The pressure at the bottom of a full barrel of water is Poriginal . Determine what happens to the pressure when the radius or height of the barrel is changed and water is added to make the barrel full again.

a)   P' = P_original, b)  P ’= P_original + ρ  g Δh

Explanation:

The expression for nanometric pressure is

          P = ρ g h

where ρ  is the density of the liquid and h is the height

a) we change the radius of the barrel, but keeping the same height

as the pressure does not depend on the radius it remains the same

        P' = P_original

b) We change the barrel height

         h ’≠ h

we substitute in the equation

      P ’= ρ  g h’

      h ’= h + Δh

      P ’= ρ  g (h + Δh)

      P ’= (ρ  g h) + ρ  g Δh

      P ’= P_original + ΔP

In this case, the pressure changes due to the new height,

*if it is higher than the initial one, the pressure increases

*if the height is less than the initial one, the pressure is less