So I am trying to find the depth of immersion of this particular boat model, which has curvilinear edges (subparabolic edges) on each side. The figure of the pontoon is shown below So now when I place this pontoon in water, the height of the water that rises, called the depth of immersion is to be found. I already know how to calculate the displacement volume, but I have no idea how to find the depth of immersion. Below are the steps taken to find the displacement volume 1. Volume of body I assumed the whole body to be a rectangle and calculated the area of the rectangle first: B*h And then, since the curves are subparabolic, it is defined by the equation: y = (h/b^2)*x^2 Integrating the above equation, gives the area under the curve to be: bh/3 So subtracting : 2*(bh/3) from (B*h) will give the cross sectional area which C.S.A = (B*h)-(2*(bh/3)) Multiplying this C.S.A with the length of the pontoon (say L) will give the volume V = (C.S.A)*L = [(B*h)-(2*(bh/3))] * L So now that volume of the body is known, the following steps are taken to find the displacement volume 2. Density of body Density = mass of body / Volume Note: The mass was found by weighing the pontoon on a weighing machine 3. Specific weight of body Specific weight of body = density of body * g Note: g = 9.81 m/s^2 4. Weight of body Weight of body = Specific weight of body * Vbody 5. Weight of water displaced Weight of displaced water = Specific weight of water * Displaced volume Note: Specific weight of water = 9810 N/m^3 6. Archimedes principle According to Archimedes Principle the weight of the body acting downwards is equal to the weight of displaced acting upwards, so Wbody = 9810 * Vdisp 7. Displaced Volume And so the displaced volume of water is given by Vdisp = Wbody/9180 Now another equation for the displacement volume is: Vdisp = [(B'*h')-(2*(b'h'/3))] * L h' is the depth of immersion and B' is the top width at this displaced volume The problem is that there are two unknowns in the above equation and I just can't figure out how to find the depth of immersion here. If anyone has any idea please please let me know.