Answer to Question #173373 in Mechanical Engineering for luke

Question

A long, solid cylinder of radius 2 ft hinged at point A is used as an automatic gate, as shown

in the figure. When the water level reaches 15 ft, the cylindrical gate opens by turning about the

hinge at point A. Determine

(a) The hydrostatic force, in lbf, acting on the cylinder and its line of action when the gate

opens and

(b) The weight, in lbf, of the cylinder per ft length of the cylinder.

Answer 1

radius of sphere is =2 ft, Water level=15 ft, density= 62.4 lbs/ft³

Horizontal force= $\rho g h_c A= 62.4\times 32.174\times (13+2/2)\times 2\times 1=56214.42$  lb-ft/s²

Now, vertical force =$\rho g h A= 62.4 \times 32.174 \times 15\times 2\times 1=60229.73$ lb-ft/s²

Net force on sphere= $\sqrt{F_X^2 +F_y^2}=82387.38$ lb-ft/s²

(b) Weight of fluid=mg= $\rho g V$

Weight =$62.4\times 32.174\times (R^2- \frac{\pi R^2}{4})=62.4\times 32.174\times (1- \pi/4)2^2=$ 1726.58 lbf