Water flows through two identical tubes A and B . In a specified...

Let the cross-sectional area of the identical tubes be $A$ and the specified time interval be $\Delta t$.

The volume flow rate in tube $A$ is $Q_A = \dfrac{V_0}{\Delta t} = A v_A$, where $v_A$ is the velocity of water in tube $A$.

The volume flow rate in tube $B$ is $Q_B = \dfrac{2V_0}{\Delta t} = A v_B$, where $v_B$ is the velocity of water in tube $B$.

From the above equations, we get $v_B = 2v_A$.

The nature of the flow is determined by the Reynolds number, $R_e = \dfrac{\rho v D}{\eta}$. Since the tubes and the fluid are identical, $R_e \propto v$.

Therefore, $R_{e,B} = 2R_{e,A}$.

For steady (streamline) flow, $R_e < 2000$, and for turbulent flow, $R_e > 3000$.

If $R_{e,A} = 800$, then $R_{e,B} = 1600$. Both are less than $2000$, so the flow can be steady in both tubes.

If $R_{e,A} = 4000$, then $R_{e,B} = 8000$. Both are greater than $3000$, so the flow can be turbulent in both tubes.

If $R_{e,A} = 1800$, then $R_{e,B} = 3600$. Here $R_{e,A} < 2000$ and $R_{e,B} > 3000$, so the flow can be steady in $A$ and turbulent in $B$.

If the flow in $A$ is turbulent ($R_{e,A} > 3000$), then $R_{e,B} > 6000$, meaning the flow in $B$ must also be turbulent. Thus, it is impossible for the flow to be steady in $B$ while being turbulent in $A$.