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Maths Problem  
User currently offlineB737200 From Malta, joined Feb 2005, 225 posts, RR: 2
Posted (4 years 11 months 1 week 4 days 19 hours ago) and read 1945 times:

Hi,

I have a maths problem and since I've seen people asking all sorts of questions over here I thought "why not?"

So I need to solve this equation: 2.64 = (a) + ln(a)

where a is the variable i'm looking for and ln is the function ln [log_e].

The only thing I could come up with is to insert values of a and repeat the process correcting a as I go.

Anything better than iteration?

Thanks.


Lady Guinness is ready to fly...
11 replies: All unread, jump to last
 
User currently offlineOly720man From United Kingdom, joined May 2004, 6848 posts, RR: 11
Reply 1, posted (4 years 11 months 1 week 4 days 19 hours ago) and read 1930 times:

Is this in any particular bit of maths?

One solution would be to use a series solution for ln(a) which would give a quadratic/cubic you could solve.

http://en.wikipedia.org/wiki/Natural...arithm#Derivative.2C_Taylor_series



wheat and dairy can screw up your brain
User currently offlineB737200 From Malta, joined Feb 2005, 225 posts, RR: 2
Reply 2, posted (4 years 11 months 1 week 4 days 18 hours ago) and read 1888 times:

Its actually a fluids problem but I got stuck on the mathematical part.

The problem has water flowing out of a tank through an orifice whilst water is also flowing into the tank.

I ended up with an integral which I solved using a given result and I ended up with the above equation. It should be correct since my calculator worked it out and the answer matched but our lecturer is a bit fussy so I'm not sure if he'd except that in an exam.

I'll take a look at the link you sent, it seems somewhat familiar, maybe we did it last year in our maths unit. Hopefully something like that would be in the equation sheet we get, good luck trying to remember all the funny mathematical solutions to stuff that MIGHT come out. I get the feeling he is going to test us on mathematics as much us he is going to test us on our fluid's knowledge.

What nudged me towards the iteration method was the fact that the question states the we are to give an approximate answer; of course using a series solution would also yield and approximate value so maybe this is it.

Thanks, series totally slipped my mind, maybe its because I can't stand them  Big grin



Lady Guinness is ready to fly...
User currently onlineBMI727 From United States of America, joined Feb 2009, 15838 posts, RR: 27
Reply 3, posted (4 years 11 months 1 week 4 days 15 hours ago) and read 1812 times:



Quoting B737200 (Reply 2):
The problem has water flowing out of a tank through an orifice whilst water is also flowing into the tank

Perhaps looking at the differential equations for a mixing problem would be of help.



Why do Aerospace Engineering students have to turn things in on time?
User currently offlineYellowstone From United States of America, joined Aug 2006, 3071 posts, RR: 4
Reply 4, posted (4 years 11 months 1 week 4 days 9 hours ago) and read 1711 times:



Quoting B737200 (Reply 2):
What nudged me towards the iteration method was the fact that the question states the we are to give an approximate answer; of course using a series solution would also yield and approximate value so maybe this is it.

What you want to use here is something called Newton's method.

http://en.wikipedia.org/wiki/Newton%27s_method

First, rewrite your equation so that it's equal to zero. f(a) = a + ln(a) - 2.64 = 0

Next, you pick some value of a, call it a_0, that is decently close to the right answer. Then, calculate the following, where f ' (a_0) is the derivative of the function f evaluated at a_0.

a_1 = a_0 - ( f(a_0) / f ' (a_0) )

Calculate a_2 in the same fashion, replacing a_0 with a_1. Repeat until a_n converges.



Hydrogen is an odorless, colorless gas which, given enough time, turns into people.
User currently offlineFabo From Slovakia, joined Aug 2005, 1219 posts, RR: 1
Reply 5, posted (4 years 11 months 1 week 4 days 7 hours ago) and read 1658 times:

Why repeat? If I understood right, you can use limit. You should get to about 1.96467 if I am not mistaken.

I will try figuring out how to isolate a, but do not expect much from me right now...



The light at the end of tunnel turn out to be a lighted sing saying NO EXIT
User currently offlineB737200 From Malta, joined Feb 2005, 225 posts, RR: 2
Reply 6, posted (4 years 11 months 1 week 4 days ago) and read 1596 times:

Firstly thanks for all the input, I wasn't expected this much help for my little mathematical conundrum.

Quoting Yellowstone (Reply 4):
What you want to use here is something called Newton's method.

I was actually studying it this week, when I was trying the fluids problem I hadn't really gone over my maths note yet. Seems to bring a bit of order to my "lets just throw in some values" method.

Quoting Fabo (Reply 5):
Why repeat? If I understood right, you can use limit. You should get to about 1.96467 if I am not mistaken

By using a limit you mean with Newton's method? The version we learned didn't use that, I'll look around but if I misunderstood you I'll be on a wild goose chase for nothing.

Quoting Fabo (Reply 5):
I will try figuring out how to isolate a, but do not expect much from me right now...

Don't worry if you're busy, I understand and thanks for your input.

Quoting BMI727 (Reply 3):
Perhaps looking at the differential equations for a mixing problem would be of help.

I derived a differential equation. The one I derived was:

Q_out - Q_in = A_tank * (dh/dt) where Qs are volume flow rates, A is area and h is the height of water level in the tank.

On working it out using a given result printed under the question itself I ended up with the 2.64 = lna +a.

Not sure if you are referring to the same thing.


Once again thanks a million, very helpful.



Lady Guinness is ready to fly...
User currently offlineAg92 From India, joined Jul 2006, 1317 posts, RR: 0
Reply 7, posted (4 years 11 months 1 week 3 days 20 hours ago) and read 1569 times:

I don't know if I will be of any help, but I would just graph it, and calculate the value through a graph

User currently offlineFlighty From United States of America, joined Apr 2007, 8774 posts, RR: 3
Reply 8, posted (4 years 11 months 1 week 3 days 19 hours ago) and read 1556 times:

Use my very most favoritest website ever:

http://www.wolframalpha.com/input/?i=2.64%3D+a+%2B+ln%28a%29

You're welcome.


User currently offlineFabo From Slovakia, joined Aug 2005, 1219 posts, RR: 1
Reply 9, posted (4 years 11 months 1 week 3 days 17 hours ago) and read 1531 times:

Flighty: That is what I used to come to 1.96467 I mentioned  Smile Nice web, for sure.


The light at the end of tunnel turn out to be a lighted sing saying NO EXIT
User currently offlineWaterpolodan From United States of America, joined Feb 2005, 1649 posts, RR: 5
Reply 10, posted (4 years 11 months 1 week 3 days 16 hours ago) and read 1507 times:

Having Maths trouble? Might I suggest this video as a useful tool-
http://www.youtube.com/watch?v=Pj2NOTanzWI


User currently offlineB737200 From Malta, joined Feb 2005, 225 posts, RR: 2
Reply 11, posted (4 years 11 months 1 week 3 days 15 hours ago) and read 1496 times:

Thanks for the website, its now in my favorites.


Lady Guinness is ready to fly...
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