Properties Of Matter Ques 1
1 Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is $5 \mathrm{~cm}$, the Reynolds number for the flow is of the order of (density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$, coefficient of viscosity of water $=1 \mathrm{mPa} \mathrm{s}$ )
(2109 Main, 8 April I)
(a) $10^3$
(b) $10^4$
(c) $10^2$
(d) $10^6$
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Answer:
Correct Answer: 1.( b )
Solution:
- Reynolds’ number for flow of a liquid is given by
$ R_e=\frac{\rho v D}{\eta} $
where, velocity of flow,
$ v=\frac{\text { volume flow rate }}{\text { area of flow }}=\frac{V / t}{A} $
So, $\quad R_e=\frac{\rho V D}{\eta A t}=\frac{\rho V 2 r}{\eta \times \pi r^2 \times t}=\frac{2 \rho V}{\eta \pi r t}$
Here, $\rho=$ density of water $=1000 \mathrm{kgm}^{-3}$
$ \frac{V}{t}=\frac{100 \times 10^{-3}}{60} \mathrm{~m}^3 \mathrm{~s}^{-1} $
where, $\eta=$ viscosity of water $=1 \times 10^{-3} \mathrm{~Pa}-\mathrm{s}$
and $\quad r=$ radius of pipe $=5 \times 10^{-2} \mathrm{~m}$
$ \begin{aligned} R_e & =\frac{2 \times 1000 \times 100 \times 10^{-3}}{1 \times 10^{-3} \times 60 \times 3.14 \times 5 \times 10^{-2}} \\ & =212.3 \times 10^2=20 \times 10^4 \end{aligned} $
So, order of Reynolds’ number is of $10^4$.
BETA
