Question #3394d

1 Answer
Feb 16, 2018

F_B = rho_WgV= (rho_W/rho_Bg)m_B

Explanation:

Let's denote
F_B larr the buoyancy force
Vlarr the submerged volume,
rho_W, rho_Blarr density of water, density of the body
m_W, m_B larr mass of water, mass of the submerged part of the body (note, not the mass of the body it self)

Buoyancy is the weight of the volume of water being displaced by
partially immersed body; hence, it's directly related to the (total) mass of body. However, the mass of the submerged part of the body is related to the submerged volume by density. So we can reformulate the buoyancy force as the followings:

The buoyancy is expressed as:

F_B = m_Wg = rho_WVg ...............................................(1)

From the mass of the submerged part of the body:

m_B= rho_BV rArr V=m_B/rho_B..................................(2)

F_B = rho_W(m_B/rho_B)g = (rho_W/rho_Bg)m_B

However, buoyancy defined this way in not very practical because m_B is not as easily determined as it's submerged volume.w

The more practical form of buoyancy is Eq.(1)