A long cylindrical rod of radius R1 is placed co-axially inside a cylindrical

Discussion Forum : Mechanical Properties Of Fluids

Question -

A long cylindrical rod of radius $R_{1}$ is placed co-axially inside a cylindrical tube of radius $R_{2} (> R_{1})$ filled withviscous liquid and pulled along the axis with a constant velocity. In steady state the velocity gradient $(\frac{d v}{d r})$ depends on the distance from the common axis 'r' as proportional to

Options:

A .

r^{\circ}

B .

r^{- 1}

C .

r^{- 2}

D .

r^{- 3}

Answer: Option B
:
B

$f = η A \frac{d v}{d x} = c o n s t η 2 π r l \frac{d v}{d x} = c o n s t \frac{d v}{d x} α \frac{1}{r}$

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