Frictional loss coefficient

Ordinarily, any numerical quantities that appear in equations that have a theoretical basis (such as that for ke above) are dimensionless and hence universal. However, many valuable engineering relations have an empirical rather than a theoretical basis, in which case this conclusion does not always hold. For example, a very useful expression for the (dimensionless) friction loss coefficient ( A) ) for valves and fittings is... 

Table 8.1 Frictional loss coefficient for turbulent flow. ...

To estimate the superficial liquid velocity in the riser, this correlation must be combined with the Fanning friction factors in the riser and downcomer, f and f, the frictional loss coefficients at the top and bottom of the airlift, and and the gas hold-up in the riser, This approach predicted their experimental data in a pilot-plant scale external-loop airlift column for a carboxymethyl cellulose solution, with an error of 20%. 

AP = dynamic pressure loss in the riser = friction loss coefficient at the... 

Ps = force Jacx G END Py = Force paint of question e = natural log base k = wobble friction loss coefficient. 

Jet pump mixing section friction loss coefficient ... 

Fig. 7. (a) Configuration for flow turning. The frictional resistance resulting from the bend length must be added (b) pressure—loss coefficient, K, for 90°... 

Ideal (Frictionless) Flow in Nozzles The flow path in well-formed nozzles follows smoothly along the nozzle contour without separating from the wall. The effects of small imperfections and small frictional losses are accounted for by correcting the ideal nozzle flow by an empirically determined coefficient of mscharge. The acceleration of a fluid initially at rest to flowing conditions in an ideal nozzle is given by ... 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

It is known from experience with vertical pneumatic transport that the influence of weight prevails at low velocities, but as the velocity increases friction gains importance. Therefore, in the calculation of the pressure loss one must find not only the weight of the solids, which could be set up theoretically, but also an empirical relationship for vertical transport from the measured data. A correlation of the pressure-loss coefficient for vertical pneumatic conveyance according to data measured by Flatow " has been developed by Weber, and the result is... 

Flashing liquids, 134-146 Flow coefficients, Gv, for valves, 81 Friction loss, 68 Incompressible fluid, 71 Laminar flow, 77, 78, 86 Liquid lines, chart, 92 Long natural gas pipe lines, 120 Non-water liquids, 99 Pipe, 71... 

Using a coefficient of discharge Co to take account of the frictional losses in the meter and of the parameters C, i, and ot2 ... 

This meter may thus be considered as an orifice meter with a variable aperture, and the formulae already derived are therefore applicable with only minor changes. Both in the orifice-type meter and in the rotameter the pressure drop arises from the conversion of pressure energy to kinetic energy and from frictional losses which are accounted for in the coefficient of discharge. The pressure difference over the float —AP. is given by ... 

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. 

Looking at the Bernoulli equation, we see that the friction loss (ef) can be made dimensionless by dividing it by the kinetic energy per unit mass of fluid. The result is the dimensionless loss coefficient, K ... 

A loss coefficient can be defined for any element that offers resistance to flow (i.e., in which energy is dissipated), such as a length of conduit, a valve, a pipe fitting, a contraction, or an expansion. The total friction loss can thus be expressed in terms of the sum of the losses in each element, i.e., ef = JT K-nVf/7). This will be discussed further in Chapter 6. 

Because the friction loss and wall stress are related by Eq. (5-47), the loss coefficient for pipe flow is related to the pipe Fanning friction factor as follows ... 

Example 5-6 Friction Loss in a Sudden Expansion. Figure 5-7 shows the flow in a sudden expansion from a small conduit to a larger one. We assume that the conditions upstream of the expansion (point 1) are known, as well as the areas A and A2. We desire to find the velocity and pressure downstream of the expansion (V2 and P2) and the loss coefficient, Kt. As before, V2 is determined from the mass balance (continuity equation) applied to the system (the fluid in the shaded area). Assuming constant density,... 

The loss coefficient is seen to be a function only of the geometry of the system (note that the assumption of plug flow implies that the flow is highly turbulent). For most systems (i.e., flow in valves, fittings, etc.), the loss coefficient cannot be determined accurately from simple theoretical concepts (as in this case) but must be determined empirically. For example, the friction loss in a sudden contraction cannot be calculated by this simple method due to the occurrence of the vena contracta just downstream of the contraction (see Table 7-5 in Chapter 7 and the discussion in Section IV of Chapter 10). For a sharp 90° contraction, the contraction loss coefficient is given by... 

Water is flowing through a 45° pipe bend at a rate of 200 gpm and exits into the atmosphere. The inlet to the bend is 1 in. inside diameter, and the exit is 1 in. in diameter. The friction loss in the bend can be characterized by a loss coefficient of 0.3 (based on the inlet velocity). Calculate the net force (magnitude and direction) transmitted to the flange holding the pipe section in place. 

Repeat Problem 7 accounting for the friction loss from the vessel to the tube, assuming a loss coefficient of 0.50 for the contraction. 

Evaluation of the friction loss in valves and fittings involves the determination of the appropriate loss coefficient (Af), which in turn defines the energy loss per unit mass of fluid ... 

A commercial steel (e = 0.0018 in.) pipeline is 1 in. sch 40 diameter, 50 ft long, and includes one globe valve. If the pressure drop across the entire line is 22.1 psi when it is carrying water at a rate of 65 gpm, what is the loss coefficient for the globe valve The friction factor for the pipe is given by the equation... 

Because the discharge coefficient accounts for the non-idealities in the system (such as the friction loss), one would expect it to decrease with increasing Reynolds number, which is contrary to the trend in Fig. 10-4. Flowever, the coefficient also accounts for deviation from plug flow, which is greater at lower Reynolds numbers. In any event, the coefficient is not greatly different from 1.0, having a value of about 0.985 for (pipe) Reynolds numbers above about 2 x 105, which indicates that these non-idealities are small. 

It is evident that the orifice coefficient incorporates the effects of both friction loss and velocity changes and must therefore depend upon the Reynolds number and beta ratio. This is reflected in Fig. 10-8, in which the orifice (discharge) coefficient is shown as a function of the orifice Reynolds number (NR d) and... 

The total friction loss in an orifice meter, after all pressure recovery has occurred, can be expressed in terms of a loss coefficient, ATr, as follows. With reference to Fig. 10-12, the total friction loss is P — P3. By taking the system to be the fluid in the region from a point just upstream of the orifice plate (Pj) to a downstream position where the stream has filled the pipe (P3), the momentum balance becomes... 

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