1. Consider a gas bubble rising in a liquidfilled tube. If the bubble volume (VB) and tube radius (RT) are such that VB1/3>RT, then the bubble will be highly elongated. In this situation, the bubble is similar to a cylinder of radius RB and length L as shown in the Figure. The liquid film between the bubble and tube wall is expected to be very thin (H=RTRBRB). Consequently, local rectangular coordinated can be used in the liquid film as shown in the Figure, and the coordinate origin is fixed on the wall. Note that U is the mean rise velocity of the bubble. The velocity at the gas-liquid interface differs from U and it is not a known quantity (do not use U ). Assuming that the flow in the liquid film is fully developed; a) Derive the steady-state differential equation for the velocity distribution in the liquid film, b) Define the boundary conditions and solve the differential equation, c) Obtain the average velocity in the liquid film