Differentiation Problem

[awibroe]

Hello,

I am working from a Naval Architecture book which gives a problem to which I want to use MatCAD Prime to go through the problem myself (as the book has no explanation).

The initial expression is:

KM=0.5T+B^2/12T

Where the expressions are:

KM is a naval arch term which represents the distance from the Keel of a ship to the Metacentre

B is the Breadth of the Ship

T is the Draught.

The book gives a plot of the above expression for a ship with a breadth (B) of 15 and shows how as T increases KM reduces to a point.

The book goes on to state that you can find the draught (T) when KM is at its lowest value by differentiating the above expression with respect to T and equating to zero. It then gives this as:

dKM/dT = 0.5-B^2/12T^2

and states in the example of a ship with B of 15 the answer would be 6.12.

I however cannot work out how this was derived or how to use MatCAD to solve such a problem.

Any advice warmly welcomed.

Andy

[RichardJ]

There's more than one way to approach this.

[LucMeekes]

Here's one more (I'm limited to Prime express, so cannot do the symbolics):

success!
Luc

[RichardJ]

In short (I'm limited to Prime express, so cannot do the symbolics):

Glad to oblige

[LucMeekes]

Thanks, Rich.

I am able to see that in your attachment (which I can open with Prime 3.1 Express); as long as I don't mess with any unsupported (by Express) equations it still shows the answers.

Luc

[RichardJ]

as long as I don't mess with any unsupported (by Express) equations it still shows the answers.

That's true. I haven't quite decided if I think that's a good feature of Prime or a bad one. I don't think it can do any harm, but I'm not 100% sure of that.

[LucMeekes]

I share your doubt. I think Mathematica offers similar behaviour: it can store the answers with the file so you don't have to recalculate all when you re-open the notebook.

Luc

[Fred_Kohlhepp · Accepted solution]

Simply done (Prime 3.0)

[awibroe]

Hello to all!

Thank you so much for all the help, I really appreciate it!

As far as I can see these are all the correct answer but I have selected the last one as the correct answer as it has a file for me to refer to (I am a kinetic learner and learn best through re creating the sheet myself).

Thanks,

Andy