# Bernoulli, Fluid Dynamics, and ships

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1. May 7, 2015

### ManicPIxie

1. The problem statement, all variables and given/known data

The Plimsoll line is a line marked on the side all ships that effectively indicates the safe maximum load the ship can carry in that type of water at that temperature.

You have been asked to stand on the dock and collect the tickets of the passengers boarding a cruise ship and notice the Plimsoll line is 1cm above the water. The crew and all the baggage are already aboard. Over the next two hours 2205 passengers of average mass 75.0kg board the ship. At the end of this time you notice that the surface of the water is now at the Plimsoll line. Assume the ship is in a fresh water dock while it is being loaded.

a) What is the horizontal cross-sectional area of the ship at the level of the Plimsoll line?

b) When the ship leaves the river and moves out into the sea will the water level remain at the height of the Plimsoll line, will it rise above the line or will it drop below the line? Explain your answer.

c) If the ship no longer sits with its Plimsoll line at sea level when it is in the sea what is the distance between the line and sea level? The Plimsoll line is 10m above the bottom of the ship.

2. Relevant equations
P = F/A
F = mg - density(water) x Vdisplaced x g
P + density x gravity x height + 1/2 density x v2
3. The attempt at a solution
I know that for (b) I need to used Bernoulli's equation, however for (a) I am having trouble finding the force and pressure to determine the area.

I'm not sure where to start, so a poke in the right direction would be great.

Thank you

2. May 8, 2015

### SammyS

Staff Emeritus
I don't think Bernoulli will be of any use here.

Archimedes should be all you need for (a) and for (b) .

3. May 8, 2015

### Simon Bridge

What is your reasoning for this? As SamyS suggests, try taking another look at Archimedes instead.
Draw a free body diagram for the ship - what are the forces?

4. May 8, 2015

### ManicPIxie

Thanks.

I already drew a free body diagram, probably should have mentioned that.
The two forces are the buoyant force provided by the fresh water, and the gravitational force. Where I'm stuck I suppose is mostly we aren't given the original weight of the ship, or does this not matter and I should only take into account the 75kg x 2205 people?

5. May 8, 2015

### SteamKing

Staff Emeritus
It doesn't matter what the original weight of the ship was.

You know how much additional weight was taken aboard the ship and by how much the draft of the ship changed after this weight was added. From these two pieces of information, and knowing (or looking up) the density of fresh water, you should be able to answer a) above.

SammyS and Simon are right. This is a problem in fluid statics, not fluid dynamics, so put Mr. Bernoulli back in the toolbox.

6. May 8, 2015

### Simon Bridge

Recall: A floating object displaces it's own weight in water.
You should express the weight of water displaced in terms of the volume of water displaced before and after the passengers get on board.
Everything you don't know, just write it down as a variable. You'll end up with two equations and two unknowns.