Question

Water is flowing through a 200 mm diameter pipe with coefficient of friction f = 0.04. The shear stress at a point 40 mm from the pipe axis is 0.00981 n/cm2. The shear stress at the pipe wall will be

Answer 1

given, diameter of pipe , d = 200mm
radius of pipe , r = 100mm
coefficient of friction, f = 0.04
shear stress at a point r = 40mm , $\tau$ = 0.00981 N/cm²

we have to find shear stress at the pipe wall.
Let shear stress at the pipe wall is $\tau_0$


first of all, we have to find where is viscous or not . we know, the flow will be viscous if Reynolds's number less than 2000.

use $f=\frac{16}{R_e}$

Re = 16/0.04 = 400 < 2000
this means flow is viscous. now shear stress in case of viscous flow through a pipe is given by,
$\tau=\frac{\delta p}{\delta x}\frac{r}{2}$
but $\frac{\delta p}{\delta x}$ is constant across a section as There is no variation of x so, there is no variation of p.

so, $\tau\propto r$

e.g., $\tau_0/\tau=100/40$

so, $\tau_0$ = 100/40 × 0.00981 =0.0245 N/cm²