# Submerged fraction buoancy force

How can I calculate the height of the submerged part of a partly filled bucket? (The liquid both inside and outside is freshwater). The bucket is trapezoidal such that the volume of the submerged can be described as:

<$$V_{bucket} = L_{bottom}*L_{bottom}*h_{submerged} + 2 \cdot (\frac{1}{2} \cdot h_{submerged}^2 \cdot (\frac{0.5 \cdot (L_{top}-L_{bottom})}{h_{bucket}}))$$>

Can I calculate this using the gravitational force alone (such that I use the mass of the water inside the bucket) as:

<$$g \cdot (m_{bucket}+m_{water}) = \rho \cdot g \cdot V_{Liquid}$$>

Or should I calculate the force from the water inside using the hydrostatical pressure as:

<$$m_{bucket} \cdot g + P_{atm} + \rho \cdot g \cdot h1 = \rho \cdot g \cdot V_{Liquid}$$>

Also in relation to the buoyancy force, should I take the angle at the sides into account or do I just use the center of buoyancy?

Thanks

That is, $$m_{bucket\,including\,liquid}= V_{displaced\,water} * \rho_{displaced\,water}$$ where the unknown is $$V_{displaced\,water}$$. Then, since the shape of the displaced water volume is given by the shape of the bucket, we have: $$V_{displaced\,water} = V_{bucket}$$ which can be solved for $$h_{submerged}$$ using the equation described by the question.