Expert: Alon Mandes - 10/3/2010

Question
QUESTION: Hi
I am confused about how to draw rough graphs of the rates of change of increasing height in a bottle with increasing volume of water.
I am attaching shapes and graphs to choose from. I have done some answers. Can u check if i have chosen the right ones.
Thanks

ANSWER: Hi Sofia,
You attached the figures of the bottles. Each shape has diffrent
equation to work with. I need to see the exercise in order to choose
one. Usually most of the questions are related to the shapes :
Conical Flask AND Bucket. However, please send me the question.
Best Regards,
Alon.


---------- FOLLOW-UP ----------

QUESTION: here are the answers

Answer
Ok Sofia, For every bottle we will assume that the volume of the water is growing lineary in time. The height will change in such
fashion that will be determined by the shape of the bottle. Because
this shape will determine the relation between volume & height .
So, lets start 1 by 1 :

Evaporating flask --> Grapg:(i)
At 1st the hight's rate is slow , the at the middle it slows down
& then it grows again, because the shape is getting tighter .


Vase --> Graph(e)
The rate at 1st is slow more than the evaporating flast , then
speeds because of the tight walls , then slows down again .


Conical flask --> Graph(d)

Bucket --> Graph(a)

Plugged Funnel --> Graph(b)

Ink Buttle --> Grapg(f)

Alon.