how is reylonds number related to critical velocity
Answers
Critical velocity is the speed and direction at which the flow of a liquid through a tube changes from smooth, or "laminar," to turbulent. Calculating critical velocity depends on multiple variables, but it is the Reynolds number that characterizes the flow of the liquid through a tube as either laminar or turbulent.
The critical velocity is the velocity of fluid at which turbulance sets in. Osborne Reynolds (1842-1912) showed that the critical velocity v for a fluid flowing through a narrow tube is a function of coefficient of viscosity , density of the fluid and the radius 'r' of the tube. That is,
.....................................................(1)
where is the Reynold Number.
The above expression can also be obtained by dimensional analysis,
i.e.
.....................(2)
From equ(2), we can arrive at, a = 1, b = -1 and c = -1
i.e., or
The critical number appears as a proportional constant. from equ(1), one can infer that the liquid of higher viscosity and lower density promotes steady state flow. The steady state flow can also be obtained with ease using narrow tubes, i.e., with smaller 'r' values. As per experiments, for values less than 1000, the fluids are under steady state flow.
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