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A spherical mass m with radius r of a known fluid with density ρ floats in the vacuum. Calculate the pressure P at the distance x from the center due its own gravity.
Alsouros said:... at the distance x from the center due its own gravity.
We are on different wavelengths, here. I'm picturing a sphere of liquid in space where g = 0 and P = ρgh is zero. Looking for the pressure inside the sphere "due its OWN gravity". Remember it "floats in vacuum" whereas if it were at the surface of the Earth, g would pull it down to smash on the bottom of its container.P=ρgh
Delphi51 said:We are on different wavelengths, here. I'm picturing a sphere of liquid in space where g = 0 and P = ρgh is zero. Looking for the pressure inside the sphere "due its OWN gravity". Remember it "floats in vacuum" whereas if it were at the surface of the Earth, g would pull it down to smash on the bottom of its container.
uros said:The mass from the radius x:
V'=4πx³/3
m'=4πx³ρ/3
The pressure at the distance x:
P=ρgh
P=ρGm'(r-x)/x²
P=ρ²G4πx(r-x)/3
uros said:P → hydrostatic pressure
P=ρgh
P=ρ²G4πx(r-x)/3
Delphi51 said:Wouldn't the spherical shell with thickness dR be easier to work with?
A thin "column" would have to be wider at the top than at the bottom, wouldn't it?
In order to calculate the pressure inside a fluid sphere due to its own gravity, you will need to use the formula P = (2/3) * (G * rho^2) * (M^2 / R^4), where P is the pressure, G is the gravitational constant, rho is the density of the sphere, M is the mass of the sphere, and R is the radius of the sphere.
The pressure inside a fluid sphere due to its own gravity is affected by the density and mass of the sphere, as well as the gravitational constant and the radius of the sphere.
No, the pressure inside a fluid sphere due to its own gravity is not constant throughout the entire sphere. It decreases towards the outer edges of the sphere due to the decreasing strength of the gravitational force.
The pressure inside a fluid sphere due to its own gravity is higher than the pressure at the surface of the sphere. This is because the weight of the fluid above the surface exerts a downward force, increasing the pressure at the center of the sphere.
No, the pressure inside a fluid sphere due to its own gravity cannot be negative. This is because the gravitational force always acts inwards, causing the pressure to be positive at all points within the sphere.