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

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∘

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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