Question

The velocity profile of a fluid over a plate is parabolic with its vertex 200 mm from the plate, where the velocity is 1.2 m/s.Calculate the velocity gradients and shear stresses at 50 mim and 200 mm from the plate, if the viscosity of the fluid is 0,8 N. s/m.

Answer 1

Velocity gradient

$\frac{du}{dy}=-0.3*2y+12=-0.6y+12$

At y= 50, Velocity gradient , $\frac{du}{dy}=-0.6*50+12= |-18m/s|=18m/s$

At y= 0, Velocity gradient , $\frac{du}{dy}=-0.6*200+12=|-108m/s|=108m/s$

Shear stress at y=50, $\tau=\mu \frac{du}{dy}=0.8*200=160 N/m^2$

Shear stress at y=200, $\tau=\mu \frac{du}{dy}=0.8*50=40 N/m^2$