Solutions - 0120-04

(1) Integral formula:

$$\begin{array}{c}W=\int dW\gg \gg \int h(y)\rho gdV\\ \\ \gg \gg \int \rho gh(y)A(y)dy\end{array}$$

Set $y=0$ at the center of the tank.

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(a) (2) Geometry:

So:

$$w(y)=2\sqrt{5^2-y^2}$$

Tank length is $7\mathrm{m}$ so a horizontal slice is a rectangle with area $w(y)\cdot 7$.

Depth is:

$$h(y)=y+5$$

Therefore:

$$W={\int }_{-5}^5\rho g(y+5)7\cdot 2\sqrt{25-y^2}dy$$

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(b) (2) Change bounds and height:

$$W={\int }_2^5\rho g(y+6)7\cdot 2\sqrt{25-y^2}dy$$