Question

consider a sphere of mass m moving through an incompressible and irrotational fluid extending to infinity. find the velocity distribution around the sphere and show that the effective mass of the sphere is m + 1 2m0, where m0 is the mass of the displaced fluid

Answer 1

Pressure at a depth h below the surface of water=atmospheric pressure + pressure due to water column of height h.If atmospheric pressure is P, then 2P=P + hρg or hρg = PBut P=10 N cm–2=l0N/(10–2 m)2=105 N m–2Hence h=P/ρg=105/(103 × 9.8)=10.2 mThus a water column of height 10.2 m exerts a pressure equal to the atmospheric pressure.