A hemispherical observation dome is proposed for a new tourist oceanarium and the owners want it as large as possible and as deep as possible. Including the engineering factor of safety, the maximum vertical shear force on the seal holding the dome in place 15 kN. The dome manufacturer states that the transparent plastic is safe from buckling at a horizontal load of 80 kN (for domes less than 2 m in diameter). The seawater density is 1027 kg m -3 .
(a) What is the maximum diameter y2 of the dome that is safe from seal failure?
(b) What is the maximum safe depth y1 that is safe from dome buckling?