Question

Assuming a velocity distribution which is a

parabola having its vertex 12 in from the boundary,

calculate the shear stress at y= 0, 3, 6, 9 and 12 inches.

Fluid’s absolute viscosity is 600 P

Answer 1

$600~P=0.6~\frac{N\cdot s}{m^2}=0.01253~\frac{lb\cdot s}{ft^2},$

$120-u=a(12-y)^2,$

$u=0,~t=0,\implies a=\frac 56,$

$u=120-\frac 56(12-y)^2,$

$\frac{du}{dy}=\frac 53(12-y),$

$\def\arraystretch{1.5} \begin{array}{|c|c|c|c|c|c|} \hline y & 0 & 3&6&9&12 \\ \hline \frac{du}{dy} & 20 & 15&10&5&0\\ \hline \eta & 0.251&0.188&0.1253&0.0627 & 0 \\ \hline \end{array}$