Solution Found!
Consider a two–dimensional hinged cylindrical gate of
Chapter 3, Problem 82P(choose chapter or problem)
Problem 82P
Consider a two–dimensional hinged cylindrical gate of radius R and width w into the page. The cylinder is resting at ground level with one quarter of its circumference submerged
in water as in Fig. P3–87. The depth of water is h. (a) Generate an equation for the force F acting on the cylinder as a function of (at most) h, R, w, g,ρ, and L. Ignore atmospheric pressure since it acts on both sides of the cylinder. (b) As a test of your equation, let h = 5 m, R = 0.5 m, w = 1 m, g =9.807 m/s2, and ρ = 998.3 kg/m3. If your equation is correct, you should get a force of 11.4 kN.
Questions & Answers
QUESTION:
Problem 82P
Consider a two–dimensional hinged cylindrical gate of radius R and width w into the page. The cylinder is resting at ground level with one quarter of its circumference submerged
in water as in Fig. P3–87. The depth of water is h. (a) Generate an equation for the force F acting on the cylinder as a function of (at most) h, R, w, g,ρ, and L. Ignore atmospheric pressure since it acts on both sides of the cylinder. (b) As a test of your equation, let h = 5 m, R = 0.5 m, w = 1 m, g =9.807 m/s2, and ρ = 998.3 kg/m3. If your equation is correct, you should get a force of 11.4 kN.
ANSWER:
Solution 82P
a.)
Consider a two–dimensional hinged cylindrical gate of radius R and width w into the page. The cylinder is resting at ground level with one quarter of its circumference submerged in water as shown in the fig below. The depth of water is h.
An equation for the force F acting on the cylinder as a function of (at most) h, R, w, g,ρ, and L can be generated by determining the hydrostatic forces acting on the vertical and horizontal plane surfaces as well as the weight of the liquid block.
Step 1 of 4
The free-body diagram of the liquid block enclosed by the circular surface of the cylinder and its vertical and horizontal projections.
Horizontal force on vertical surface is
=)A
= )