Transition from streamline to turbulent flow

For flow in an open channel, only turbulent flow is considered because streamline flow occurs in practice only when the liquid is flowing as a thin layer, as discussed in the previous section. The transition from streamline to turbulent flow occurs over the range of Reynolds numbers, updm/p = 4000 — 11,000, where dm is the hydraulic mean diameter discussed earlier under Flow in non-circular ducts. 

Water flows at a velocity of 1 m/s over a plane surface 0.6 m wide and 1 m long. Calculate the total drag force acting on the surface if the transition from streamline to turbulent flow in the boundary layer occurs when the Reynolds group ReXc = 105. 

In a straight pipe, the transition from streamline to turbulent flow occurs at Re 2300. For flow through packed beds, the transition occurs at a value of Rep of approximately 40. 

In laminar flow there are no disturbances, and therefore all flow particles move in the same direction. Transitional flow is the flow regime that takes place during the change from streamline to turbulent flow. In the case of turbulent flow the particles move in a given flow direction, but the flow is erratic and random. 

Equation 5.2 is found to hold well for non-Newtonian shear-thinning suspensions as well, provided that the liquid flow is turbulent. However, for laminar flow of the liquid, equation 5.2 considerably overpredicts the liquid hold-up e/,. The extent of overprediction increases as the degree of shear-thinning increases and as the liquid Reynolds number becomes progressively less. A modified parameter X has therefore been defined 16 171 for a power-law fluid (Chapter 3) in such a way that it reduces to X both at the superficial velocity uL equal to the transitional velocity (m )f from streamline to turbulent flow and when the liquid exhibits Newtonian properties. The parameter X is defined by the relation... 

In laminar flow, all elements of a fluid passing a certain point follow the same path or streamline. In turbulent flow, all components of a fluid passii a certain point do not follow the same path. The flow velocity corresponding to the transition from laminar to turbulent flow a>nditions, or vice... 

Measurement of particle size with Eq. (4.24) has a limited validity range. Stokes law is valid for laminar or streamline flow, i.e., there is no turbulent flow. There are also assumptions that the particles have no interparticle collisions or interactions. There is a critical velocity, Vc, at which transition from laminar to turbulent flow occurs. This critical velocity is given by ... 

Forced convection cooling can be divided into laminar flow and turbulent flow. The transition from laminar to turbulent flow in air usually occurs at a velocity of 180 ft/min (180 Ifm). In laminar (or sfreamline) flow, the fluid particles follow a smooth, continuous path where the velocity vectors of the particles are always parallel and never intersect. The heat is transferred by molecular conduction in the fluid and by the solid-fluid interface. Tm-bulent flow, characterized by the irregular motion of fluid particles, has eddies in the fluid in which the particles are continuously mixed and rearranged. The heat is transferred in turbulent flow from the eddies back and forth across the streamlines. The greater heat transfer occurs for turbulent flow. 

If Re is of the order of 105, the drag on the sphere may be reduced if the fluid stream is turbulent. The flow in the boundary layer changes from streamline to turbulent and the size of the eddies in the wake of the particle is reduced. The higher the turbulence of the fluid, the lower is the value of Re at which the transition from region (c) to region (d) occurs. The value of Re at which R /pu2 is 0.15 is known as the turbulence number and is taken as an indication of the degree of turbulence in the fluid. 

At Johns Hopkins Clauser established the Department of Aeronautics. He pubUshed widely in the fields of aerodynamics, of non-linear meehanies, fluid dynamies and on the reduetion of combustion engine emissions. His 1937 PhD thesis deals with the cmwature effect on the transition from laminar to turbulent boundary layers, a topie in which his tutor Theodor von Karman (1881-1963) was interested since deeades. The result was applied to flows over the upper surface of a wing. The discrepancy between the predieted and the actual transition point was due to the effect of streamline emwature, which may become relatively large due to the relatively small wing curvature radius. 

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

When a fluid flowing at a uniform velocity enters a pipe, the layers of fluid adjacent to the walls are slowed down as they are on a plane surface and a boundary layer forms at the entrance. This builds up in thickness as the fluid passes into the pipe. At some distance downstream from the entrance, the boundary layer thickness equals the pipe radius, after which conditions remain constant and fully developed flow exists. If the flow in the boundary layers is streamline where they meet, laminar flow exists in the pipe. If the transition has already taken place before they meet, turbulent flow will persist in the... 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

The sedimentation technique is reliable for particle size determination when rf is in a size range of 2-50 pm. The falling rate of smaller particles is affected by Brownian motion resulting from collisions with the molecules of the liquid and other interactions between particles. Stokes law is valid only for laminar or streamline flow (i.e., when there is no turbulence). The Reynolds number (Re) is a measure of when the process transitions from turbulent to laminar flow ... 

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