Fluid Mechanics Viscosity Question 300
Question: Water is flowing on a horizontal fixed surface, such that its flow velocity varies with y (vertical direction) as$ v=k\left( \frac{2y^{2}}{a^{2}}-\frac{y^{3}}{a^{3}} \right) $ . If coefficient of viscosity for water is$ \eta $ , what will be shear stress between layers of water at$ y=a. $
Options:
A) $ \frac{\eta k}{a} $
B) $ \frac{\eta }{ka} $
C) $ \frac{\eta a}{k} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Newton’s law of viscosity, $ F=\eta A\frac{dv}{dy} $ Stress$ =\frac{F}{A}=\eta \left( \frac{dv}{dy} \right)=\eta k\left( \frac{4y}{a^{2}}-\frac{3y^{2}}{a^{3}} \right) $ At$ y=a $ , Stress$ =\eta k\left( \frac{4}{a}-\frac{3}{a} \right)=\frac{\eta k}{a} $
BETA
