Water flows through two identical tubes A and B. A volume V₀ of water passes through the tube A and 2V₀ 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

 

Reynolds number, R =$\frac{\mathrm{\rho ud}}{\mathrm{\mu }}$

If R > 4000, the flow is considered turbulent.
If volume V flows through tube A and volume 2V flows through tube B in the same amount of time, then the mean velocity, u in tube B is higher than that in tube A.

${\mathrm{u}}_{\mathrm{B}}>{\mathrm{u}}_{\mathrm{A}}$

${\mathrm{R}}_{\mathrm{B}}>{\mathrm{R}}_{\mathrm{A}}$

$\mathrm{Option} \mathrm{D},$

${\mathrm{R}}_{\mathrm{A}}>4000$

${\mathrm{R}}_{\mathrm{B}}>{\mathrm{R}}_{\mathrm{A}}>4000$

$\mathrm{Option} \mathrm{C},$

${\mathrm{R}}_{\mathrm{B}}>4000,2000>{\mathrm{R}}_{\mathrm{A}} \mathrm{is} \mathrm{possible}$

Hence the correct answer is a, b and c are correct.