I cannot work out constants a and b --

[tosingoodnessamao]

Homework Statement

If the velocity v of the air in a boundary layer having a dynamic viscosity of 18 × 10−6
kg/ms is given in terms of the distance y from the surface by:
v = ay + by^2
where a and b are constants, calculate the surface shear stress if at 1.5 mm from the surface
the velocity is 75 m/s, and at 3.0 mm from the surface it is 105 m/s.

I know that a is the shear strain/rate and i need to times it by the dynamic viscosity but i really cannot work out a and b.

* update - realised that I forgot to square the value for y when multiplying by b.

Relevant Equations

shear stress = (shear strain/rate) x du/dy

75 = (1.5 x 10^-3)a + (1.5 x 10^-3)b
105 = (3 x 10^-3)a + (3 x 10^-3)b

 

[phyzguy]

You are given three things:
(1) v = ay + by^2 where a and b are constants
(2) at 1.5 mm from the surface the velocity is 75 m/s
(3) at 3.0 mm from the surface the velocity is 105 m/s.

From these, you should be able to set up two equations with two unknowns and solve them for a and b. Have you tried that?

 

[Mayhem]

Two equations with two unknowns. Have you tried solving them?

 

[tosingoodnessamao]

You are given three things:
(1) v = ay + by^2 where a and b are constants
(2) at 1.5 mm from the surface the velocity is 75 m/s
(3) at 3.0 mm from the surface the velocity is 105 m/s.

From these, you should be able to set up two equations with two unknowns and solve them for a and b. Have you tried that?

Yes finally found the unnowns a and b because initially I kept multiplying b by y rather than y^2 which was my mistake.

 

[tosingoodnessamao]

Two equations with two unknowns. Have you tried solving them?

Yes I have managed to solve them now I recognised my mistake.