$A$ highly viscous liquid of viscosity coefficient $\eta$ flows through a fixed horizontal cylindrical tube (fixed from the outer surface) of internal radius $r$,thickness $t$ $(t \ll r)$,and length $l$. The volume of liquid flowing per second is $Q$ and the pressure difference across the tube is $P$. If the modulus of rigidity of the material of the tube is $\beta$,the shear strain in the tube will be:

  • A
    $\frac{8\eta Q}{\pi \beta r^2}$
  • B
    $\frac{4\eta Q}{\pi \beta r^3}$
  • C
    $\frac{\pi \beta r^3}{16\eta Q}$
  • D
    $\frac{\beta r^2}{8\eta Q}$

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