Fully developed flow, entrance length

This expression has been used to correlate results obtained in a rectangular channel, Eq. (14) in Table VII, the hydrodynamic entrance length of the channel (Le = 0.0575 d Red) being too short to assure a fully developed flow. The results were still 24/ high, compared with Eq. (31) modified by a relaxation assumption ... 

Entrance and Exit Effects In the entrance region of a pipe, some distance is required for the flow to adjust from upstream conditions to the fully developed flow pattern. This distance depends on the Reynolds number and on the flow conditions upstream. For a uniform velocity profile at the pipe entrance, the computed length in laminar flow required for the centerline velocity to reach 99 percent of its fully developed value is (Dombrowski, Foumeny, Ookawara, and Riza, Can.. Chem. Engr., 71,472-476 [1993])... 

Consider fully developed flow in a circular pipe with negligible entrance effects. If the length of the pipe is doubled, the pressure drop will (ft) double, (b) more than double, (c) less than double, (c/) reduce by half, or (e) lemain constant,... 

Heat transfer to a laminar flow in an annulus is complicated by the fact that both the velocity and thermal profiles are simultaneously developing near the entrance and, often, over the length of the heated channel. Natural convection may also be a factor. It is usually conservative (i.e., predicted heat-transfer coefficients are lower than those experienced) to use equations for the fully developed flow. 

Transition length for laminar and turbulent flow. The length of the entrance region of the tube necessary for the boundary layer to reach the center of the tube and for fully developed flow to be established is called the transition length. Since the velocity varies not only with length of tube but with radial distance from the center of the tube, flow in the entrance region is two dimensional. 

The thermal entrance length (Lu,) is defined as the microchannel length required to achieve a value of the local Nusselt number Nu equal to 1.05 times the value of the Nusselt number for fully developed flow. 

At entry point, the fluid flow profile can be significantly different from the parabolic profile of Poiseuille flows. There is a characteristic distance before the steady-state Poiseuille profile can be established. This distance, between the entry point and the full establishment of Poiseuille flow, is called the entrance length. At the end of the entrance length, the pressure gradient matches that of the fully developed flow. The entrance length, 4. can be expressed in terms of the dimensionless entrance length number El ... 

The experimental system is shown schematically in figure 1. Experiments were performed in a straight, smooth-walled acrylic glass pipe 50 mm in diameter. In order to determine the drag reduction from pressure drop measurements the test pipe was provided with 14 pressure taps positioned at I m intervals down the pipe. A sufficient entrance pipe length was provided to ensure fully developed flow at the injection point. The water was pumped from a reservoir tank by a Mohno pump, the speed of which was controlled by a microcomputer to maintain a constant Reynolds (Re) number, during the experiments (between 10 and 10 ). The microcomputer continously measured the temperature of the water with a resistance thermometer and the discharge with a turbine wheel flow meter. 

If the velocity profile at the entrance region of a tube is flat, a certain length of the tube is necessary for the velocity profile to be fully established. This length for the establishment of fully developed flow is called the transition length or entry length. This is shown in Fig. 2.10-6 for laminar flow. At the entrance the velocity profile is flat i.e., the velocity is the same at all positions. As the fluid progresses down the tube, the boundary-layer thickness increases until finally they meet at the center of the pipe and the parabolic velocity profile is fully established. 

The pressure drop or friction factor in the entry length is greater than in fully developed flow. For laminar flow the friction factor is highest at the entrance (L2) and then decreases smoothly to the fully developed flow value. For turbulent flow there will be some portion of the entrance over which the boundary layer is laminar and the friction factor profile is difficult to express. As an approximation the friction factor for the entry length can be taken as two to three times the value of the friction factor in fully developed flow. 

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