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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.

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Answer:


\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

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