Stability Question

[Caimbeul]

Hallo folks

I've started studying for my Chief mates unlimited. I'm 6 months short of the required sea time and I'm hoping my company (North Star) will support me through it next September. Anyway, I've begun studying stability from the book "Ship Stability For Mates and Masters" the 5th edition by Captain D.R. Derrett, and I've come stuck on a question that I am hoping one of you fine ladies or gents could take a look at for me? Or possibly ask a college lecturer?


A ship arrives at the mouth of a river in water of density 1016 kg per cubic meter with a freeboard of "S" meters. She then discharges 150 tonnes of cargo, and proceeds up the river to a second port, consuming 14 tonnes of bunkers. When she arrives at the second port the freeboard is again "S" meters, the density of the water being 1004 kg per cubic meter. Find the ship's displacement on arrival at the second port.


I believe the subject of this question comes under the heading "Effect of density on displacement when the draft is constant" and I think the equation that's needed to solve it is

NEW DISPLACEMENT / NEW DENSITY = OLD DISPLACEMENT / OLD DENSITY

I presume there is some algebra required to solve this. Unfortunately I don't remember much about Algebra from school.

The answer at the back of the book is 13,721.3 tonnes

Any help at all with this will be much appreciated.

[Clanky]

Not going to tell you how to do it because that would defeat the purpose, but you are on the right tracks.

You know the weight which has been removed from the ship, you know the difference in the density, and you know that the displacement is the same in both cases. You need to come up with a mathematical expression which represents what you have.

[Caimbeul]

Okay so here is the answer I get. I rearranged the equation but that doesn't affect the answer.

(New Displacement - Weight discharged) / Old Displacement = New density / Old Density

( x - 164) / x = 1004 / 1016

1016x - 166624 = 1004x

1016x-1004x = 166624

12x = 166624

x = 166624 / 12

x = 13885.333 tonnes

Then I put that back into the equation to get

New displacement / Old displacement = New density / Old density

x / 13 885.33 = 1004 / 1016

x / 13 885.33 = 0.98818897637

x = 13 885.33 multiplied by 0.98818897637

x = 13 721.33 CORRECT!!

Thanks Guys

[GHedges]

Couple comments on your algebra.

(New Displacement - Weight discharged)

Should be Old displacement - Weight discharged, which would equal New displacement. Presuming that's what you meant, because you replaced both New displacement and Old displacement with x.

Secondly, in the first part you worked out the Old displacement, which you don't really need to do. Remember, if New displacement = Old displacement - weight discharged, then Old displacement = New displacement + weight discharged.

Defining New displacement as x:

New displacement / Old displacement = New displacement / (New displacement + weight discharged) = x / (x + 164)

Therefore:
New displacement / Old displacement = New density / Old density
New displacement / (New displacement + weight discharged) = New density / Old density
x / (x + 164) = 1004 / 1016
1016x = 1004(x + 164)
1016x = 1004x + 164656
1016x - 1004x = 164656
12x = 164656
x = 164656 / 12 = 13,721.33

[Caimbeul]

Couple comments on your algebra.



Should be Old displacement - Weight discharged, which would equal New displacement. Presuming that's what you meant, because you replaced both New displacement and Old displacement with x.

Secondly, in the first part you worked out the Old displacement, which you don't really need to do. Remember, if New displacement = Old displacement - weight discharged, then Old displacement = New displacement + weight discharged.

Defining New displacement as x:

New displacement / Old displacement = New displacement / (New displacement + weight discharged) = x / (x + 164)

Therefore:
New displacement / Old displacement = New density / Old density
New displacement / (New displacement + weight discharged) = New density / Old density
x / (x + 164) = 1004 / 1016
1016x = 1004(x + 164)
1016x = 1004x + 164656
1016x - 1004x = 164656
12x = 164656
x = 164656 / 12 = 13,721.33

Nice one. That's made it all crystal clear now. Much appreciated