Range Of Flow Ratios Research Articles

Boundary-integral study of a freely suspended drop in a T-shaped microchannel

The motion of small droplets through microfluidic channels, membrane pores, and other confined geometries presents considerable computational challenge due to drop deformation, small clearances, and complex geometries. This paper addresses the challenge by developing a moving-frame boundary-integral method and demonstrating its utility with simulations of a three-dimensional, freely-suspended deformable drop moving through a T-shaped microchannel at small Reynolds number. The drop size is comparable to the channel height, which is much smaller than the channel depth. The drop is fed into a straight channel or arm of the T-junction, with prescribed flow ratio through the other two branches. This setup typically results in strong drop interaction with the furthest corner of the junction. For computational efficiency, the base flow in the channel without the drop is first determined. Then, a “moving-frame” or computational cell around the drop is dynamically generated, using the first solution to provide the fluid velocity on the cell boundary. This method is used to map the outcomes (movement into one branch or the other, or breakup and partitioning between the branches) as a function of the flow ratio between the two branches and the drop capillary number, size relative to the channel height, and viscosity ratio with the carrier fluid. A critical capillary number or size ratio is observed, below which the drop does not break. Above the critical value, the range of flow ratios over which impending breakup is predicted increases with increasing capillary number and size ratio. The volume partitioning in the range where breakup occurs is essentially unity for equal flow rates between the two branches, even though the geometry is asymmetric, and then the volume partition of the daughter drops favors the branch with higher flow rate and with a stronger dependence on the flow ratio for the smaller drop sizes and capillary numbers. The viscosity ratio has a small but noticeable effect, with drops of similar viscosity to the carrier fluid breaking most easily.

Phantom validation of quantitative susceptibility and dynamic contrast-enhanced permeability MR sequences across instruments and sites.

Quantitative susceptibility mapping (QSM) and dynamic contrast-enhanced quantitative permeability (DCEQP) on magnetic resonance (MR) have been shown to correlate with neurovascular disease progression as markers of vascular leakage and hemosiderin deposition. Applying these techniques as monitoring biomarkers in clinical trials will be necessary; however, their validation across multiple MR platforms and institutions has not been rigorously verified. To validate quantitative measurement of MR biomarkers on multiple instruments at different institutions. Phantom validation between platforms and institutions. T1 /susceptibility phantom, two-compartment dynamic flow phantom. 3T/QSM, T1 mapping, dynamic 2D SPGR. Philips Ingenia, Siemens Prisma, and Siemens Skyra at three different institutions were assessed. A QSM phantom with concentrations of gadolinium, corresponding to magnetic susceptibilities of 0, 0.1, 0.2, 0.4, and 0.8 ppm was assayed. DCEQP was assessed by measuring a MultiHance bolus as the consistency of the width ratio of the curves at the input and outputs over a range of flow ratios between outputs. Each biomarker was assessed by measures of accuracy (Pearson correlation), precision (paired t-test between repeated measurements), and reproducibility (analysis of covariance [ANCOVA] between instruments). QSM accuracy of r2 > 0.997 on all three platforms was measured. Precision (P = 0.66 Achieva, P = 0.76 Prisma, P = 0.69 Skyra) and reproducibility (P = 0.89) were good. T1 mapping of accuracy was r2 > 0.98. No significant difference between width ratio regression slopes at site 2 (P = 0.669) or site 3 (P = 0.305), and no significant difference between width ratio regression slopes between sites was detected by ANCOVA (P = 0.48). The phantom performed as expected and determined that MR measures of QSM and DCEQP are accurate and consistent across repeated measurements and between platforms. 1 Technical Efficacy Stage: 2 J. Magn. Reson. Imaging 2020;51:1192-1199.

An experimental study of immiscible liquid–liquid dispersions in a pump–mixer of mixer–settler

Abstract Drop size distribution (DSD) or mean droplet size (d32) and liquid holdup are two key parameters in a liquid–liquid extraction process. Understanding and accurately predicting those parameters are of great importance in the optimal design of extraction columns as well as mixer–settlers. In this paper, the method of built-in endoscopic probe combined with pulse laser was adopted to measure the droplet size in liquid–liquid dispersions with a pump-impeller in a rectangular mixer. The dispersion law of droplets with holdup range 1% to 24% in batch process and larger flow ratio range 1/5 to 5/1 in continuous process was studied. Under the batch operation condition, the DSD abided by log-normal distribution. With the increase of impeller speed or decrease of dispersed phase holdup, the d32 decreased. In addition, a prediction model of d32 of kerosene/deionized system was established as d32/D = 0.13(1 + 5.9φ)We−0.6. Under the continuous operation condition, the general model for droplet size prediction of kerosene/water system was presented as d32/D = C3(1 + C4φ)We−0.6. For the surfactant system and extraction system, the prediction models met a general model as d32/D = bφn We−0.6.

CFD pretending of vapor and liquid refrigerant mixing in variable speed scroll compressor

The mixing of two-phase refrigerant dual ports through a variable speed scroll compressor has been simulated numerically using the shear stress transport turbulence model of the Ansys-CFX code taking into consideration the variable refrigerant flow (VRF) rate, inlet ports ratio range (0.1–0.3) at corresponding R407C flow pressure ratio of suction to secondary flow (1.5–1.8) at two variable speeds of the compressor. The investigation of the increased pressurized flow due to the mixing of the two-phase mixture with the main vapor flow port was performed. The proof of the numerical solution technique showed a percentage error within the orbit of (6–8%) with the mathematical and experimental works. The pressure ratio resultant related to refrigerant mixing volume fraction after reaching the steady state condition has been calculated, the and total mass flow rate ratio influence on the volumetric efficiency is introduced in this report. The injection technique with the designated flow ratio range has achieved an increment in the scroll compressor volumetric efficiency by 6% and achieved a decline in the outlet flow discharge temperature by (13–17) %.

Study on extraction phenol from coal tar with high flux centrifugal extractor

Solvent extraction phenol from coal tar were carried out with novel composite YH-3 as extraction agent, and the high flux centrifugal extractor was used as extraction device. Under the premise of high phenol extraction rate, composite YH-3 extraction agent reduces π–π interaction between phenolic compounds and aromatic hydrocarbons, thus decreasing the entrainment of neutral oil. The optimization of operation conditions, such as the diameter of heavy phase weir HWD, the flow ratio, the total flow rate and the rotation speed, are necessary. For single stage extraction experiment, the mass transfer efficiency was up to 84% while the rate of extraction agent loss was lower than 0.28% with the operation conditions of 29 mm of the heavy phase weir diameter (HWD), 1:1–1.4:1 of the flow ratio range, 160–200 mL/min of the total flow rate and the rotation speed varied from 2200 to 2600 r/min. For three stage counter-current test, the mass transfer efficiency reached up to 92.6% with the optimum operation condition of 29 mm of the HWD, 1:1 of the flow ratio, 200 mL/min of the total flow rate and 2400 r/min of the rotation speed. The results indicated that phenol could be extracted effectively from coal tar in the process of multistage continuous count current centrifugal extraction.

Experimental study on droplet generation in flow focusing devices considering a stratified flow with viscosity contrast

High throughput analysis is highly demanded in a variety of chemical reactions. Droplet microfluidics offers unique advantages over traditional multi-well plate systems for high throughput analysis such as providing a confined and more controllable environment for single particle or cell analysis. Driven by the need to improve the efficiency of encapsulating one particle or cell into one individual droplet without complicating geometric and operating conditions, this study experimentally investigated the effects of viscosity contrast between two miscible fluids that together serve the dispersed fluid on the ordering of particles before they are encapsulated into droplets by another immiscible fluid. Five scenarios with different viscosity contrast were systematically considered and a physical model of droplet size for each scenario was developed based on experimental results and scaling laws. The five different scenarios include two with pure 10% glycerol and pure 80% glycerol as the dispersed phase, respectively, and three others where these two fluids are either side by side or one is accompanied by the other. Droplet size and formation period for these scenarios were compared and analyzed considering the same geometric and flow conditions. It is found that the stratified flow structures formed in the first junction by the two miscible fluids (10% and 80% glycerol solutions) strongly influence droplet formation dynamics such as droplet size and formation frequency. Each scenario finds its own applications. The scenario with 80% glycerol surrounded by 10% glycerol provides the optimized means for particle encapsulation. However, the scenario with two fluids side by side in the first junction generates droplets with high monodispersity for the largest range of flow ratios, which is useful for high throughput reactions involving different reagents.

Water-oil Janus emulsions: microfluidic synthesis and morphology design.

In this work we developed a facile method to prepare water-oil Janus emulsions in situ with tunable morphologies by using a double-bore capillary microfluidic device. In addition, by combining the theory model and our liquids' properties, we propose a method to design the morphology of water-oil Janus emulsions. To systematically research Janus morphologies we combined the theory model and the fluids' properties. Under the model guidance, we carefully selected the liquids system where only the interfacial tension between the water phase and the continuous phase changed while keeping the other two interfacial tensions unchanged. Thus we could adjust the Janus morphology by changing the surfactant mass fraction in the continuous phase. In addition, with the double-bore capillary, we prepared water-oil Janus emulsions with a large flow ratio range. By adjusting the flow ratio and the surfactant mass fraction, we successfully prepared Janus emulsions with gradual morphology changes, which would be meaningful in fields that have a high demand for morphology designing of amphiphilic Janus particles.

Vortex-induced vibration (VIV) of a circular cylinder in combined steady and oscillatory flow

Vortex-induced vibration (VIV) of a circular cylinder in the combined steady and oscillatory flow is investigated numerically by solving the two-dimensional Reynolds-Averaged Navier-Stokes equations. The focus of the study is to investigate the effects of flow ratio, a, on the response of the cylinder. The flow ratio is defined as the percentage of the steady flow velocity component in the total fluid velocity. Simulations are carried out for a constant Keulegan–Carpenter (KC) number of 10 and flow ratios ranging from 0 to 1 with an increment of 0.2. The reduced velocities for each flow ratio range from 2 to 25 to ensure that the whole lock-in regime is covered. In the resonance regime, the frequency of the cross-flow vibration component may lock onto the oscillatory flow frequency or the natural frequency of the system, depending on the flow ratio. It locks onto twice the oscillatory flow frequency if the flow ratio a≤0.2, and locks onto the natural frequency of the system if a≥0.6. It is found that the lock-in regime in the combined steady and oscillatory flow is wider than both the one in the pure steady flow and the one in the pure oscillatory flow. The widest lock-in regime occurs as the flow ratio is 0.4 and 0.6 and it is about twice as wide as that in the pure oscillatory or pure steady flow. The response at a=0.2 is very similar to that in the pure oscillatory flow case (a=0), while at a=0.8 the response is very similar to that in the pure steady flow case. At a=0.8, the amplitude of the cylinder in the cross-flow direction reaches as high as 1.5 diameters in the “Super upper” branch because of the slowly increasing fluid velocity. It is also found that the vortex shedding goes through 2S, 2P and 2T modes in one period of oscillatory flow at a=0.8 and Vr=7, where the cross-flow amplitude is the maximum.

CFD based analysis of flow distribution in a coaxial vacuum tube solar collector with laminar flow conditions

A computational fluid dynamics (CFD) analysis has been conducted to find the pressure losses for dividing and combining fluid flow through a tee junction of a solar collector manifold. Simulations are performed for a range of flow ratios and Reynolds numbers, and equations are developed for pressure loss coefficients at junctions. A theoretical model based on successive approximations then is employed to estimate the isothermal and non-isothermal flow distribution in laminar range through a collector consisting of 60 vacuum tubes connected in parallel in a reverse (U-configuration) and parallel (Z-configuration) flow arrangement. The results are in reasonable agreement with the available experimental results for U-configuration. The proposed CFD based strategy can be used as a substitute to setting up and performing costly experiments for estimating junction losses.

Influence of Excess Hydrogen and Nitrogen on Temperature Distribution of a Hydrogen-Fluorine Flame Reactor

The exothermicity of the reaction between hydrogen and fluorine can be used for chemical processing, or in generation of HF based chemical laser, where higher temperatures are required. The ratio of H2 to F2 flow and the flow rate of nitrogen affect the reactor temperatures. The authors report their experimental and computational study on the effect of excess hydrogen and nitrogen flow on reactor temperatures in a tubular reactor. The experiments have been performed over a wide range of flow ratios to generate reliable data for reactor scale-up. The computational studies predict the temperature, velocity, and species concentration at different locations of the reactor. The temperature predictions show a good match with the experimental findings. This study may be helpful in designing a large scale H2-F2 flame reactor.

Effect of O2 Gas during Inductively Coupled O2/Cl2 Plasma Etching of Mo and HfO2 for Gate Stack Patterning

In this study, we investigated the etching characteristics of Mo and HfO2 single layers and Mo/HfO2 stacked structure for metal electrode/high-k gate stack patterning in O2/Cl2 inductively coupled plasmas and the effects of O2 addition on the etch rates and etch selectivity of the Mo to the HfO2 layer. By controlling the process parameters such as the O2/Cl2 flow ratio, the top electrode power and the dc self-bias voltage (Vdc), the Mo/HfO2 etch selectivity as high as \\cong67 could be obtained. Addition of O2 gas to the O2/Cl2 chemistry improved the Mo/HfO2 etch selectivity because the O2 gas in a certain flow ratio range reduced the HfO2 etching reactions due to less chlorination of Hf but enhanced the Mo etch rate presumably due to effective formation of highly volatile Mo–O–Cl etch by-products.

Silicontetrachloride based microcrystalline silicon for application in thin film silicon solar cells

The replacement of the process gas silane by silicontetrachloride for the deposition of microcrystalline silicon thin films is explored. The films were prepared by plasma enhanced chemical vapor deposition from mixtures of silicontetrachloride and hydrogen. Deposition conditions similar as employed for efficient silane-based microcrystalline silicon solar cells of high deposition rate were applied. Structural and electronic properties of the films are studied by infrared optical absorption and Raman spectroscopies and conductivity measurements. Increasing the flow ratio of silicontetrachloride to hydrogen, the transition from the crystalline to the amorphous state is found to occur in a similar range of flow ratio as in silane-based material. The lowest porosity is observed for a crystalline fraction near 80%. Porosity, void-related microstructure and chlorine content are found to decrease with increasing substrate temperature. For boron doped material deposited at a substrate temperature of 250 °C, conductivity values exceeding 50 (Ω cm) −1 were achieved. This latter material was incorporated as p-layer into microcrystalline pin silicon solar cells. Solar cell efficiencies similar as for solar cells with a silane-based p-layer were obtained.

A numerical and experimental investigation on the coefficients of discharge and the spray cone angle of a solid cone swirl nozzle

Numerical and experimental investigations have been made on the coefficient of discharge C d and the spray cone angle ψ of a swirl spray solid cone pressure nozzle. The theoretical predictions are made from a numerical computation of flow in the nozzle using the standard k– ε model of turbulence. The values of C d and ψ have been evaluated from the radial distributions of velocity components of liquid flow at the nozzle exit. The experiments have been carried out to measure the values of C d and ψ of a solid cone spray nozzle at different operating conditions to validate the numerical predictions. It has been established, from a fair agreement between the theoretical and experimental results, that the adaptation of the standard k– ε model for turbulence in nozzle flow serves well the purpose of predictions of C d and ψ within the range of operating parameters studied in the present work. It has been observed that the coefficient of discharge and the spray cone angle remain almost constant with the Reynolds number Re of the flow at inlet to the nozzle. The coefficient of discharge C d is almost uninfluenced by inlet swirl number S in its lower range, but decreases with S in its higher range. The spray cone angle ψ, on the other hand, always increases with an increase in S. For a given Re, an increase in flow ratio q r (the ratio of flow rate through inlet central port to the total flow through the nozzle) increases the value of C d and decreases the value of ψ. However, the influence of q r on C d is prominent at lower values of D 2/ D 1 (the ratio of the diameters of inlet axial port to the swirl chamber of the nozzle). An increase in the value of C d takes place with a decrease in D 2/ D 1 mainly in the range of higher q r and for values of D 2/ D 1 less than 0.17. The spray cone angle ψ, on the other hand, is almost uninfluenced with D 2/ D 1, except in the situation when ψ increases with an increase in D 2/ D 1, from 0.38 to 0.75 mainly in the lower range of flow ratio q r .

Study of a novel rotary cyclone gas-solid separator

Based on the analytical study of the characteristics of fine particle motion in swirling flow, a new design idea on flow organization and construction aimed at increasing the positive radial flow in the separation chamber of the rotary cyclone separator (PRV type) was proposed. Experimental verification including the test of variation of separation efficiency and pressure loss with the first and secondary flow ratio show that this new type separator has higher and more stable separation efficiency in broad flow ratio range while the pressure loss is far below the conventional rotary cyclone separator and even comparable with that of simple cyclone separator

Growth of Tantalum Nitride Films on Si by Radio Frequency Reactive Sputtering of Ta in N 2 / Ar Gas Mixtures: Effect of Bias

Tantalum nitride films are deposited on silicon substrates by radio frequency (rf) reactive sputtering of Ta in gas mixtures. The deposition rate, chemical composition, and crystalline microstructure are investigated by cross‐sectional‐transmission electron microscopy, X‐ray photoelectron spectroscopy, Auger electron spectroscopy, X‐ray diffraction, and atomic force microscopy, respectively. According to those results, the deposition rate, film composition, and microstructure correlate with the bias. A stepwise change in deposition rate is observed at a flow ratio of 0.2 for all biases. The deposition rate increases with the bias throughout the whole range of flow ratio. Crystalline TaN can be deposited on Si substrates at a flow ratio of 0.25 and all biases. The TaN lattice is distorted due to the change of N concentration. In addition, the experimental data which were interpreted using the deposition mechanism and the kinetic model which were published previously. © 2000 The Electrochemical Society. All rights reserved.

Design and evaluation of a nanometer aerosol differential mobility analyzer (Nano-DMA)

A nanometer aerosol differential mobility analyzer, Nano-DMA, has been developed for measuring the size distribution of nanometer aerosols in the particle size range of 3–50 nm. The design is based on a cylindrical configuration and is optimized by means of the numerical model of Chen and Pui (1997, J. Aerosol Sci. 28, 985–1004). Important design features include high particle penetration (low loss) through the Nano-DMA and high sizing resolution. For reducing particle loss in the aerosol transport passage, the aerosol residence time in the Nano-DMA is reduced by shortening the inlet transport passage. An optional feature of high inlet flow (up to 16.5 lpm) is designed in order to further reduce the residence time between the aerosol inlet and the slit in the classifying region of the Nano-DMA. A new entrance slit is designed to have optimal aerosol and sheath flow matching at a flow ratio of 1 : 10, and has a wide dynamic flow-ratio range (up to aerosol/sheath flow ratio of 1/70) compared with the TSI-standard DMA design. This slit improvement makes the Nano-DMA suitable for high resolution particle sizing and classification. For reducing the effect of Brownian diffusion broadening on the transfer function of the Nano-DMA, the collector tube length is shortened to 5.0 cm compared to the TSI-Standard DMA of 44.44 cm and TSI-Short DMA of 11.11 cm. At the design flow condition of 1.5 lpm aerosol (or 16.5 lpm aerosol high inlet flow case) and 15.0 lpm sheath flow rates, the measurable size range is from 3–50 nm. The lower detection limit of 3.0 nm coincides with the lower detection limit of the TSI UCPC (Ultrafine Condensation Particle Counter). The base of the Nano-DMA is completely re-designed to avoid particle loss due to the undesirable electrostatic effect observed by Kousaka et al. (1986, J. Chem. Eng. Japan 19, 401), and to obtain an uniform electric field in the entire classifying region. The overall performance of the Nano-DMA is then evaluated by the numerical model of Chen and Pui (1997, J. Aerosol Sci. 28, 985–1004) before its construction and experimental evaluation. By comparing with the experimental results obtained using the Tandem DMA technique described in Hummes et al. (1996, J. Aerosol Sci. 27, S135–S136; Part. Part. Syst. Charact. 5, 327–332), it is concluded that the Nano-DMA is performing well in the designed size range and its transfer function agrees well with the numerical prediction.

Myocardial contrast echocardiography and the transmural distribution of flow: A critical appraisal during myocardial ischemia not associated with infarction

Objectives. This study was undertaken to determine whether myocardial contrast echocardiography can be used to estimate the transmural distribution of flow.Background. Myocardial contrast echocardiography has been shown to reliably measure average transmural blood flow during myocardial ischemia. However, there is controversy regarding its ability to determine the transmural distribution of flow.Methods. The transmural distribution of flow was measured in 21 open chest anesthetized dogs with use of radiolabeled microspheres and sonicated albumin microbubbles (mean size 4.5 μm). In the 11 Group I dogs, myocardial contrast echocardiography was performed at baseline and during left anterior descending artery stenosis. In five of these dogs, it was also performed during left circumflex artery stenosis. In these dogs large (mean 12 μm) hand-agitated bubbles were also used. In the five Group II dogs, myocardial contrast echocardiography was performed before and 45 s after intracoronary injection of 6 mg of papaverine in the presence of a critical left circumflex artery stenosis. The five Group III dogs were studied during cardiopulmonary bypass at baseline and during left anterior descending artery stenosis. Off-line image analysis of the echocardiographic images was performed and timeintensity curves obtained from thess images were correlated with radiolabeled microsphere-derived flows.Results. The ratios of the parameters derived from the endocardium and epicardium during myocardial contrast echocardiography were found to correlate poorly (ranging from R2= 0 to R2= 0.35) with radiolabeled microsphere-derived endocardial/ epicardial flow ratios over a wide range of flow ratios (0.01 to 2.58). These results were not influenced either by the location of the regions of interest (left anterior descending vs. left circumflex artery bed) or by the size of the bubbles (4.5 vs. 12 μm).Conclusions. Myocardial contrast echocardiography cannot be used to assess the transmural distribution of flow during myocardial ischemia not associated with infarction.

A streaming birefringence study of the flow at the junction of the aorta and the renal arteries

Streaming birefringence with an organic dye (Milling Yellow) was used to investigate the flow near the junction of the renal arteries and the descending aorta in a model of human vessels. The dye concentration was adjusted to give fluid rheological properties, typical of blood. Steady and pulsatile flow were investigated at branch-to-trunk flow ratios of 0.050–0.350. The flow ratio range over which flow separation and simple secondary flows were identified during systole near the renal ostia are reported. Streaming birefringence has the advantage of allowing visualization of the entire flow field. Also, the fluid rather than suspended particles are observed. An important disadvantage, however, is that three-dimensional flows make interpretation difficult.

Void fractions in two‐phase flow

AbstractVoid fractions (fraction of the flow cross‐sectional area occupied by the gas phase) have been measured for steam‐water flows in an adiabatic, horizontal test section of 0.484 in. I.D. at 400, 600, 800, and 1,000 1b./sq. in. gauge. A comprehensive survey of void data for two‐phase concurrent flow is included in the paper, and the data, including the Martinelli and homogeneous flow model predictions, are compared. System characteristics, involving one‐ and two‐component flows in horizontal and vertical test sections with and without heat transfer over a range of flow ratios, total flow rates, and pressure, are too complex, and the data available are neither extensive nor precise enough to warrant the generation of over‐all correlations. Use of the void data in correlating two‐phase frictional pressure drops is discussed. A model has been presented for the prediction of critical flows based upon the void data, and calculations have been made for steam‐water critical flows over a range of critical pressures from 15 to 2,000 1b./sq. in. abs.

Flow through the Two-stage Hydraulic Cyclone

As the authors discussed in the previous paper2), the sharpness of classification of hydraulic cyclones may be markedly improved by combining them in series as shown in Fig.1. In such a system, as we call the two-stage cyclone system, the overflow-side back pressure Po of the first cyclone I is not always the same as the underfiow-side back pressure Pu, because pressure drops through the two second cyclones (ΔpIIo and ΔpIIu) may differ from each other. Consequently, flow rate and flow ratio through cyclone I will be functions of the overflow-side pressure drop Δpo (=Feed pressure Pf-Po), the underfiow-side pressure drop Δpu (=Pf-Pu) and the dimension of the cyclone.To see the effect of back pressures on the flow rate and the flow ratio of cyclone I, an experimental apparatus as shown in Fig.2 was constructed. The underfiow nozzle of the cyclone I was enclosed in a back pressure chamber A. Overflow and underfiow rates were adjusted by valves E and D and the back pressures were measured with manometers C and F. Thus full range of flow ratio from zero to 100% could be surveyed with this apparatus.Typical examples of the results are shown in Figs.3 and 4, where the observed points are plotted on the Δpo/γ vs ΔPu/γ chart. Numbers above the points show the flow rate Qf and numbers in bracket under the points represent the flow ratio Rf. It may be seen from these charts that the points of equal flow ratios lie on the straight lines (equi-flow-ratio lines) which cross the origin. All the observed points fall between those two limiting lines which represent zero and 100% flow ratio. Inclinations of equi-flow-ratio lines are correlated to De/Du and Rf as shown in Fig.7 and equation (6). Do and Du seem to have equivalent effects on the flow rate and the flow ratio. Similarly the points of equal flow rate lie on the straight line which ties the same flow rate points on two limiting lines. The flow rate Qf is represented in equation (8) as a function of Δpo, Δpu and the dimension of the cyclone.Applying these results, dimension, pressure drop and Newton's classification efficiency are calculated for the purpose of designing two-stage, circulation type hydraulic cyclone system. Results of the calculation are shown in Fig.12, 14 and Table 3.