Shear stress is simply the component of stress coplanar with a material cross-section
The relation for shear stress is: [tex]\mathbf{\tau = \mu(a - 2by)}[/tex] or [tex]\mathbf{\tau = a\mu - 2by\mu}[/tex]
The variation of velocity is given as:
[tex]\mathbf{u(y) = ay - by^2}[/tex]
Differentiate both sides with respect to y
[tex]\mathbf{u'(y) = a - 2by}[/tex]
The shear stress is calculated as:
[tex]\mathbf{\tau = \mu \times u'}[/tex]
Substitute [tex]\mathbf{u'(y) = a - 2by}[/tex]
[tex]\mathbf{\tau = \mu \times (a - 2by)}[/tex]
[tex]\mathbf{\tau = \mu(a - 2by)}[/tex]
Open bracket
[tex]\mathbf{\tau = a\mu - 2by\mu}[/tex]
Hence, the relation for shear stress is: [tex]\mathbf{\tau = \mu(a - 2by)}[/tex] or [tex]\mathbf{\tau = a\mu - 2by\mu}[/tex]
Read more about shear stress at:
https://brainly.com/question/15730801
