical distance of centroid of window from free surface.
Here, is the vertical distance of the centroid of the window from the free surface of water.
Substitute for and for .
Calculate the density of the sea water.
Here, is the density of the sea water, is density of fresh water.
Substitute for and for .
Calculate the hydrostatic force on the window.
Here, is the hydrostatic force that acts on the window, is the density of seawater and is the acceleration due to gravity.
Substitute for , for , for and for .
Write the expression for the moment of inertia of the object.
Here, is a moment of inertia.
Substitute for .
Write the expression for the center of pressure for the window.
Here, is center of pressure of the window.
Substitute for , for , for and for .
The hydrostatic force that acts on the window is .
The center of pressure of window is from top of the surface of water.
As shown, a round viewing window of diameter D = 0.8 m is situated in a...
Q3. 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 1.5 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 Window Sea water 60
Hydrostatic Force- Inclined Surface 3. The round viewing window shown (D=0.8 m) is situated in a large tank of seawater (SG 1.03). If h= 2m, and the window is angled at 60° from the horizontal, find the hydrostatic force acting on the window, and locate the corresponding center of pressure (CP) Window Sea water 60
A viewing window 30 cm in diameter is installed with its center 3.0 m below the surface of an aquarium tank at the Seaquarium. Determine the force that the window must withstand. Physics 1 College level. Please show all work and formula used. Thanks!
A circular gate with diameter 4 m lies in a vertical plate of a tank filed with oil of specific gravity 0.8. The oil surface is 8 m above the top of the gate. Find the force exerted by the oil on the gate and the position of the center of pressure.
QUESTION TWO (15 marks) A. A small chemical-industry tank fitted with a manometer as shown contains a dense fluid with specific gravity S 3.0 and 20 cm deep. Workers should have added water to a depth of 15 cm above the dense fluid. What height Ah do you expect to find when you inspect the tank? (7 marks) 15 cm Water Ah? 20 cm S 3.0 B. A sea-water aquarium is planned to have a circular window with diameter D-80...
A rectangular gate 1.2 m wide and 3.5 m long is inclined 35°from a smooth wall. The gate is hinged at point B, and rests against a smooth wall at A which is 2.7 m below the water surface. a. Compute the force on the gate due to seawater pressure (s.g. = 1.03). b. Determine the location of the force from the center of gravity of the gate. c. determine the horizontal force P exerted by the wall at point...
The figure shows a cylindrical tank of 80 em in diameter which is fully filled with water. In order to increase the flow from the tank to the exit pipe on the left, an additional pressure is applied to the water surface by an air compressor to supply air to the upper air chamber of the tank. The external walls of the tank are exposed to the atmospheric conditions of the area. You are required to determine the hydrostatic conditions...
(13) A brewery fermentation tank 12 m in diameter is situated in a room, which has a temperature of 15°C. The tank is constructed of 10-mm welded steel plate with 12-mm glass lining. The temperature at the inner surface of the glass lining is 50°C. Assume that the convective resistance offered by the air film on the outside of the tank equals the combined resistance of the glass and steel. The thermal conductivity of glass is 0.80 W/mK and that...
Solve the following A vertical rectangular surface has a base of 1.2 m and a height of 3 m. If the center of pressure is o.150 m below the center of gravity, how far is the base below the liquid surface 1. h: ? o. 150 m 1-12 t.2 2. A circular gate 1.50 m in diameter is inclined at an angle of 45 Sea water stands on one side of the gate to a height of 10 m above...
Dam Wall (7 marks) Fig 6 6. A circular gate AB of diameter 4 m is designed to close the water flowing out from the sloping wall of a dam structure. The gate is hinged at A as in Fig 6. Calculate (a) the magnitude of hydrostatic force acting on the circular gate and (b) the position of hydrostatic force from the water surface. (6 marks) 7. Using the data in Fig 7, (a) find va if vb is 3...