Ship draft (draught) word problem buoyancy

In summary, the draft of a ship is the distance between the waterline and the bottom of the ship. In this problem, a ship arrives from the Atlantic to the Baltic sea and the density of the water changes due to salinity. Using Archimedes' principle, the volumes of water displaced by the ship in both the Atlantic and Baltic seas can be calculated. The difference in these volumes is then divided by the cross-sectional area of the ship to find the change in height of the displaced water. This results in a deepening effect of approximately 5.3 cm.
  • #1
301
15

Homework Statement


ship arrives from the Atlantic to the Baltic sea. How much does the draft of the ship deepen due to the saltyness of the water...

density of atlantic water = 1027kg/m^3
density of baltic water = 1005kg/m^3

at these depths the crosssectional area of the ship can be assumed to be 4000m^2
ship and cargo mass = 10000 metric tons
g= 9,81m/s^2

Homework Equations


N= ρ V g

G=mg

The Attempt at a Solution



I have no idea what ship draft is. I have only once been on a ship in my life. I have no idea why the the cross-sectional area would be relevant in this problem.

But I decided to calculate the volumes of water, which the ship displaces in atlantic,

And then displaces in the baltic.

I think those volumes will be different because water density changes.

Natlantic = ρatlantic x Vatlantic x g

Vatlantic= 9737, 0983 m^3Nbaltic = ρbaltic x Vbalticx g

Vbaltic = 9950,2487 m^3I was later on thinking that maybe if I were to take all the water into a huge box

Then you could divide the displaced water volumes, by the area

Therefore you end up with height ( I think) Or something to this effect could be done.

If this is calculated so, then the difference between the heights of the displaced water is

(9950,2487m^3) / 4000m^2 = 2,4875 m = height baltic

9737,0983 m^3 / 4000m^2= 2,4342 m height atlantic.

calculate Δheight = 0,0533m

the deepening effect ought to be about 5,3 cm

please notify whether or not errors of understanding of judgement were made.
 
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  • #2
late347 said:

Homework Statement


ship arrives from the Atlantic to the Baltic sea. How much does the draft of the ship deepen due to the saltyness of the water...

density of atlantic water = 1027kg/m^3
density of baltic water = 1005kg/m^3

at these depths the crosssectional area of the ship can be assumed to be 4000m^2
ship and cargo mass = 10000 metric tons
g= 9,81m/s^2

Homework Equations


N= ρ V g

G=mg

The Attempt at a Solution



I have no idea what ship draft is. I have only once been on a ship in my life. I have no idea why the the cross-sectional area would be relevant in this problem.
You have a computer connected to the internet. "I have no idea" is no longer much of a reason for not looking stuff up. There are dictionaries on line which can help you find the meaning of unfamiliar terms.

BTW, the draft of a vessel is the distance it sinks in the water when it is floating.
But I decided to calculate the volumes of water, which the ship displaces in atlantic,

And then displaces in the baltic.

I think those volumes will be different because water density changes.
Good. Remember Archimedes' Principle.
Natlantic = ρatlantic x Vatlantic x g

Vatlantic= 9737, 0983 m^3Nbaltic = ρbaltic x Vbalticx g

Vbaltic = 9950,2487 m^3I was later on thinking that maybe if I were to take all the water into a huge box

Then you could divide the displaced water volumes, by the area

Therefore you end up with height ( I think) Or something to this effect could be done.

If this is calculated so, then the difference between the heights of the displaced water is

(9950,2487m^3) / 4000m^2 = 2,4875 m = height baltic

9737,0983 m^3 / 4000m^2= 2,4342 m height atlantic.

calculate Δheight = 0,0533m

the deepening effect ought to be about 5,3 cm

please notify whether or not errors of understanding of judgement were made.
Sounds like some solid reasoning here.
 
  • #3
To begin with
Draft ; It is the distance between the waterline and the bottom of the ship(hull)
That should help you .And looking at your work it seems legit
Be sure to check your calculation
 
  • #4
Edit : Removed duplicate information
 

1. What is the definition of ship draft (draught)?

Ship draft (draught) refers to the vertical distance between the waterline and the bottom of the hull of a ship. It is a measure of the ship's immersion in the water.

2. Why is ship draft (draught) important?

Ship draft (draught) is important because it affects the buoyancy of the ship, which in turn affects its stability, speed, and ability to navigate through shallow waters. It is also a crucial factor in determining the amount of cargo a ship can carry.

3. How is ship draft (draught) calculated?

Ship draft (draught) is calculated by measuring the distance from the waterline to the bottom of the hull at the deepest point of the ship. This measurement is then compared to the ship's design draft, which is the intended maximum immersion of the ship.

4. What is the relationship between ship draft (draught) and buoyancy?

The ship draft (draught) and buoyancy are inversely related. As the draft of the ship increases, the amount of water displaced by the ship also increases, resulting in greater buoyancy or upward force on the ship. This buoyancy helps to keep the ship afloat and stable.

5. How do ship draft (draught) word problems relate to real-life situations?

Ship draft (draught) word problems are often used in naval architecture and marine engineering to determine the stability and seaworthiness of a ship. They are also relevant for ship captains and navigators who need to calculate the ship's draft in order to safely navigate through shallow waters or narrow channels.

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