Why do ships float? If this question bothers you don’t worry you are not alone, many others have been baffled by this very question. So lets take a deeper look to understand…

When an object is placed in water it is acted upon by two forces a) Buoyancy & b) Gravity.

What is Buoyancy?

Is an upward force exerted by a fluid on objects immersed in it.

What’s the reason behind this upward force?

Pressure difference! Pressure increases as depth increases (P = ρgh).

 

pressure

Consider a cube placed in water. The pressure at the top surface will always be lesser than the bottom surface by ρgH. Since P = F/A therefore the total vertical force due to pressure would be (horizontal forces will cancel out)

F buoyancy = (P bottom)A- (P top)A

F buoyancy =  (ρ fluid)(g) (H bottom -H top) A

Since H bottom-H top is nothing but the height of the cube H

F buoyancy = (ρ fluid)(g)(H) A

Now lets take a closer look at the above equation. (H)(A) is the volume of the cube which is also equal to the volume occupied by the cube in water. Which implies that the cube has taken up that volume by replacing equivalent volume of water, which is commonly referred as displacement.

So we can say that displacement is equal to the volume of the object’s  submerged volume.

 

submerged-vol

Now we can state the famous Archimedes principle

Archimedes principle: An object that is partly or completely submerged in a fluid will experience a buoyant force equal to the weight of the fluid the object displaces.

F buoyancy = (ρ fluid ) (g) (V Displaced)

The other force acting on the object is Gravity/ Weight of the object which acts downwards.

fbd

 

From the free body diagram, as shown above, let us write an equation using Newton’s second law

∑F = M.A                                   { F = Force , M = Mass, A = Acceleration }

For the body to be at rest F gravity = F buoyancy.

M.g = (ρ fluid ) (g) (V Displaced)

It’s a no brainier, that the ship weighs a lot, which usually baffles us how can a ship float and while a pin sinks.What we do not realise is that because of the ship’s shape it displaces equivalent amount of water, which enables it to float.

To know more about how the ship’s shape (aka Hull Form) is developed stay tuned…

 

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