Balloon buoyant force

The first term on the right-hand side is known as the buoyant force, the second is known as thrust. If this were just a puff of hot air without the balloon exhaust, we would only have the buoyant force acting. In this case we could not ignore (d/dt) Jjf pvxdV since the puff would rise (vx +) solely due to its buoyancy, with viscous effects retarding it. Buoyancy generated flow is an important controlling mechanism in many fire problems. 

A spherical balloon is 10 ft in diameter and has a buoyant force 0.1 Ibf greater than its weight. What is its terminal velocity when rising through air ... 

When the loop is placed at the bottom of the frame, where the film is thickest, there is a buoyant force that causes it to move upward. As it rises the surrounding film becomes thinner, and the loop loses its buoyancy until it stops where F = 0. This is exactly similar to the case when a balloon is rising in the stratified atmosphere where the density decreases with height. This, therefore, is the experimental demonstration of the similarity of the equilibrium of the atmosphere. Figure 4.23a illustrates the rising of a hole with Re5molds number Re = 200. 

This is a very important result which is significant for problems involving buoyant fluids. Finally, the last force to consider is the weight for the balloon consisting of the massless membrane and the hot air pg Vb ... 

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