A fine tube whose section k is a function of its lengths s, in the form of a closed plan curve of area A, filled with ice, is moved in any manner. When the component angular velocity of the tube about a normal to its plan is Ω, the ice melts without change of volume. Prove that the velocity of the fluid relativity to the tube at a point where the section is K at any subsequent time when ω is the angular velocity is,the internal being taken once round the tube.