Inverse Proportionality?

Question

I'm currently working though the below problems in parallel to asking this question, so any help is greatly appreciated.

The shear stress, q, across the wall of a thin walled tube is proportional to the applied torque, T, inversely proportional to the square of the mean radius, r, of the tube and inversely proportional to the thickness of the wall of the tube, t.

q = 30000kPA

T = 3620Nm

r = 80mm

t=3mm

Determine the shear stress across the wall of the tube when applied torque, T, is 5000Nm

TYIA

Answer 1

q = k T / ( r ² t ² )

3000 = k (3620) / (80² x 3²)

q = k (5000) / (80² x 3²)

q / 3000 =  (5000)  / (3620 )

q = 3000 x 5000 / 3620

q = 4144 kPA

Answer 2

From your datas, we write the math model as :

q ~ T / (tr^2)

Proportionality means there's a constant, say "k" taking part in the equation. We now have an equation :

q = kT / (tr^2)

Finding the value of k will give us a proper formula :

q = kT / (tr^2)

3*10^4 KPA = 3620k Nm / (6400*9*10^-6 m^4)

3620k Nm = 1728 KPAm^4

k = 0.477 KPA N m^3 (on 3 d.p.)

Our formula is now

q = (0.477)T / (tr^2)

And you may enter any value to the variables.

Note :

* Use more than 3 d.p. for more accurate result.

* "~" is proportional sign

* I'm not good in units. You may want to recheck them.

* A shorter, simpler method is available. I don't use it for your better understanding.

* Contact me for more discussion

"como"'s (above) answer is what I meant with simpler method. Even if without explanation and the thickness, t, is squared (should be not), his final answer is correct.