![]() ![]() When the Re value exceeds a level known as the “critical Reynolds number,” the flow becomes fully turbulent. At a certain range of Re values, the flow enters a transition period between the laminar and turbulent flow. d is the characteristic dimension (such as pipe diameter) chosen for the measurementĪt low Re values the fluid flow is laminar.The Reynolds number is defined mathematically as: Although the concept was originally introduced by George Gabriel Stokes in 1851, it was Osborne Reynolds who applied it to the transition phase between the laminar and turbulent flow. The Reynolds number (Re) is a dimensionless value for the ratio between viscous and inertial forces. In this experiment, Reynolds demonstrated that there are two types of flow – turbulent and laminar – and that there is a transition period between them. As the velocity increased, the line of dyed water quickly broke up and diffused into the volume of the tube. Reynolds added a small amount of dyed water to the flow and observed the action of the water at various flow rates.Īt low flow speeds, the dyed layer could be seen as a straight, uninterrupted line through the glass pipe. The experiment involved measuring and observing water flow in a large glass pipe. In 1883, his first publication on the properties of water motion through parallel channels appeared in the proceedings of the Royal Society of London. He first noticed the distinction between turbulent and laminar flows in the latter half of the 1800s. History of Laminar Flowġ9th-century scientist Osborne Reynolds specialised in the study of fluid dynamics. As the water flow accelerates due to gravity the contrast shows up as rough, foamy, choppy flow (turbulent flow). The smooth, clear flow of some of the slower-moving water (laminar flow) can be seen as large sheets of clear water flowing over the top of the waterfall. As the velocity increases, it reaches a threshold at which the flow begins to act turbulently.īoth types of flow can be seen in some waterfalls. Laminar flow can only be maintained at lower velocities. The laminar state of the flow leads to relatively high momentum diffusion with reduced momentum convection. 29–48.The absence of any eddy currents, cross-currents, or swirls means that the flow is perfectly laminar. ![]() Todd, L., 1977, “Some Comments on Steady, Laminar Flow Through Twisted Pipes,” J. and Hartnett J.P., 1973 “Handbook of Heat Transfer”, Mc Graw-Hill. “Steady Laminar Flow Through Twisted Pipes Heat Transfer in Square Tubes,” ASME Journal of Heat Transfer, Vol. and Nandakumar, K., 1981a, “Steady Laminar Flow Through Twisted Pipes Fluid Flow in Square Tubes,” ASME Journal of Heat Transfer, Vol. and Bergles, A.E., 1969, “Heat Transfer and Pressure Drop in Tap-Generated Swirl Flow of Single-Phase Water,” ASME Journal of Heat Transfer, Vol. ![]() P., 1975, “Methods of Numerical Integration”, Academic Press. “Prediction of Fully Developed Flow in a Tube Containing a Twisted Tape”. Rotational Cartesian coordinates \(\bar x, \bar y, \bar z\)Ĭoordinates in the computation domain \(\vec \omega \)Ĭounter-clockwise angle from the x-axis 〈 T w〉:ĭate, A.W., 1974. Relative velocity component with respect to the cross-section Wĭeviation of the axial velocity from the Poiseuille flow x, y, z ![]() Velocity vector ( V x, V y, V z) V′ x, V′ y: Maximum axial velocity in Poiseuille flow V oĪxial velocity in Poiseuille flow \(\vec V\) The inward unit vector normal to the tube wall U o Unit vector along a curve on which x, y is fixed and z varies \(\hat t\) Pressure gradient vector ( P x, P y, P z) Re The distance from the y-axis to the wall \(\vec P_g \) Unit vector in x, y, z-coordinate direction l(y) Minor and major semi-axis of an ellipse, respectively EĪxial length of a twisted tube over a half rotation ( H=H */ a) \(\hat i, \hat j, \hat k\) ![]()
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