A water trough of semicircular cross section of radius 0.6 m consists of two symmetric parts hinged to each other at the bottom, as shown in Fig. P3-72. The two pans are held together by a cable and turnbuckle placed every 3 m along the length of the trough. Calculate the tension in each cable when the trough is filled to the rim.
The tension in the cable.
Answer to Problem 72P
The tension in the cable is
Explanation of Solution
Given information:
A water trough of semicircular cross section of two symmetric parts hinged at each other at the bottom and held together by a cable.
The figure below shows the free body diagram of the right-hand side part of water trough.
Figure-(1)
Write the Equation for the horizontal hydrostatic force on the part.
Here, density of fluid is
Write the Equation for vertical projected area.
Here, radius of the quarter circle is
Substitute
Write the Equation of the vertical force for curved surface.
Here volume of fluid above curved surface is
Write the Expression for volume of fluid above curved surface.
Substitute
Write the Expression for centre of pressure.
Write the Expression for moment of Inertia.
Substitute
Write the moment Equation about the hinge point.
Here, distance between the line of action of vertical force and hinged point is
Write the Expression for distance between the line of action of vertical force and hinged point.
Substitute
The figure below shows the free body diagram of water trough.
Figure-(2)
Write the expression for horizontal force equilibrium.
Figure-(2)
Calculation:
Substitute
Substitute,
Substitute
Substitute
Substitute
Substitute
Substitute
Here the tension value is same
Conclusion:
The tension in the cable is
Want to see more full solutions like this?
Chapter 3 Solutions
Fluid Mechanics: Fundamentals and Applications
- 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.arrow_forwardIn Fig. , vertical, unsymmetrical trapezoidal panelABCD is submerged in fresh water with side AB 12 ft belowthe surface. Since trapezoid formulas are complicated,( a ) estimate, reasonably, the water force on the panel, in lbf,neglecting atmospheric pressure. For extra credit, ( b ) lookup the formula and compute the exact force on the panel.arrow_forwardConsider a cubical water tank with a side length of 3.5 m. The tank is half filled with water, and is open to the atmosphere. Now, a truck carrying this tank is accelerated at a rate of 7 m/s^2 on a flat road. The maximum vertical rise (in meters) of free surface of the water is ?"arrow_forward
- A circular plate 3.0 m diameter 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 water. Determine the position of the center of pressure from the free surface when the upper edge of the plate is 2 m below the free water surface.arrow_forwardA vertical rectangular plate is submerged half in oil (s = 0.80) and half in water such that its topedge is flushed with the oil surface. What is the ratio of the force exerted by water acting on thelower half to that by oil acting on the upper half?arrow_forwardA cylindrical tank contains 1.0m of mercury (SG-13.6) and 3.0m of water. To look into the tank. a viewport measuring 0.60m by 0.60m was installed 0.60m above the base of the tank as shown in the figure. (a) using the pressure prism concept. determine the total force (in kN) acting on the view port due to water. (b) using the pressure prism concept. determine the total force (in kN) acting on the view port due to mercury. (c) What is the total force acting on the view port in KN? (The total force acting on the view point is equal to the sum of the component forces due water and mercury.)arrow_forward
- 6-m-wide rectangular gate shown is hinged at B and leans against the floor at A making an angle of 45° with the horizontal The gate is to be opened from its lower edge by applying a normal force at its center. Determine the minimum force F required to open the water gate.arrow_forwardHow can I get the solutions for this problem? (answers are given) If the upper base of the vertical rectangular plate with ( height =10ft and base= 5ft) is submerged 12ft below the water's surface, determine the hydrostatic force and the location of the center of pressure. (Answers: 53040 lbf and 17.4902 ft)arrow_forwardCalculate the depth of the center of pressure for vertical rectangular plate having a height h = 10ft and base b = 5ft, and submerged in a liquid with its base at the liquid surface. If the upper base of the vertical rectangular plate given in the example problem is submerged by 12ft below the water surface, determine the location of the hydrostatic force and center of pressure. Answer should be (53,040 lbf and 17.4902ft)arrow_forward
- A bottle consist of a cylinder 35 cm in diameter and 30 cm high and a neck 5 cm in diameter and 30 cm long. The bottle is inserted into a body of water, with the open end of the neck first until the neck is completely filled with water. Assuming the pressure of the atmosphere is standard, and neglecting vapor pressure, what is the depth to which the open end is submerged below the free surface? Show correct figure. Please be clear and write explanation in every solution. Thank you.arrow_forwardA closed, 0.4-m-diameter cylindrical tank is completely filled with oil (SG= 0.90) and rotates about its vertical longitudinal axis with an angular velocity of 40 rad/s. Determine the difference in pressure just under the vessel cover between a point on the circumference and a point on the axis indicate free body diagramarrow_forwardA conical vessel r=(b-z)tanA, rests with its open end downward on a flat surface, as shown in the figure. We want to fill it to a height h with a liquid of density p. What will be the lifting force on the vessel? (tanA: tangent of A)arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L