Question

The tank contains a fluid with a specific weight of 80.7 lb/ft3 . Determine (a) magnitude of the resultant force exerted by the fluid on the bottom of the tank; (b) magnitude of the resultant force exerted by the fluid on side ABCD; (c) location of the center of pressure on side ABCD (vertical distance below liquid surface); (d) magnitude of the resultant force exerted by the fluid on side AEFD; (e) location of the center of pressure on side AEFD (vertical distance below liquid surface).

2 (t 2 f0 2 f0 3 fu 6 ft

Answer 1

a) Force = Weight of water = Volume times r_w = 1/2 (6 + 2) times 3 times 6 times 80.7 F = 5810.4 lb b) Force of wall face ABCD h^- = (a + 2b/a + b) times h/3 h^- = (6 + 2 times 2/6 + 2) times 3/3 h^- = 1.25 Ft F = r_w h^- A F = 80.7 times 1.25 times 1/2 (6 + 2) times 3 F = 1210.5 lb \r\n c) Location of center of pressure on ABCD h^-_cp = (a + 3b/a + 2b) times h/2 = (6 + 3 times 2/6 + 2 times 2) times 3/2 = 1.8 ft from top d) AEFD F_h = (pg)h^- A = 80.7 times 3/2 times 3 times 6 = 21768.9 lb F_v = 1/2 2 times 3 times 6 times 80.7 F_v = 1452.6 lb R = squareroot F_v^2 + F_H^2 = squareroot (2178.9)^2 + (1452.6)^2 R = 2618.7 lb e) Location of R h_c_p = 2h/3 = 2 times 3/2 = 2 ft from top