Q146 / 160 · TS EAMCET 2017 · Physics

A horizontal pipeline carrying gasoline has a cross-sectional diameter of $5 \mathrm{~mm}$. If the viscosity and density of the gasoline are $6 \times 10^{-3}$ Poise and $720 \mathrm{~kg} / \mathrm{m}^3$ respectively, the velocity after which the flow becomes twrbulent is

  • A
    $>1.66 \mathrm{~m} / \mathrm{s}$
  • B
    $>3.33 \mathrm{~m} / \mathrm{s}$
  • Correct answer
    C
    $>1.6 \times 10^{-3} \mathrm{~m} / \mathrm{s}$
  • D
    $>0.33 \mathrm{~m} / \mathrm{s}$

Solution

Given, Diameter of pipe $(d)=5 \mathrm{~mm}=5 \times 10^{-3} \mathrm{~m}$ Density of gasoline $(\rho)=720 \mathrm{~kg} / \mathrm{m}^3$. Viscocity of gasoline $(\eta)=6 \times 10^{-3}$ Poise We know that, $v_c=\frac{\eta}{\rho d}=\frac{6 \times 10^{-3}}{720 \times 5 \times 10^{-3}}$ $$ \begin{aligned} =\frac{6 \times 10^{-3}}{3600 \times 10^{-3}} & =\frac{1}{600}=\frac{1}{6} \times 10^{-2} \\ & =1.66 \times 10^{-3} \mathrm{~m} / \mathrm{s} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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