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Question

# Water flows through two identical tubes A and B. Water of volume V0 passes through the tube A and volume 2V0 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.
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B
Flow in both the tubes is turbulent.
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C
Flow is steady in A but turbulent in B.
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D
Flow is steady in B but turbulent in A.
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Solution

## 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, ∴ Mean velocity of flow in tube B is more than the mean velocity of flow in tube A (i.e) uB>uA .......(1). We know that, Reynold's number R=ρudμ where ρ=density,u=mean velocity,d=diameter, μ=viscosity ⇒RB>RA [∵ρ,d and μ are constants] If flow in B is steady (i.e RB<1000), then flow in A must be also be steady in nature as RA<1000 ∴ option (a) is a correct answer. We know flow is turbulent if R>2000 Suppose, RB>2000⇒RA 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 (1) ∴ option (b) and option (c) are correct answers. Hence, options (a),(b) and (c) are correct answers among the given options.

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