Consider a flat plate of thickness t, width w into the page, and length b submerged in water, as in Fig. P3–90. The depth of water from the surface to the center of the plate is H, and angle θ is defined relative to the center of the plate.

(a) Generate an equation for the force F on the upper face of the plate as a function of (at most) H, b, t, w, g, r, and θ. Ignore atmospheric pressure. In other words, calculate the force that is in addition to the force due to atmospheric pressure. 

(b) As a test of your equation, let H = 1.25 m, b = 1 m, t = 0.2 m, w = 1 m, g = 9.807 m/s², ρ = 998.3 kg/m³, and θ = 30°. If your equation is correct, you should get a force of 11.4 kN.

FIGURE P3–90

Transcribed Image Text:

H F.