Answer to Question #269103 in Classical Mechanics for joseph

Question

1. A room on the lower level of a cruise ship has a 40-cm-diameter circular window. If the midpoint of the window is 2 m below the water surface, determine the hydrostatic force acting on the window, and the pressure center. Take the specific gravity of seawater to be 1.025.

2. The water side of the wall of a 70-m-long dam is a quarter circle with a radius of 7 m. Determine the hydrostatic force on the dam and its line of action when the dam is filled to the rim.

Answer 1

1.

$F=pS=(p_0+\rho gh)\frac{\pi d^2}4=15.3~kN.$

2.

$A=rw=490~m^2,$

$V=w\frac{\pi r^2}4=2700~m^3,$

$F_x=\rho ghA=16.8~MN,$

$F_y=\rho gV=26.5~MN,$

$F=\sqrt{F_x^2+F_y^2}=31.4~MN,$

$\theta=\arctan \frac{F_y}{F_x}=57.6°.$