Solving an equasion Implicitly, Hydraulics Question

Ok, so I am trying to solve this equasion for y

0.33392=(1/0.027)*(y+2*y^2)*((y+2*y^2)/(2.236+4.472*y))^(2/3)

I should probably know how to do this myself (I've done a million and one math courses over the past 5 years :P) but I would rather get a refresher from one of you guys/gals

The problem involves trying to find the height of water in an open channel given the rate of flow and channel cross section. y is the height of water in question.

Thanks!

Re: Solving an equasion Implicitly, Hydraulics Question

Hey CivilEngineer1988.

Is a numerical approximation OK for your purposes (i.e. to so many decimal places)?

Re: Solving an equasion Implicitly, Hydraulics Question

Hi CivilEngineer1988 !

Don't you see that ((y+2*y^2)/(2.236+4.472*y)) = y/2.236 ?

0.33392=(1/0.027)*(y/2.236)^(2/3)

y = 2.236*(0.33392*0.027)^(3/2) = 0.00191417

Re: Solving an equasion Implicitly, Hydraulics Question

Very nice: I'm glad someone is paying attention :)

Re: Solving an equasion Implicitly, Hydraulics Question

Sorry, there is something wrong in my precceding answer, because I consider the equation :

0.33392=(1/0.027)*((y+2*y^2)/(2.236+4.472*y))^(2/3)

instead of :

0.33392=(1/0.027)*(y+2*y^2)*((y+2*y^2)/(2.236+4.472*y))^(2/3)

So, after simplification, the equation is not :

0.33392=(1/0.027)*(y/2.236)^(2/3)

but :

0.33392=(1/0.027)*(y+2*y^2)*(y/2.236)^(2/3)

0.33392*0.027*2.236^(2/3) = (1+2y)*y^(5/3)

which can be solved thanks to numerical computation, as chiro suggested first.

y = 0.075210480866976