Buoyant Force

Buoyant Force

BUOYANT FORCE
When an object is immersed in a liquid, it experiences an upward force. This force is called buoyant force. 
Let us consider a cylindrical object of height ‘h’ with cross sectional area ‘A’ and let ‘d’ be the density of the liquid.
                    

Pressure at a depth h₁ is P₁ = P_o + h₁ d g ( here P_o = atmospheric pressure) 
    Force F₁ = P₁A = (P_o+h₁dg) A ....... (a)
    This force acts downward on the body by liquid
    Similarly, pressure P₂ at depth h₂ is given by
    P₂ = P_o + h₂ d g 
    Force F₂ = P₂A = (P_o+h₂dg) A ....... (b)
    This force acts upward on the body by liquid
    As h₂ > h₁ so F₂ > F₁
    From equations (a) and (b) we get
    F₂ - F₁ = (h₂ - h₁)A d g
    from the figure h = h₂ - h₁ so we have, F₂ - F₁ = Ahdg
    Pressure difference P₂-P₁ = (h₂-h₁)dg=hdg
    As Ah = V (volume of body = volume of displaced liquid)
     so F₂ - F₁ = Vdg
    As Vd = m (mass of displaced liquid) so 
    F₂ - F₁ =F= mg = W (weight of the displaced liquid)
Here ‘F’ is the force applied on the object and ‘W’ is the weight of the displaced liquid. So the force applied on the object by the liquid is equal to the weight of the displaced liquid.The force applied on the object in upward direction is called “Buoyancy”. As per the above equation this buoyant force is equal to the weight of the liquid displaced by the object.

Factors Affecting Bouyant Force:
The magnitude of buoyant force acting on an object immersed in a liquid depends on two factors:
(i)  volume of object immersed in the liquid, and
(ii) density of the liquid.