Chemical Engineering - Fluid Mechanics - Discussion
Discussion Forum : Fluid Mechanics - Section 5 (Q.No. 43)
43.
What is the force required (in Newtons) to hold a spherical balloon stationary in water at a depth of H from the air-water iterface? The balloon is of radius 0.1 m and is filled with air.
Discussion:
1 comments Page 1 of 1.
Sirius Rankine said:
3 years ago
The force required = Buoyancy force - gravitational force.
Buoyancy force = mass of fluid displaced x g.
The mass of fluid displaced = density of fluid x volume of the balloon = 1000 x 4/3 x π x (r^3) = 4/3π.
Buoyancy force = 4/3 x π x g.
Gravitational force = mass of the balloon x g.
mass of the balloon = density of air x volume = 1.225 x 4/3 x π x (r^3) = 0.001225 x 4/3 π.
Gravitational force = 0.001225 x 4/3 x π x g.
The force required = Buoyancy - gravitational = 4/3 x π x g (1 - 0.001225) = 4/3 x π x g x 0.998 = 4/3 x π x g.
Buoyancy force = mass of fluid displaced x g.
The mass of fluid displaced = density of fluid x volume of the balloon = 1000 x 4/3 x π x (r^3) = 4/3π.
Buoyancy force = 4/3 x π x g.
Gravitational force = mass of the balloon x g.
mass of the balloon = density of air x volume = 1.225 x 4/3 x π x (r^3) = 0.001225 x 4/3 π.
Gravitational force = 0.001225 x 4/3 x π x g.
The force required = Buoyancy - gravitational = 4/3 x π x g (1 - 0.001225) = 4/3 x π x g x 0.998 = 4/3 x π x g.
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