How Can You Solve the Equation (U2-U1)=259.2(U2*U1) with Two Unknowns?

[skaboy607]

Hi

I have the following equation:

(U2-U1)=259.2(U2*U1)

Both U1 and U2 are unknowns. Its been suggested to use an iterative process like Newton Raphson to solve but all examples using this technique are only for one unknown.

(U2-U1) is the value of interest.

Thanks

 

[I like Serena]

You have 1 equation with 2 unknowns.
There is no single solution for that.

If you want a solution, you can take U1=0 and U2=0.

The set of all solutions is a hyperbola.

 

[Studiot]

Sometimes it is possible to solve these types of equation if we know what U₁ and U₂ refer to.

For instance if they are sides of a rectangle and there is some area restriction.

Another case (coupled chemical reactions) is solved in posts 57 - 61 of this thread

https://www.physicsforums.com/showthread.php?t=398208&highlight=seawater

go well

 

[stevenb]

(U2-U1) is the value of interest.

Thanks

I don't see a way to solve for the difference between the variables, but you can solve for the ratio of them U2/U1.

U2/U1-U1/U2=259.2

Let x=U2/U1

x-1/x=259.2

x^2-259.2x-1=0

Now you can solve the quadratic.

 

[skaboy607]

Its an equation for drag that has been reduced to its current format. The constant 259.2 comes from the delta t. I need to find how much the speed drops by, i.e. delta U.

 

[stevenb]

I need to find how much the speed drops by, i.e. delta U.

The ratio U2/U1 could be considered a measure of how much the speed drops by. And, once you know one value (either U2 or U1) you can calculate the other and identify U2-U1.

 

[Studiot]

Hello, Steve, nice analysis.

Amazing what you can squeeze out of something if you really try!

Perhaps you would like to try your hand at this equation now?

https://www.physicsforums.com/showthread.php?t=496285