Solutions - 0100-03

(1) Integral formula:

$$F={\int }_a^b\rho gh(y)w(y)dy$$

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Option 1:

(2) Using $y=0$ at water line, increasing downwards: (a) Left:

$$F={\int }_0^4\rho gy(3+\frac{0-3}{4}y)dy$$

(b) Center:

$$F={\int }_2^5\rho gy(0+\frac{2-0}{3}(y-2))dy$$

(c) Right:

$$F={\int }_0^4\rho gy(4+\frac{0-4}{5}(y+1))dy$$

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Option 2:

(2) Using $y=0$ at top of shape, increasing downwards: (a) Left:

$$F={\int }_0^4\rho gy(3+\frac{0-3}{4}y)dy$$

(b) Center:

$$F={\int }_0^3\rho g(y+2)(0+\frac{2-0}{3}y)dy$$

(c) Right:

$$F={\int }_1^5\rho g(y-1)(4+\frac{0-4}{5}y)dy$$