Calculating Buoyancy Rate of Rise for a Ship

[gloo]

Can someone give me a formula or give an approximate approach to calculating the time it would take for an object to be raised up (due to buoyancy) from a certain depth of water?
For instance, take a ship (say it weighs 300,000kg and it's a rectangular shape with surface area of 100m square (10m by 10m). If i attach enough air ballons around the ship , what would be the variables and formula to use to get an approximate time it would take to raise the ship to the surface from say 100meters of water (sea water).

I assume that the the surface area of the ballons might be a factor too but let's just leave those out (say i put the underneath the ship). I am not concerned about the acceleration at the end destroying the ship near the surface. I am fearful of this solution turning into a series of calculus equations b/c of the rate of change of pressure as the ship goes higher.

 

[jasc15]

I am fearful of this solution turning into a series of calculus equations b/c of the rate of change of pressure as the ship goes higher.

I'm afraid this will be the case. It will be the same as an object falling through the atmosphere and reaching terminal velocity. The object will have a constant buoyant force acting upward, tending to increase its speed, however increase in speed will increase the resistance of the water. It will reach an equilibrium where the resistive drag force will equal the buoyant force. The transient portion may be small compared to the steady state portion, so you could probably get away with finding which speed through the water will give a drag force equal to the buoyant force.

 

[sir-pinski]

The formula for calculating buoyancy force is Fb = ρVg, where ρ is the density of the fluid (in this case, sea water), V is the volume of the object submerged in the fluid, and g is the acceleration due to gravity.

To calculate the time it would take for the ship to rise, we can use the equation d = 1/2at^2, where d is the distance traveled, a is the acceleration, and t is the time. In this case, d is the depth of the water (100 meters) and a is the acceleration due to buoyancy (calculated using the formula above).

Since the ship is rectangular, we can use the formula V = lwh, where l is the length, w is the width, and h is the height of the ship. So, the volume of the ship is 10m x 10m x h.

Now, to find the time it would take for the ship to rise, we can set the two equations equal to each other and solve for t.

1/2at^2 = 100

Substituting in the values we have calculated, we get:

1/2(ρVg)t^2 = 100

Solving for t, we get:

t = √(200/ρVg)

We can plug in the values for density (since we are working with sea water, we can use an average density of 1025 kg/m^3), the volume of the ship (10m x 10m x h), and the acceleration due to gravity (9.8 m/s^2).

So, the formula for calculating the approximate time it would take for the ship to rise would be:

t = √(200/1025 x 10m x 10m x h x 9.8 m/s^2)

This formula takes into account the weight of the ship, the density of the fluid, and the depth of the water. However, as you mentioned, there are other factors that could affect the time it takes for the ship to rise, such as the surface area of the balloons and the acceleration at the end. To get a more accurate calculation, you may need to consider these factors and use a more complex equation that takes them into account.