- #1

jared30

## Main Question or Discussion Point

what are the effects on gravity if the object is dropped underwater?

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- #1

jared30

what are the effects on gravity if the object is dropped underwater?

- #2

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gravity's pull is the same, you just have a lot more drag underwater so it falls more slowly

- #3

jared30

so are there any equations for the free fall acceleration of an object underwater?

- #4

Integral

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To model dynamics underwater you would need to take bouyancy and drag into account. There are different ways of modeling drag, usually it is a lossy term in the inital differential equations which is depentend on velocity.

- #5

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m(d2x/dt2) = (rhoB-rhoA)(g*V) - 0.5(Cd)(rhoA)(A)(dx/dt)^2

Where m = body's mass, rhoA = fluid's density, rhoB = body's density, g = gravity (may be assumed to vary with height -> which is where the "effects of gravity" come in), x = displacement, t = time, Cd = drag coefficient, V = body volume, A = body area.

If the height changes are vast, you would also probably want to make rho, V and A a function of x as well.

Be a bit careful with the drag term in the equation - some quoted values of Cd use, for example,*wetted* area while others use *cross-sectional* area. Check the definitions before using it.

You can analytically solve that, write up your own program to solve it numerically or buy a math program which is capable of solving differential equations - MathCad comes to mind. Option 1 will help you only in the most ideal circumstances, while option 3 is a bit more general. Option 2 is the most general but most difficult to learn, and will solve even your nasty partial integro-differential equations with the most unusual boundary conditions, etc.

*Edit*: Note that the equation here is for a fully submerged body. For a partially submerged one, break the first RHS term to the body weight and a bouyant force, the latter as per Archimedes' principle.

Where m = body's mass, rhoA = fluid's density, rhoB = body's density, g = gravity (may be assumed to vary with height -> which is where the "effects of gravity" come in), x = displacement, t = time, Cd = drag coefficient, V = body volume, A = body area.

If the height changes are vast, you would also probably want to make rho, V and A a function of x as well.

Be a bit careful with the drag term in the equation - some quoted values of Cd use, for example,

You can analytically solve that, write up your own program to solve it numerically or buy a math program which is capable of solving differential equations - MathCad comes to mind. Option 1 will help you only in the most ideal circumstances, while option 3 is a bit more general. Option 2 is the most general but most difficult to learn, and will solve even your nasty partial integro-differential equations with the most unusual boundary conditions, etc.

Last edited:

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krab

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