a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic equilibrium. Show that the buoyancy force acting on the fluid element may be written as -(Pe - p)g where pe is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation. Pe dv dt
a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic equilibrium. Show that the buoyancy force acting on the fluid element may be written as -(Pe - p)g where pe is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation. Pe dv dt
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Transcribed Image Text:Question 1
a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic
equilibrium. Show that the buoyancy force acting on the fluid element may be written as
Pe
dv
dt
=
-(Pe - p)g
where
Pe
is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of
the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation.
b) With the aid of a diagram, explain the condition required for convection to occur by considering the small displacement of a
fluid element from its original equilibrium location within a star.
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