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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
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The correct answer is:
$>1.6 \times 10^{-3} \mathrm{~m} / \mathrm{s}$
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, $v_c=\frac{\eta}{\rho d}=\frac{6 \times 10^{-3}}{720 \times 5 \times 10^{-3}}$
$$
\begin{aligned}
=\frac{6 \times 10^{-3}}{3600 \times 10^{-3}} & =\frac{1}{600}=\frac{1}{6} \times 10^{-2} \\
& =1.66 \times 10^{-3} \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
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, $v_c=\frac{\eta}{\rho d}=\frac{6 \times 10^{-3}}{720 \times 5 \times 10^{-3}}$
$$
\begin{aligned}
=\frac{6 \times 10^{-3}}{3600 \times 10^{-3}} & =\frac{1}{600}=\frac{1}{6} \times 10^{-2} \\
& =1.66 \times 10^{-3} \mathrm{~m} / \mathrm{s}
\end{aligned}
$$
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