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

`\tau=`2452.5 N/m^2

Step-by-step 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* A`

A=
`\rho*(\pi)/(4) d^2* L`

m=
`\rho*(\pi)/(4) d^2* L`

therefore

`\rho*(\pi)/(4) d^2* Lg= \tau*{\pi} d* L`

putting values we get

`\ 500*(\pi)/(4) 2^2* g= \tau*{\pi}* 2`

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