Question

The velocity distribution in a laminar flow adjacent to a solid wall is given by u=3.0 sin (5$\pi$y). The viscosity of the fluid is 5 poise. What is the shear stress at a section (i) y= 0.05; (ii) y= 0.12 m?

• A. 16.7 N/$m^2$ and 6.1 N/$m^2$
• B. 33.4 N/$m^2$ and zero
• C. 16.7 N/$m^2$ and 12.3 N/$m^2$
• D. 16.7 N/$m^2$ and zero

Answer 1

The correct option is D 16.7 N/$m^2$ and zero

Shear stress, $\tau =\mu .\frac{\partial u}{\partial y}=0.5\frac{\partial }{\partial y}\left[3sin\right(5\pi y\left)\right]Here,\mu =5Poise=0.5Pa-s=\tau =0.5\times 3\times 5\pi cos\left(5\pi y\right)=23.56cos\left(5\pi y\right)N/m^{2}So,aty=0.05m\tau =23.56cos(5\pi \times 0.05)\tau =16.7N/m^{2}andaty=0.12m\tau =23.56cos(5\pi \times 0.12)\tau =-7.28N/m^2$
Since Negative value is not acceptable.
$\therefore$ It is taken as zero.