Question

Water flows through two identical tubes $A$ and $B$. A volume $V_0$ of water passes through the tube $A$ and $2V_0$ through $B$ in a given time. Which of the following may be correct?

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

Reynolds number, R = $\frac{\rho ud}{\mu }$
where $\rho$ = density, u = mean velocity, d = diameter and $\mu$ = viscosity
We know flow is Turbulent if R > 4000
In identical tubes, if volume V flows through A and 2V flows through B in a given time, then mean velocity,u in tube B is greater than that in A
$u_B$ > $u_A$
$⟹$ $R_B>R_A$
option(D) $⟹$ $R_A$ > 4000
$⟹$ $R_B$ > $R_A$ > 4000
So $R_B$ > 4000 $⟹$ Flow is turbulent in B
option (C) $⟹$ $R_B$ > 4000 , 2000 > $R_A$ is possible
(A)(B) options are also possible