Question

A viscous liquid of constant density 500 kg/m3 and viscosity 10 Pa s falls down with constant velocity due to gravity in a long vertical tube with 2 m diameter. There is no pressure applied. Gravity is the only driving force. Calculate the shear stress at the wall.

Answer 1

Answer:

$\tau=$2452.5 N/m^2

Explanation:

given:

density $\rho$=500kg/m^3

viscosity $\mu$= 10 Pa-s

diameter of tube= 2 m

and L be length

since gravity is the only force shear force will balance it

so we can write

mg= $\tau\times A$

A=  $\rho\times\frac{\pi}{4} d^2\times L$

m=  $\rho\times\frac{\pi}{4} d^2\times L$

therefore

$\rho\times\frac{\pi}{4} d^2\times Lg= \tau\times{\pi} d\times L$

putting values we get

$\ 500\times\frac{\pi}{4} 2^2\times g= \tau\times{\pi}\times 2$

calculating we get $\tau=$2452.5 N/m^2