Question

A car plunges into a lake (water density 𝜌 = 1000 kg m^-3). Using the steps below, calculate the resultant hydrostatic force on the door, and the distance from the bottom of the door to the point at which the force acts. Discuss if someone could open the door and describe the what the effect would be of opening a window. Note that the door is hinged at 𝐶𝐷.

 

 

    i.    Using the standard table method, find the

a.      Position of the centroid (𝑥_𝑐, 𝑦_𝑐), its depth ℎ_𝑐 and

b.     second moment of area 𝐼_𝑐 about the horizontal axis through the centroid

of the door by splitting it into rectangles, triangles and quarter-circles.

ii.    Compute the hydrostatic force on the door using 𝐹 = 𝜌 𝑔 ℎ_𝑐 𝐴. iii. Find the depth of the centre of pressure using ℎ_𝑃 = ℎ_𝑐 + _ℎ^𝐼𝑐^𝑐_𝐴. 

Answer 1

As the diagram mentioned in the question is not given, so i am assuming a standard process to find the centroid of any irregular shape-

i) If we assume it as a rectangular shape, then area of the rectangular shape object $=l^2$

if there is any other shape such as circle and triangle then we remove the area of these shape from the area of the rectangular box.

here l = b then it means it is a square sheet.

area of the triangle $=\frac{l^2}{8}$

area of the quarter circle $=\frac{1}{4}\times \pi \times (\frac{l}{4})^2 =\frac{l^2}{64}$

Hence the area of the remaining part $=l^2-\frac{l^2}{8}-\frac{l^2 \pi}{64}$

Find $\Sigma A=\frac{64l^2-8l^2-l^2}{64}=\frac{55l^2}{64}$ $\Sigma Ax$ and $\Sigma Ay$

Then co-ordinate of the centroid will be $\Sigma C_x = \frac{\Sigma Ax}{\Sigma A}$

$\Sigma Cx = \frac{\Sigma Ay}{\Sigma A}$

It will gives the co-ordinate of the centroid.