Given the velocity profile u in a liquid flowing along a fla

Given the velocity profile u in a liquid flowing along a flat plate is: u(y) = 5y^2 + y where u is the velocity in m/s, y is the coordinate normal to the plate in m. The viscosity of the liquid is 1.0 Pa.s Determine the shear stress at y =10 cm. Select one: 1.5 N 1.5 N/m^2 2 N 2 Pa 1 Pa

Solution

u(y)= 5y²+y

du/dy=10y+1 for y=10cm=0.1m, du/dy=10 x0.1 + 1 = 2 s^-1

Shear stress = = du/dy = 1 (Pa.s =N s/m²) x 2 (s^-1) = 2N/m² = 2 Pa

Hence answer is option d.