Find the force applied by support BC to the gate AB. The width of the gate and support is 3 m and the weight of the gate is 1500N.
The force applied by support
Answer to Problem 87P
The force applied by support
Explanation of Solution
Given information:
The width of the gate is
Write the expression of force applied by the water on the gate.
Here, the density of the water is
Write the expression for depth of centre of gravity of the immersed area from free surface of water.
Here, the width of the gate is
Write the expression for area of the gate immersed in the water.
Here, the
The below figure shows the forces acting on the gate.
Figure-(1)
The below figures shows the triangle
Figure-(2)
Write the expression for the length
Write the expression for distance of centre of pressure from free surface of liquid.
Here, the moment of inertia of area about an axis passing through centre of gravity of the area and parallel to the free surface of liquid is
Write the expression for moment of inertia.
Write the expression for cosine rule in the triangle
Write the expression for
The figure below shows the triangle
Figure-(3)
Write the expression for the angle
The below figure shows the moment about point
Figure-(4)
Write the expression for taking moment of all forces about point
The below figure shows the triangle
Figure-(5)
Write the expression for
The below figure shows the triangle
Figure-(6)
Write the expression for
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The force applied by support
Want to see more full solutions like this?
Chapter 3 Solutions
Fluid Mechanics: Fundamentals and Applications
- Find the elevation h (km) where the weight of an object is one-tenth its weight on the surface of the earth.arrow_forwardThe properties of the unequal angle section are Ix=80.9in.4,Iy=38.8in.4, and Iu=21.3in.4. Determine Ixy.arrow_forwardA vertical gate 6 m x 6 m holds water on one side with the free surface at its top. The moment about the bottom edge of the gate of the water force will be (yw is the specific weight of water)arrow_forward
- The figure below shows the cross-section of a tank full of water under pressure. The pressure in the tank is 19.62 kN m² and its length is 2 m in the paper. An empty cylinder lies along the length of the tank on one of its corner as shown. Find the resultant force acting on the curved surface ABC. 19.62 kNm R-1m 1.5m Tank fal of waterarrow_forwardA face of a dam adjacent to the water has the shape of an isosceles trapezoid of altitude 20 m, upper base 50 m, and the lower base 40 m. Find the total force exerted by the water on the dam when the water is 15 m deep.arrow_forwardFind the hydrostatic force in kN acting in a triangular plate of base 2 m and height 3 m which is immersed in water in such a way that the plane of the plate makes an angle of 60 degrees with the free surface of the water. The base of plate is parallel to water surface and at a depth of 2.5 m from the water surface.arrow_forward
- Find the magnitude and depth of the point of application of the force on circular gate shown in figure if h=5 ft and D=4 ft dia. Water Circular gate 60 dia Darrow_forward2. Gate AB is a quarter circle 10 ft wide into the paper and hinged at point B. Find the force F that is enough to keep the gate from opening. The gate is uniform and weighs 3000 lbf. Water r = 8 ft Вarrow_forwardTwo spheres, each 1.20 m in diameter, weighs 4kN and 12kN respectively. They are connected with a short rope and placed in water. Find the tension in the rope in kNarrow_forward
- The flat surface shown is submerged vertically in water. Find the fluid force against the surface. The weight density of water is 9810 N/m³. 4 m Enter the exact answer. F = i 1m 3 m Narrow_forwardYou are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.) 8 ft 5 ft O 416 lb O 1,040 lb 208 lb O None O 2,080 lbarrow_forwardA trapezoidal plate shown in the figure is submerged in water is 3.1 m below the surface. The bases of the plate is 2 m and 8 m, respectively. The height is 11 m. Find the location of the force from the bottom in meters. Unit weight of water is 9.8 KN/m³. Answer is in KN. Write only the value of your answer. FFS d b₂arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L