Friction factor and pressure drop

Rearranging equation 2.5, the frictional pressure drop is given as 

Owing to its complexity, turbulent flow does not admit of the simple solutions available for laminar flow and the approach to calculating the pressure drop is based on empirical correlations. 

It was noted in Section 1.3 that the frictional pressure drop for turbulent flow in a pipe varies as the square of the flow rate at very high values of Re. At lower values of Re the pressure drop varies with flow rate, and therefore with Re, to a slightly lower power which gradually increases to the value 2 as Re increases. The pressure drop in turbulent flow is also proportional to the density of the fluid. This suggests writing equation 2.7 in the form 

The quantity ipu2 will be recognized as the kinetic energy per unit volume of the fluid. 

The term rj pu2) in equation 2.9 defines a quantity known as the Fanning friction factor /, thus 

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Table 3-17 gives the Reynolds number, friction factor, and pressure drop of catalyst pellets of 0.25 inch and at different particle length. Table 3-18 shows a typical input data and computer output with PL = 0.25 inch. The simulation exercise gives a pressure drop of 68.603 Ib/in. The results show that the pressure drop in a packed bed depends on size and shape of the particles. 

THiS PROGRAI- CALCULATES THE TUBE SIDE HEAT TRANSFER COEFFICIENT, REYNOLDS NUMBER, PRANDTL NUMBER, FRICTION FACTOR AND PRESSURE DROP. ... 

Rgure 12-13. Correlation for estimating friction factor and pressure drop coefficient for use in calculation of pressure drop of gas flowing through beds of granular adsorbents. DataofUOP(miB)... 

Determine the friction factor and pressure drop for the low-pressure side of a coiled-tube heat exchanger where the fluid flows past 100 tubes in a staggered-tube arrangement. An air flow rate of 0.5 kg/s enters the low-pressure side of the heat exchanger at 0.121 MPa and 183 K. The outside diameter of each tube is 10 mm while the minimum flow area between each tube is 0.0125 m. The transverse pitch is 0.0003 m. 

Wallis states that if bubbles were uniformly dispersed, and nonrigid, then their effect at a constant total mass-flow rate would be simply to increase the stream velocity, and at a constant friction factor, the pressure-drop would be,... 

Table I. Asymptotic dimensionless laminar flow heat or mass transfer coefficients Nu = a dh/V, (constant wall conditions) and Fanning friction factor / for pressure drop Ap = 2f r 7.ijd ) g for ducts of different cross section [10).

The relationship between the friction factor, axial pressure drop, and incremental pressure drop number is the following ... 

TABLE 5.55 Fully Developed Friction Factors, Incremental Pressure Drop Numbers, and Nusselt Numbers for Some Quadrilateral Ducts [278]... 

Simultaneously developing flow in annular sector ducts for air (Pr = 0.7) has been analyzed by Renzoni and Prakash [287]. In their analysis, the outer curved wall is treated as adiabatic, and the boundary condition is imposed on the inner curved wall as well as on the two straight walls of the sector. The fully developed friction factors, incremental pressure drop numbers, hydrodynamic entrance lengths, and thermal entrance lengths are presented in Table 5.62. The term L y used in Table 5.62 is defined as the dimensionless axial distance at which /app Re = 1.05/ Re. The fully developed Nusselt numbers are represented by Nu/< in order not to confuse the reader since the thermal boundary condition applied in Renzoni and Prakash [287] is different from those defined in the section. 

Since Reynolds number is greater than 4000, the flow is turbulent and the roughness factor for the cast-iron pipe is e = 0.00026 m (Table 2.1). The relative roughness of a cast-iron pipe is (e/D) = (0.00026 m)/(0.15 m) = 0.0017. From the relative roughness and Re = 7.14 x 10, we can find the friction factor f = 0.024 (Figure 2.2). Using the calculated friction factor, the pressure drop... 

Friction Factor and Reynolds Number For a Newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length AP/L to the pipe diameter D, density p, and average velocity V through two dimensionless groups, the Fanning friction factor/and the Reynolds number Re. 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

Friction factor Describes the relationship between the wall roughness, Reynolds number, and pressure drop per unit length of duct or pipe run. 

Fluid properties are evaluated at the average bulk temperature. Heat transfer and fluid friction inside the tubes are evaluated with the hydraulic diameter method discussed in Chap. 6. Pressure drop is calculated with the chart friction factor / and the following relation ... 

B Obtain analytic relations for the velocity profile, pressure drop, friction factor, and Nusselt number in fully developed laminar How, and B Determine the friction factor and Nusselt number in fully developed turbulent flow using empirical relations, and calculate the pressure drop and heat transfer rdte. 

In the previous analysis, we have obtained the velocity profile for fully developed flow in a circular tube from a force balance applied on a volume element, and determined the friction factor and the pressure drop. Below we obtain the energy equation by applying the energy balance on a differential volume eicineiit, and solve it to obtain tlie temperature profile for tlie constant surface temperature and the constant surface heat flux cases. 

Reynolds number, friction factor, and coefficient of resistance. The pressure drop per 100 feet of pipe is then computed. For a given volumetric rate and physical properties of a single-phase fluid, AP,oq for laminar and turbulent flows is laminar flow... 

The following sections will discuss the Heat Mass Transfer and Pressure Drop Factors of catalyst supports of various channel shapes through the identification of the open frontal area, the geometric surface area, and the channel shape-related quantities of Friction Factor and Nusselt Number. 

The remaining information necessary to derive the heat mass transfer and pressure drop relationships for the regular polygons are the Nusselt Number and Friction Factor (9) for each of these shapes. A set of data for these two shape related quantities is given in Figure 1, where the Friction Factor and average Nusselt Number are plotted against a shape value [l/(l+l/fl)], where n... 

For any given Reynolds number, one can read the value of friction factor, and then use Eq. (1) to determine the pressure drop. In the turbulent region, for Re > 2200, one correlation is the Blasius formula [Eq. (3)] ... 

Thus, in laminar flow in a straight channel, the density of the fluid does not affect the pressure drop. To use the correlation for friction factor, or Fig. 8.1(a), one must know the density. This problem is avoided if one plots the product of friction factor and Reynolds number versus Reynolds number, since from their definition ... 

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