Question

The velocity profile over a plate is v= 16y2 +2y and the velocity is in m/s. Determine the
shear stress at y = 0 and y = 8.5 cm. The viscosity of the fluid is 9.35 Poise.​

Answer 1

Given:-

$\text{velocity profile, }v=16y^{2}+2y\\\\\text{coefficient of viscosity, }\mu=9.35\text{poise}=0.935\text{Pa-s}$

To Find:-

shear stress at y=0 and y=8.35 cm

Explanation:-

$\text{According to Newton's law of viscosity,}\\\\\text{shear stress, }\tau=\mu\times\dfrac{dv}{dy}\text{ where,}\\\\\dfrac{dv}{dy}=\text{velocity gradient}\\\\\Rightarrow\dfrac{dv}{dy}=16\times2y+2=32y+2\\\\\text{at y=0, }\dfrac{dv}{dy}=32\times0+2=2s^{-1}\\\\\Rightarrow\tau_{y=0}=0.935\times2=1.87Pa$

$\text{at y=8.5cm=0.085m, }\dfrac{dv}{dy}=32\times0.085+2=4.72s^{-1}\\\\\Rightarrow\tau_{y=0.085m}=0.935\times4.72=4.4132Pa$