Question

5 Figure P4.3.5 shows a vertical surface composed of a rectangle of altitude L and a semicircle of radius R. If the upper edge of the rectangle is at the free surface find the value of L/R that makes the hydrostatic thrust on the rectangle equal to that on the semicircle Figure P4.3.5. 3.6 Figure P4.3.6 shows a vertical surface composed of an isosceles triangle of altitude a and base L, and a square of altitude L. If the apex of the triangle is at the free surface, find the value of a/L that makes the hydrostatic thrust on the triangle and on the square equal. tatic thrust ner radius below the Figure P4.3.6.

Answer 1

Hydrostatic thrust on Rectangle: F_R F_R = S middot g middot h^bar middot A_s = S middot g middot L/2 middot(L middot 2R) Hydrostatic thrust on semicircle: F_s.c F_s.c = S middot g(L + 4R/3 pi) middot (pi R^2/2) F_R = F_sc S middot g L/2 middot (L middot 2R) = S_g (L + 4R/3 pi) (pi R^2 /2) 2L^2 = pi L R + 4/3 R^2 2L^2/R^2 = pi L/R + 4/3 2 L^2 /R^2 - pi (L/R) - 4/3 = 0 therefore L/R = 1.92 h^bar: center of gravity A_s: Surface Area h^bar of isosceles triangle = 2/3 times a F_triangle = S middot g middot 2/3 a middot 1/2 middot L middot a F_Squarebox = S middot g (a + L/2) middot L^2 F_triangle = F_Squarebox S middot g middot 2/3 a L/2 middot = Sg(a + L/2)L^2 a^2/3