An under-sea laboratory is sealed by a circular door of radius 1.2m at the bottom of an access shaft. The shaft is filled from the top with 50m of crude oil of density 850kgm−3 floating on 200m of seawater of density 1030kgm−3. The free surface of the oil is open to the atmosphere.
(i) Derive an expression for the absolute pressure on the outside of the door in terms of the given thicknesses and densities.
(ii) Using the derived expression, calculate the total force exerted on the door. Take atmospheric pressure as 1.01×105Pa.
(iii) If the oil layer were removed while the seawater height remained the same, by what percentage would the force on the door change?