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Ergun equation for pressure drop example. The Ergun equation tells us a number of things.
Ergun equation for pressure drop example. The Ergun An equation used to determine the pressure drop per unit length of a fixed bed of particles such as catalyst at incipient gas velocity, v: We use cookies to enhance your experience on our website. numbers is the so-called Ergun equation [10], which is widely used in practice for predicting the pressure drop across the bed. Jan 10, 2019 · For exam. ΔP is the pressure drop. D p = diameter of particles in packed bed. When you use this model, you define a cell zone in which the porous media model is applied and the pressure loss in When it comes to fluid flow through packed beds, the Ergun equation is the most popular model for relating fluid pressure drop to flowing fluid Reynolds number. 즉 packing의 높이에 따른 차압으로서 ΔP/L으로 표현하며 이를 위해 촉매 vendor로부터 data가 필요하지만 available하지 않다면 아래와 같이 rough하게 예측할 수 있다. The temperature is constant along the length of pipe at 260°C. Recently, Zhang et al. 25, 0. may instead be correlated in terms of the Blake-Plummer equation: f p =1. 6 ) in Ergun’s equation is given by: Here, d p is the effective (average) particle diameter in the porous medium and ε p is the porosity. The equation was found to be a linear function of fluid mass flow rate and pressure gradient. Introduction. 4) are additive. The Ergun equation that is commonly employed is given below. Wall effect. Dp is the particle diameter. WOLFRAM. Pressure conversions starting with psi 4. The plot below represents the Ergun equation (the first equation shown above), where the left hand side of the equation is the pressure drop. ple, Kunii and Levenspiel (1 991) re ported t hat Ergu n. Voila! 50. com/sayanseal3This equation is useful in estimating the pressure drop in a Packed Bed !Learn about Sp Apr 5, 2021 · The method is based on permeability considerations using the Ergun equation to describe the pressure losses of packages of mono-dispersed spheres. Nov 24, 2015 · An equation covering the entire range of flow rates is obtained by assuming that the pressure drop due to viscous losses (Eq. Calculations indicate that the kinetic term contributes the total pressure drop; therefore, the exact values of b and c is not critical to the pressure drop calculation. The Ergun equation, an extension of Darcy law, is the most popular equation used up to now to represent the relationship between pressure drop and fluid flow in fludized or packed beds. Ergun Modification of the Blake-Kozeny Equation for Pressure-Flow 3. The packed bed behavior, shown on the left of these figures is reasonably represented by the Ergun equation (6. and inertial loss terms are additive, an e ect completely at odds with observed ow behaviour in straight pipes, and in- Apr 1, 1993 · Equations can then be grouped by similarity of the mathematical expression. in the slowest limit of laminar Nov 1, 2019 · The constant B, an empirical value in the classical Ergun equation, typically equals 1. cles Jan 1, 2014 · Eisfeld and Schnitzlein’s equation predicts a lower pressure drop than Ergun’s equation for all Reynolds numbers, even in streamline flow. 4 D where η is the fluid viscosity, 10 is the superficial velocity, , is the particle diameter, ρ is the fluid density, and e is the void fraction of the bed. 45K views 11 years ago Kinetics/Reactor Design: Isothermal Reactor Design. 3. The optimization method was conducted in the Matlab software to inversely determine the structural parameters, the coefficients of the Ergun-type equation and the modified Blake–Kozeny–Carman constant of May 1, 2008 · The variation of pressure drop (ΔP) with respect to Reynolds number in both fixed and expanded beds is shown in Fig. 2. However, no simple or uniform prediction has been Jan 1, 2012 · Figure 6 the correlation between Ergun and Blake-Kozeny at Re < 10; Ergun and Burke-Plummer equation at Re > 1,000 (adapted from Bird, 1960). Please be patient. Ma et al. (1995) used the Ergun equa- tion in the high interaction regimes. The equation is only valid for creeping flow, i. The. Describes how to use the Ergun equation to calculate the pressure drop in a packed bed. The effect of fixed beds' length on the pressure drop is significant and, as the example, it is evident, that at the actual velocity of 1. 78 m/s the pressure drop is changing from 985 Pa for the length of the fixed bed H = 35. wolfram. 4 to 1000 [6], [8]. Other different correlations basically have been developed based on these two equations [ 15 ]. from the Darcy-Forchheimer law: k = \frac ~\frac, and k_1 = \frac ~\frac. EXAMPLE 4-28. 24 For a packed bed, the Ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed, L. 5. 10-3 m. The most widely used equation for pressure drop calculation was proposed by Ergun [1]: p (1 ) 2. (1 ) H. Provide the equations needed for Newton's method along with evidence from mum program that the solution has quadratic convergence. 75 and 0. L is the height of the bed. velocity graph, as shown in Figs. In order to create a significant pressure drop along the bed, a small particle diameter and a high gas velocity are used. Under construction. 9 when the Sauter diameter is used, which, per Eisfeld and Schnitzlein, is The modified equation yields substantial improvement for the pressure drop prediction. Jun 26, 2023 · The flow of fluids through porous media and packed beds of granular solids is sub-jected to pressure losses due to the simultaneous action of viscous and kinetic energy losses. 4 to 20. 3 and 3. The coupling of the two Ergun equations permits to predict pressure drop and liquid saturation in two-phase flow conditions. An ideal packed bed reactor with single-phase flow can be described by the Ergun equation, which describes the pressure drop across the bed and how it is related to particle size, bed length, void space or porosity, fluid velocity, and viscosity. (a) Write a program that uses Newton's method to determine the void fraction of the bed and outputs it to screen along with the number of iterations and the value of |f(x)|. Zakeri et al. Oct 1, 2015 · For incompressible flow through a bed of spherical particles of identical size, the Ergun equation can be written as follows: (1) − Δ P L = 150 μ 1 − ε ε 3 2 V d p 2 + 1. Jul 29, 2015 · The design pressure drop should consider a safety margin on the calculated pressure drop. 10-3 m to 1530 Pa for the length of the fixed bed H = 75. 20 MS & H (4) While both equations (3) and (4) have a sound theoretical basis, Ergun empirically found that the friction factor could be described for all values of the Reynolds number by simply adding the right-hand sides of equations (3) and (4). How would the pressure drop parameter B) change if the particle diameter was The above equation is similar to equation [4. [22] investigated the hydrogen output and thermal behavior of a plant-scale fixed-bed reformer for methanol steam reforming based on a 2-D pseudo-homogenous model. Oct 5, 2023 · The pressure drop through a packed bed is often described by the Ergun equation (Ergun & Orning, 1949): (3) Δ P L = K 1 μ u s 1-ε 2 D p 2 ε 3 + K 2 ρ u s 2 1-ε D p ε 3, where Δ P is the pressure drop, L is the length, D p is the particle diameter, K 1 is the laminar coefficient and K 2 is the turbulent coefficient. Important Equations: Ergun equation for pressure drop in a packed bed: d P d z = − ( 1 − ϕ) ν D p ϕ 3 A c [ 150 ( 1 − ϕ) μ D p + 1. For incompressible flow through a bed of spherical particles of identical size, the Ergun equation can be written as follows: − Δ P L = 150 μ 1 − ε ε 3 2 V d Pressure drop was determined for Re ¼ 0. For Non-Darcy flow in LPMs, it is necessary to consider a modified larger constant B to improve the accuracy of the Ergun empirical equation. 963 dp r G= A 1. A commonly used equation for this is the Ergun-equation and combines both the laminar and turbulent components of the pressure loss across a packed bed, $$-\frac{\Delta P Effects of Pressure Drop. Then, an Ergun equation modifying method and the dimensional analysis method Jan 11, 2024 · The Ergun Equation, a fundamental tool in fluid dynamics for estimating pressure drop across packed beds#ErgunEquation #FluidDynamics #EngineeringEducation # Jul 10, 2011 · Ergun equation. com/watch?v=-kLR-MiprzsChapter-2FM T2 - Fluid St Oct 1, 2015 · The equation published by Ergun [1] about sixty years ago remains the most popular and the most widely-quoted pressure drop–flow rate relation for fluid flow through packed beds. taught as “the gospel†in most top-tier engineering schools. Chemical Engineering questions and answers. The pressure drop in the fixed bed was calculated through the Ergun equation. Effects of Pressure Drop. The rule of thumb for reactors is that the inlet pressure drop should be less than 10% of the inlet pressure. Bed Pressure Drop: For both gases and liquids this should be calculated based on the "Ergun" equation given as: (ΔP/L) = K*Re*(150 + 1. 75 Similar to7. 3 Porous Media Conditions. The porous media model can be used for a wide variety of single phase and multiphase problems, including flow through packed beds, filter papers, perforated plates, flow distributors, and tube banks. 75G B = 9cpd. Your retention of material in this module will increase if you write down reasons for your answers to ConcepTests, questions in screencasts, and questions to answer before using the interactive Mar 21, 2005 · Fixed bed reactor인 경우 Ergun equation을 적용할 수 있다. zip, to simulate frictional pressure drop liquid holdup, and liquid axial dispersion. Specifically, the Ergun equation gives the following permeability. 2 and 7. The form of the solution is an expansion in spatial derivatives, and we 2) Flooded-Bed Reactor (upward cocurrent two-phase flow) Download our flooded-bed simulator, flbsimul. error) of press ure drop in packed bed that contai ns part i. It is well known that the pressure loss during one-dimensional flow through a packed bed (fixed bed) of granular material is given by the sum of two terms: a viscous energy loss term, proportional to the fluid velocity, and an inertial loss (kinetic energy) term, proportional to the velocity squared, i. 26] is for the special case when z = ∆ 0. Pressure-Flow Calculations . Theory 7. Overview: This module uses screencasts and an interactive simulation to explain pressure-drop in a packed bed as calculated by the Ergun equation. Example 5-4 Calculating Pressure Drop in a Packed Bed: Pressure drop in a packed bed reactor is given by G (1 – 9) (150 (1 – )H +1. Jul 18, 2023 · Pressure drop (or friction factor) correlations are presented for each of the flow regimes. zip file that contains an Excel worksheet simulator to compute Nov 22, 2016 · In this contribution pressure drop predictions with correlations from literature are compared with the measured pressure drop obtained in a milli-structured reactor having a rectangular cross section filled with differently shaped particles for D/d<15. Isothermal, T = T 0. In fact, I would like to find the adapted constants for different shapes and sizes of Sep 1, 2013 · The Ergun equation, commonly used for predicting packed bed pressure drop, over-predicts the pressure drop through randomly packed or structured beds of smooth spheres at Ergun Reynolds numbers in Apr 20, 2022 · Say hi to me on my new instagram !https://www. example, we can easily move solids about just by pumping or by gravity flow. 0) = diameter of particle in the bed, rt (m) viscosity of gas passing through the bed, h (kg/m s) length down the packed bed of pipe, rt (m) Jun 19, 2013 · The Ergun equation for pressure drop in a packed bed reactor (PBR) is: , where is pressure, is PBR length, is void fraction, is volumetric flow rate, is viscosity, is the diameter of catalyst particles, is cross sectional area of the PBR, is mass flow rate, is a laminar flow term, and is the turbulent flow term. Oct 15, 2015 · The Ergun equation gives satisfactory predictions for the particle Reynolds numbers, Re p, in the range from 0. 26] of the textbook, however, it is more general to account for non-horizontal beds. 1, and the results were found to be in good agreement with the manual calculations as shown in Figure 4. 2005): Nov 1, 2008 · Although the Ergun equation was the most accurate for predicting pressure drop, a newly developed equation that requires only grain size as the physical parameter of each medium also showed good Aug 1, 2009 · In addition, many predictions of pressure drop correlations have been established based on the Forchheimer and Ergun equations [7] [8][9]. ϕ = void fraction (volume of tube not occupied by particles) ν = volumetric flow rate. Worksheet example: Counter-Current Packed-Bed Column. Later analytical efforts were directed at computing the pressure drop-velocity relationship for a well-defined geometry of packed beds of equal-sized spheres arranged in a periodic array [11-13]. The region covered by the Ergun equation is the rising portion of the plot (section I: . Hobbs et al. μ is the gas viscosity. It also tells us that the pressure drop depends on the packing size, length of bed, fluid viscosity and fluid density. You can get the packedbedsimulator. Aug 9, 2021 · For example, Ergun equation fails to predict pressure drop in porous media with R e ε > 500 . A commonly used equation for this is the Ergun-equation and combines both the laminar and turbulent components of the pressure loss across a packed bed, − Δ P Δ L = 150 (μ Flow through a packed bed can be described by the Ergun Equation. 1) and the pressure drop due to the kinetic energy losses (Eq. To obtain the grid The more homogenous the packing, the lower the pressure drop across the bed. A good agreement was found between Sep 1, 2014 · For example: [28], [33], [39], [43], [44] employed Ergun or Ergun-type equations, while [2], [10], [45], [46], [47] utilized Forchheimer equation to correlate their pressure drop data. in diameter when 104. Thus: Complete Fluid Mechanics TutorialsChapter-1Part1-Introduction to fluid mechanics tutorialhttps://www. Next go to the Parameters portion of the Design window. This pressure drop in fixed beds. youtube. Let us consider, therefore, a worked example in which a conduit packed with spherical rigid particles to an external porosity of 0. 174 lbm IVs? "bf (conversion factor) - 4. Analyze the following second order gas phase reaction that occurs isothermally in a PBR: Mole Balance. By continuing to use our website, you are agreeing to our use of cookies. Pressure conversions starting with kPa 7. 150 p 1. Must use the differential form of the mole balance to separate variables: Rate Law. If the fluid were a liquid I think Ergun equation would be the right way to go. The superficial slurry velocity is then predicted as U → = U s → + ε V →. The result is called the Ergun equation (McCabe et al. Apr 1, 2016 · Since the original Ergun equation was developed for the media composed of spherical particles, directly using the Ergun equation usually overestimates the pressure drop of the media packed by energy balance. 75 in front of the turbulent term) or by making changes to the k–ε model for turbulent flow in May 31, 2016 · It is shown that the widely used correlations for predicting pressure drop in porous media continuously under-predict the experimentally obtained pressure drop profiles. Here, we only focus on the pressure drop issue. Apr 1, 2022 · The Ergun-type equation and the Kozeny-type equation were applied to compare the experimental airflow velocity-pressure drop relationship. The Ergun equation tells us a number of things. It is named after Josef Kozeny and Philip C. In the developed modified Ergun equation, the overall pressure gradient was the summation of viscous Jan 1, 2001 · According to Ergun’s correlation, the parameters that affect pressure drop are particle diameter, flow velocity, interparticle porosity and column length. 4 lb/h of gas is passing through the bed. (1) Δ P L = A E 1 - ε 2 ε 3 ρ ν U d 2 + B E 1 - ε ε 3 ρ U 2 d where ΔP is the pressure drop, L is the bed length, U is the superficial flow velocity (i. e. Δ - = 150 − ε. DEMONSTRATIONS PROJECT. Of course, such high values of R e p and R e ε are not expected in the uniform flow zone of packed bed filters for drip irrigation since superficial velocities are very modest. 1. Such wall effects on the pressure drop in packed beds have received limited attention, in spite of the fact that a great deal of Nov 1, 1997 · The frictional pressure drop is calculated by s = ~ + P~g' 12) For the gas phase, the authors apply also an Er- gun-type equation. Pressure Drop in a Packed Bed Reactor (PBR) Using the Ergun Equation. In 1952, Sabri Ergun derived the following equation to predict the pressure drop in packed beds. Thus, future engineers leave university with the Ergun Feb 1, 2002 · 1. 40 (a measure of its packing density). On the continuum level, the second order velocity term demonstrates that the Ergun equation also includes the pressure drop due to inertia, as described by the Darcy–Forchheimer equation. Theoretical changes in pressure after changing particle size 2. Carman. If n is the fluid viscosity, vo is the superficial velocity Dp is the particle diameter, ρ is the fluid density, and ε is the void fraction. Hydraulic radius. 1, 0. Head Loss Modeling. Delete the outlet reactor pressure in the worksheet or workbook 49. : (1) Δ P L =aU+bU 2, where ΔP is the piezometric pressure loss, L the Dec 21, 2018 · The modified Ergun equation for the evaluation of pressure drop across the packed bed, that includes the impact of porosity and wall impact, is presented b y the article a s follows: Chemical Engineering. ε is the porosity of the bed. [9] recommended the use of this equation for estimating pressure drop in fixed-bed coal gasifiers since the Re p values are there usually lower than 500. Click on the radio button next to the pressure drop calculation by the Ergun equation. 75*Re)*((1 – ε) / ε)^3*(µ^2 / (ρ*D p ^3)) where: (ΔP/L) = pressure drop kPa/m (psi/ft) of bed In this case, the equations for the thermodynamic equilibrium were incorporated into the kinetic constants. The pressure drop for flow through a packed bed of spheres can be evaluated using the Ergun equation [1], i. , 1960). In this paper, first, a series of experiments are carried out by changing the particle size and material mass to explore their effects on U0mf and ΔPmf. Equation for Nukon and CalSil Mixture Debris Beds. The simulated results agreed well with experimental data and the pressure drop was considered to be negligible. As expected, the Ergun correlation underestimates the measured pressure drop values considerably. Ergun formulated a correlation that amalgamates the Blake–Kozeny and Burke-Plummer equations to estimate the pressure drop across a packed bed. Pressure conversions starting with kg/cm 2 6. 75 p f Re = + Here, the friction factor . Pressure conversions starting with bar 5. Jul 1, 2016 · This study recasts the correlation for pressure drop in terms of a modified Ergun equation. 6, 2. The Forchheimer and Ergun relations look very similar in the sense that they both have a viscous term proportional to the average velocity and a form/inertia Apr 1, 2017 · 3. Jan 1, 2009 · The aim is to determine the pressure drop of a dry as well as an irrigated Mellapak structured packing, type 250Y, in a column with d S = 1. 40, ID = 1. 9) Nov 1, 2019 · In the flow through porous media, two well-known equations, Ergun correlation and Forchheimer equation are widely used to predict pressure drop as a function of velocity. The deviation of the modified Ergun equation is generally less than 3% compared to CFD-DEM and experimental results, a significant improvement from 30% difference when is used in both inertial and viscous terms. Rearranging the Ergun equation, the following equation can be written for the pressure drop across non-horizontal Pressuredrop due to Apr 22, 2014 · The Ergun equation gives the pressure drop for unit length of a fluid flowing through granular media. to develop an Ergun-type equation [6] and the same in membrane sparger in wastewater treatment was reported by Jun 1, 2020 · (High Pressure Liquid Chromatography) analyses [1], and the Ergun equation, both in the laminar (linear) and turbulent (non-linear) regions of the fluid flow regime [2-4]. Calculate the pressure drop in a 60 ft length of 1 1/2-in. Click on the curve to see the effects of increased gas velocity on particle movement. 0 m, for F V factors of F V = 1. On. For analytical predictions, the negative deviations from the experimentally obtained pressure drop using the unmodified Ergun and Dietrich equations could be as high as 95 and Thus, the pressure drop parameter increase …. It can be observed that, in comparison with Ergun's equation, the simulated pressure drop values are overestimated in the creeping flow regime and underestimated in the turbulent flow regime. (Sch. When designing packed bed reactors understanding the pressure drop across the reactor is very important as this can affect the flow in the bed and the reaction pressure. Uses POLYMATH to solve mass balances and the Erg I am looking for the constants used in Ergun's equation to estimate the pressure drop through a packed bed. V0 is the superficial velocity (the volumetric gas flowrate divided by the cross-sectional area of the bed) Jan 1, 2014 · When the frictional pressure drop is large, meaning when \( \Delta p > 0. Nov 13, 2012 · 234. , 1 ≥ ≥ 1,000 (12) Dec 1, 2023 · Ergun and Orning [16] developed an equation relating pressure drop to gas flow. 22 m, are known. 5, 0. The overview of the pres-sure drop correlations proposed by different authors is given in Table 1 together with the range of their applicability suggested by the authors. z = distance down the reactor. One correlation is suggested for the permeability k over the entire range of mean velocities U 0. It tells us the pressure drop along the length of the packed bed given some fluid velocity. [6] measured experimentally the pressure drop in three different types of packing on a column with a packing height of 5 m. May 1, 2008 · The Ergun equation is a superposition of pressure drop due to viscous and inertial effects of the flow, which are known as Blake-Kozeny and Burke-Plummer equations, respectively. Hence, equation [4. com/PressureDropInAPackedBedReactorPBRUsingTheErgunEquationThe Wolfram Demonstrations Project contains thousands of free intera Jan 8, 2018 · A sample question for Ergun equation and Fluidization Engineering; Chemical Engineering; Chemical Engineering questions and answers; 3. Aspen Plus allows proper fields for computing the pressure drop across packed-bed reactors in Plug Flow configuration and packed-bed pipes. Such conditions are commonly utilized in RPSA. Dec 8, 2020 · The modeling of the minimum fluidization velocity (U0mf) and the incipient fluidization pressure drop (ΔPmf) is a valuable research topic in the fluidization field. 75 ρ 1 − ε ε 3 V 2 d p where − ΔP = piezometric pressure drop in the bed, L = depth of the bed, V = velocity based on the empty cross-section of the bed, ε Dec 5, 2012 · Calculates the change in conversion in a packed bed catalytic reactor when the reactor length increases 50%. Ergun equation would differ significantly from measurements [3]. ) pipe packed with catalyst pellets 1/4 in. Δptotal = Δp debris bed + Δp irreversible loss. 7. The popularity of this equation results from it being. 75 Pa 1/2. the value of 150 in front of the laminar term, and the value of 1. engths (14 and 21 m). In the REV-scale approach, the most commonly used equation for calculating the pressure drop has been proposed by Ergun [27]. Jul 12, 2001 · Pressure drop by the sparger in a bubble column was investigated by Thorat et al. e May 13, 2015 · http://demonstrations. Beyond this are the regions of fast fluidization and of purely entrained flow. 40, 41 F I G U R . We have shown how to construct approximate solutions of the new Dynamic Ergun Equation for the slip velocity U s → given the charge velocity V → field and the pressure drop. The reactor was operated in a turbulent regime. et pressure. 75. Often, the proposed relations are based on the Ergun equation for the pressure drop through a bed and modified after an experimental evaluation based on a limited number of data and a limited number of materials, and sometimes the literature relations are purely empirical. instagram. The Ergun equation, derived from extensive experimental data, represents the pressure drop along the bed as a function of several parameters and is considered a benchmark, as demonstrated by Eq. Feb 1, 2002 · Normalised plot of the Ergun equation (after Ergun, 1952; Bird et al. The constants for determining the resistance coefficient for Mellapak, used in a pilot plant with d S = 0. The case of Of the various pressure drop correlations that have been presented, the Ergun equation [1] is one of the most widely adopted: D p U B U A L P 2 3 2 3 2 (1 ) 1 U H H P H ' (1) where the coefficient A is 150 and B is 1. 75 ( ρ ν) A c] where P = pressure. Made by faculty at = pressure, 1b/ (kPa) volume of void = porosity = void fraction total bed volume volume of solid total bed volume 32. 610 in. For a packed bed, the Ergun equation provides a relationship between the pressure drop per unit length and the properties of the bed. Jul 1, 2006 · The Ergun and CFD model predictions can fairly easily be tuned to predict similar pressure drop values, either by adjustment of the empirical constants in the Ergun equation (i. 1\ \overline{p}, \) one should properly account for the change of density with pressure. 12 ), dropping the kinetic and potential energy terms, dividing by u 2 0 , and introducing the The region covered by the Ergun equation is the rising portion of the plot (section I: . Since the sphericity effectively reduces the particle diameter, the tank-to-particle ratio increases from 10. A suitable measuring set-up was designed, built and used to measure the permeability of plates of Effects of Pressure Drop. 2. The pressure drop ( Ref. s fed to the reactors. Second order in A and irreversible: Stoichiometry. The effectiveness of the proposed correlation is also experimentally verified. In Ergun’s seminal publication, previous theories and equations on pressure loss through a bed were utilized in The Kozeny–Carman equation (or Carman–Kozeny equation or Kozeny equation) is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. Pressure drop depends on a series of factors such as void fraction, media particles diameter, Reynolds number, fluid density and velocity. 17 x (Recall that for the metric system gr — 1. The pressure drop in the bed is 416 Pa. Thus, combining equation (9) with the mechanical energy balance of equation ( 6. The section of the figure where the pressure drop remains essentially constant over a wide range of velocities is the region of bubbling fluidization (section II: cm/s). equation resulted in under-prediction (greater tha n 25 %. In Ergun equation the linear relation between pressure drop and velocity is augmented by a quadratic term. Conclusions. The progression from packed bed to fluidized bed is best followed on a pressure drop vs. |. well. Twenty-seven samples of sintered metal porous resistances were tested and results of the experimental study are presented. The inertial pressure loss in LPMs can be significantly different from it in single lager porous media. f p for the packed bed, and the Reynolds number Re p, are defined as follows. jo nw ax av xx yf bg af se xl