Hydrostatic Pressure and Force — Question 3

Question 3 – Solution

Step 1: Use the centroid form of the hydrostatic-force formula. For a submerged vertical plane region, $$F=\gamma A\bar y,$$ where $A$ is its area and $\bar y$ is the depth of its centroid.

Step 2: Find the area of the porthole. The radius is $1$ m, so $$A=\pi r^2=\pi(1)^2=\pi\ \mathrm{m^2}.$$

Step 3: Identify the centroid depth. The centroid of a circle is its center, which is $3$ m below the surface. Therefore, $$\bar y=3\ \mathrm m.$$

Step 4: Substitute. $$\begin{align*} F&=(9800)(\pi)(3)\\ &=29{,}400\pi\ \mathrm N. \end{align*}$$ $$\boxed{F=29{,}400\pi\ \mathrm N}$$ No strip integration is needed because the area and centroid depth are known.