Solving this equation

carnagesri

Could someone help me with this equation. It is for calculating viscosity in centi-stokes using an ISO flow cup. The formula is as follows:


Time T1= 75

Cst= (1.37*T1)-(200/T1)
Cst= (4.57*T2)-(452/T2)

T2 is what I want to calculate. So how do I isolate T2.

Any help would be greatly appreciated. Thanks in advance.

bnt

Here's how I would do it:
First step is to substitute T1 in to the first equation to get a value for Cst. Substitute that value in to the second equation.

What you have then is basically a Quadratic equation which you can then solve. You get it in "standard" form if you multiply both sides by T2 and rearrange:
(Cst)*T2 = 4.57*T2² - 452
4.57*T2² - (Cst)*T2 - 452 = 0
Then solve e.g. quadratic formula.

carnagesri

Would you mind going through it from start to finish.

764dak

Time T1= 75

Cst= (1.37*T1)-(200/T1)
Cst= (4.57*T2)-(452/T2)

You can equate the first equation to the second one.

(1.37*T1)-(200/T1) = (4.57*T2)-(452/T2)

You can then replace T1 with 75.

(1.37*75)-(200/75) = (4.57*T2)-(452/T2)

Simplify
102.75-8/3 = (4.57*T2)-(452/T2)
1201/12 = (4.57*T2)-(452/T2)
You can times both sides by 12*T2
1201*T2 = 54.84*T2^2 - 5424
54.84*T2^2-1201*T2-5424= 0

You must solve the quadratic.

http://www.wolframalpha.com/input/?i=1201*T+%3D+54.84*T%5E2+-+5424 (Solution of this quadratic)

http://www.wolframalpha.com/input/?i=T%3D+75%3B+C%3D+%281.37*T%29-%28200%2FT%29%3BC%3D+%284.57*K%29-%28452%2FK%29 (Solution of the entire problem from the beginning where Cst=C, T1=T, T2 = K)

The approximate solutions are T2 = 25.7422 and -3.84216

bnt

What he said - I just substituted 75 for T1 one step earlier. Equating them in this way didn't make a difference this time, but it might in other problems, so I suppose it's a good idea.