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Danimal
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If you had a tube a couple of miles long filled with very compressed air, say 6,000 PSI, would an object you dropped in it fall very slowly? Even a heavy object like an anvil, how long would it take to drop?
Welcome to PF.Danimal said:Even a heavy object like an anvil, how long would it take to drop?
What's the viscosity of air at 6000 psi, and how does that come in for the drag?phyzguy said:Another way to look at it is that at 6000 psi, air has a density of about 500 kg/m^3, so about 1/2 the density of water. So you can get a rough idea by asking how fast it will fall in water. An iron anvil will certainly fall in water, but much more slowly than in air. You can calculate how fast with the formula in Post #2. It is estimated that the Titanic took about 5 minutes to fall the 13,000 feet to the ocean floor, which works out to about 30 miles/hour.
Good question. If I understand correctly, the viscosity of air, even at 6000 psi, is approximately 50X less than the viscosity of water. So I think you are saying that my analogy with water is false, and an object will fall a lot faster through 6000psi air than through water. Is that correct? How do I take the viscosity into account when calculating the drag force?Chestermiller said:What's the viscosity of air at 6000 psi, and how does that come in for the drag?
I don't know the exact viscosity (it is, of course, available or can be obtained from a corresponding states plot). If the body were a sphere, you could use the drag coefficient vs Reynolds number for a sphere.phyzguy said:Good question. If I understand correctly, the viscosity of air, even at 6000 psi, is approximately 50X less than the viscosity of water. So I think you are saying that my analogy with water is false, and an object will fall a lot faster through 6000psi air than through water. Is that correct? How do I take the viscosity into account when calculating the drag force?
That formula makes terminal velocity inversely proportional to fluid density. But if you look at an energy analysis and consider the energy imparted to the column of air displaced in one unit of time then if you fall twice as fast...Halc said:Terminal velocity is ((2mg)/(ρAC))
mass, gravity/acceleration, ρ density of fluid, Area and C=drag coefficient
So 6000 psi is about 400 times the density of atmosphere at sea level, so the anvil falls at around 1/400th the speed. This formula doesn't take into account the buoyancy of the falling object. If it is low density and immune to compression by the fluid, eventually its weight reduces to zero and it doesn't fall at all. Hence I suspect the mg part of the equation (which equates to force in a vacuum) should be converted to weight, which already has buoyancy worked in.
So 2f/(ρAC) where f is weight, is how I would express it.
The density of the air has a significant impact on the speed of an object falling through highly compressed air. As the air becomes more compressed, its density increases, which creates more resistance against the falling object. This resistance, also known as air resistance, slows down the object and causes it to fall at a slower speed.
The acceleration of an object falling through highly compressed air can be affected by several factors. These include the mass and shape of the object, the density and viscosity of the air, and the force of gravity. The more massive the object, the faster it will accelerate due to the force of gravity. Objects with a larger surface area or streamlined shape will experience less air resistance and therefore accelerate faster.
The temperature of the air has a minor effect on the speed of an object falling through highly compressed air. As the air becomes colder, it becomes denser, which can slightly increase the amount of air resistance the object experiences. However, this effect is minimal compared to other factors such as the mass and shape of the object.
Yes, the shape of the falling object can have a significant impact on its speed through highly compressed air. Objects with a streamlined shape, such as a bullet, will experience less air resistance and therefore fall at a faster speed compared to objects with a larger surface area, such as a feather. This is because the streamlined shape allows the air to flow smoothly around the object, reducing the amount of resistance.
The air pressure plays a crucial role in the speed of an object falling through highly compressed air. As the air becomes more compressed, the air pressure increases, which creates more resistance against the falling object. This resistance slows down the object and can even cause it to reach a terminal velocity, where the force of gravity is equal to the force of air resistance, resulting in a constant falling speed.