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
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Chapter 3 Solutions
EBK FLUID MECHANICS: FUNDAMENTALS AND A
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- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L