Question

Water flows through two identical tubes A and B. Water of volume $V_0$ passes through the tube A and volume $2V_0$ through tube B in a given time interval. Which of the following options given is/ are possible?

• A. Flow in both the tubes is steady.
• B. Flow in both the tubes is turbulent.
• C. Flow is steady in A but turbulent in B.
• D. Flow is steady in B but turbulent in A.

Answer 1

Answer: (A), (B), (C)

The correct options are
A Flow in both the tubes is steady.
B Flow in both the tubes is turbulent.
C Flow is steady in A but turbulent in B.

From the data given in the question:


Tubes are identical and more volume of water passes through tube B than through tube A in a given time interval,
$\therefore$ Mean velocity of flow in tube B is more than the mean velocity of flow in tube A (i.e) $u_B>u_A.......\left(1\right)$.
We know that, Reynold's number $R=\frac{\rho ud}{\mu }$
where $\rho =\text{density},u=\text{mean velocity},d=\text{diameter},\mu =\text{viscosity}$
$\Rightarrow R_B>R_A$
[$\because \rho ,d$ and $\mu$ are constants]
If flow in B is steady (i.e $R_B<1000)$, then flow in A must be also be steady in nature as $R_A<1000$
$\therefore$ option (a) is a correct answer.

We know flow is turbulent if $R>2000$
Suppose, $R_B>2000\Rightarrow R_A$ can or cannot be greater $2000$.
From this we can conclude that, if flow in tube B is observed to be turbulent, we can deduce that the flow in A can either be turbulent or unsteady, but it cannot be possible that if flow in B is steady, the flow in A will be turbulent as it violates condition of $\left(1\right)$
$\therefore$ option (b) and option (c) are correct answers.
Hence, options (a),(b) and (c) are correct answers among the given options.