Friction pressure loss laminar flow

The flow changes from laminar to turbulent in the range of Reynolds numbers from 2,100 to 4,000 [60]. In laminar flow, the friction pressure losses are proportional to the average flow velocity. In turbulent flow, the losses are proportional to the velocity to a power ranging from 1.7 to 2.0. 

Figures 28a and 28b compare the measured and calculated frictional pressure losses for laminar and turbulent flow of the drilling fluid through...

A low molecular weight polymer melt, which can be modelled as a power-law fluid with m = 5 kPa-s" and n = 0.25, is pumped through a 13 mm inside diameter tube over a distance of 10 m under laminar flow conditions. Another pipe is needed to pump the same material over a distance of 20 m at the same flow rate and with the same frictional pressure loss. Calculate the required diameter of the new pipe. 

You will have noticed that there is just one line on the friction factor chart (Fig. 48.6) for < ) in terms of Re in the laminar flow region (Re less than 2 x 10 ) of slope < ) = 8/Re. This means that for Reynolds numbers of less than 2000 we can very simply calculate the frictional pressure loss by the relationship... 

Laminar flow after transition usually turns into turbulent flow when Re > 2000. It has been shown that the pressure loss of a turbulent flow is caused by a friction factor with the magnitude of... 

In the previous sections of this chapter, the calculation of frictional losses associated with the flow of simple Newtonian fluids has been discussed. A Newtonian fluid at a given temperature and pressure has a constant viscosity /r which does not depend on the shear rate and, for streamline (laminar) flow, is equal to the ratio of the shear stress (R-,) to the shear rate (d t/dy) as shown in equation 3.4, or ... 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

In equation 1.14, z, P/(pg), and u2/(2ga) are the static, pressure and velocity heads respectively and hf is the head loss due to friction. The dimensionless velocity distribution factor a is for laminar flow and approximately 1 for turbulent flow. 

We see that Apjl, the frictional pressure drop per unit depth of bed, is made up of two components. The first term on the right-hand-side accounts for viscous (laminar) frictional losses, cc pu. and dominates at low Reynolds numbers. The second term on the right-hand-side accounts for the inertial (turbulent) frictional losses, oc pu2, and dominates at high Reynolds numbers. For further information about flow through packed beds, see Chapter 7 An Introduction to Particle Systems . 

Viscous Transport. Low velocity viscous laminar tiow in gas pipes is commonplace. Practical gas flow can be based on pressure drops of <50% for low velocity laminar flow in pipes whose length-to-diameter ratio may be as high as several thousand. Under laminar flow, bends and fittings add to the frictional loss, as do abrupt transitions. 

Related Calculations. Helical Coils. The same procedure can be used to calculate the pressure drop in helical coils. For turbulent flow, a friction factor for curved flow is substituted for the friction factor for straight tubes. For laminar flow, the friction loss for a curved tube is expressed as an equivalent length of straight tube and the friction factor for straight tubes is used. The Reynolds number required for turbulent flow is 2100[1 + 12(Dj/Dc)1/2], where Dt is the inside diameter of the tube and Dc is the coil diameter. 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

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