What is the equation to calculate the time a submerged object takes to float in to the surface?

Question

buoyancy force.. time to take submerge objects to the surface

Answer 1

The net force on the submerged object will be the buoyancy force (a constant, in the up direction) countered by the drag force (a function of velocity, opposite in direction to the velocity) and the force of gravity (a constant, in the down direction).

So F = Fb - Fd - Fg

Fb = ρ V g
Fd = 1/2 C A ρ v² (C = drag coefficient)
Fg = m g

F = ρ V g - 1/2 C A ρ v² - m g

Since acceleration = F/m, then

a = ρ V g / m - 1/2 C A ρ v² / m - g

Here is where it gets tricky. Acceleration is the derivative dv/dt. If you plug that into the equation above, you have a differential equation. You need to integrate that equation to solve for the velocity of the submerged object, after which you can solve for the time it takes to surface.

You can get an approximate answer easier by assuming that the submerged object reaches "terminal velocity" quickly, where terminal velocity is defined as the velocity at which Fb = Fg + Fd. Now that you have a constant velocity, solving for the surfacing time becomes trivial.

Answer 2

There are the kinetics, F = m a to find the forces, and the kinematics, a = dv/dt to find the time to travel a given distance under constant acceleration.

Answer 3

you may sort it right into a shape that could displace an quantity of water that weighs a minimum of as lots through fact the textile. Thickness and floor section are in basic terms components of the answer.