Studies on transfer processes in mixing vessels: effect of gas on solid-liquid hydrodynamics using modified Rushton turbine agitators

The effect of gas on solid-liquid hydrodynamics in mixing vessels was studied to determine the agitation speed required to just completely suspend all the particles under gassed conditions, N _jsg and by measurement of the power consumption associated with this agitation speed. The solid particles have a mean diameter between 15–1000 μm. For their mixing are used standard and modified Rushton turbine agitators positioned singly or doubly on the same shaft. The modified turbine with a surface fraction of the perforations equal to 0.353 (TP3) was obtained through increase in the blade height of the Rushton turbine simultaneously with the perforation of the blade surface. The filled surface of the modified blade is equal to the blade surface of the standard Rushton turbine.     

Turbulence Model Selection for Low Reynolds Number Flows

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Re_θ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.     

Studies on transfer processes in mixing vessels: suspending of solid particles in liquid by modified Rushton turbine agitators

The modified blade turbines are attractive alternatives to the standard Rushton turbine as they do not require any modification in the electrical engine motor and drive assemblies are simple to manufacture and have a reduced power consumption.The modified blades were obtained through increase in the blade height of the Rushton turbine simultaneously with perforation of the blade surface. The field surface of the modified blade is equal to the blade surface of the standard Rushton turbine.In this study the modified blade turbine with the surface fraction of the perforations equal to 0.353 is used.The complete suspension speed and the power dissipation in transition and turbulent regimes using standard and modified Rushton turbine agitators positioned singly or doubly on same shaft, in five solid-liquid systems were investigated.The solid particles used have the mean diameter between 15–1000 m.The modified blade turbine, noted as TP3, was found to be more efficient than the standard turbine in complete and homogeneous suspension.List of Symbols A distance between turbine and the vessel bottom (m) - c dimensionless constant (-) - d agitator diameter (m) - d _p surface-to-volume mean diameter of the particle (m) - D vessel diameter (m) - (H _L )₁ suspension height for one turbine immersed (m) - (H _L )₂ suspension height for two turbines immersed (m) - K consistency index (Pa s ⁿ ) - l _k eddy-size characteristic (m) - N flow behaviour index (-) - N _p number of blades of the mixing system (-) - N agitator speed (s^–1) - N _js agitator speed that just causes complete suspension (s^–1) - Ne P_L/_LN³d⁵ power number in liquid system (-) - (Ne) _g P_g/_spN³d⁵ power number in solid-liquid system (-) - P _L power consumption in liquid system (W) - P _s power consumption in solid-liquid system (W) - r coefficient of correlation (-) - R distance between turbines (m) - Re _spNd²/ _a Reynolds number (-) - S suspension parameter in Zwietering equation (2) (-) - S _C full surface of the blade (m²) - S _G surface of the perforations applied on the blade (m²) - S _G /S _C surface fraction of the perforations (-) - X particle concentration (g/l) - w baffle width (m) - _js specific power input per mass at the complete suspension state (W/kg) - _a apparent viscosity under mixing conditions (Pa s) - _L kinematic viscosity of the liquid (m²/s) - _L density of liquid (Kg/m³) - _s density of solid (Kg/m³) - _sp density of suspension (Kg/m³)     

Flow-induced forces on free-floating macrophytes

Free-floating macrophytes have buoyant petioles and unanchored roots; certain species are highly invasive, owing to characteristics such as high growth rates and the formation of dense floating mats that drift on wind and water currents. Water hyacinth (Eichhornia crassipes) is one example; its invasion of tropical and subtropical freshwater systems worldwide harms native ecosystems and impedes human activities. This research examines flow-induced forces and biomechanical properties of E. crassipes to better understand flow interactions and transport mechanisms. Drag forces were measured in a flume and a wind tunnel for varying approach velocities and raft configurations; from this data, drag coefficients in water (C _D^w) and air (C _D^a) were developed. Over similar Reynolds number (Re _b ) regimes, C _D^w decrease as Re _b increases while C _D ^a are invariant. For the same raft tested in air and water, water drag exceeds air drag and the value of C _D^w approaches C _D^a at high Re _b . Force–velocity relationships indicate root canopies reconfigure by streamlining in higher flow velocities while leaf canopies do not. Root canopy streamlining is further explained through biomechanical testing: we found the major vegetative structures of E. crassipes (roots, stolons, and petioles) have similar moduli of elasticity but second moments of area are three orders of magnitude smaller in roots compared to stolons or petioles, leading to significantly lower flexural rigidity in roots than in stolons or petioles. Flow interactions with the root canopy differ for an individual plant compared to a raft assemblage. Laboratory results suggest that water currents are the dominant mechanism for E. crassipes dispersal.     

Carbon footprint and embodied energy of a wind turbine blade—a case study

Purpose

The main goal of this work is to evaluate the environmental impact of a 63-m blade for wind generators. The embodied energy and the carbon footprint are used as supporting tools for material selection in the initial project stages.

Methods

Real industrial data regarding the most used materials for wind turbine blade construction are used. Two eco-parameters, embodied energy and carbon footprint, were calculated from each selected material together with values of manufacture, transport, use, and final disposal. The blades must be built to have a mechanical strength high enough to withstand vibrations caused by manufacturing flaws, turbulence, or irregular loading. In this sense, Young’s modulus, yield strength, and density were compared to the environmental footprint data to support the final material choice. This evaluation process of the possible materials to be used in the blade manufacture was carried out in the initial stages of the project.

Results

Composite materials such as glass fiber-reinforced polymer (GFRP) and carbon fiber-reinforced polymer (CFRP), bonded together with an adhesive material, are used to build modern wind turbine blades. Those composites comprise a considerable number of different materials that can be mixed to reach adequate performance. Comparisons were made with 46 pre-selected materials, considering the mechanical behavior and environmental impacts. The final selected materials have better properties than the reference material. Finally, two materials with the desired mechanical properties and with a potential lower negative environmental impact than the reference material were selected.

Conclusions

Replacing the reference resin—epoxy/E-glass fiber—with the epoxy resin with the lowest environmental impact—epoxy/S-glass fiber—will reduce the total value of the environmental load to 102 GJ of energy and 3.4 t of CO₂. As important as the material selection in the early stages of product development is the end of life (EoL) choice. In this case, the glass fiber has an EoL potential of 370 GJ of energy and 460 t of CO₂ in the remanufacturing option, against zero for the landfill. This work shows that carefully selected raw materials and EoL alternatives for WTB can significantly reduce the environmental impact of this component.

     

Translocation of C in Macrocystis pyrifera (Giant Kelp)

The pattern of import and export of ¹⁴C-labeled assimilates in Macrocystis pyrifera (L.) C. A. Agardh in southern California was studied by labeling single blades on fronds, in situ, with [¹⁴C]NaHCO₃ for 24 hours. The pattern was found to be similar to that known in dicotyledons: actively growing tissue imported and did not export. As a blade reached maturity it began to export, at first only acropetally to the apex which formed it, later also down the frond to sporophylls and frond initials at the base of the frond, and into the apical regions of juvenile fronds; finally there was a phase of declining export, late in the life of the blade, when transport was only downward. Young fronds imported from older fronds until they were approximately 3 meters long, by which time they had developed mature, upward exporting blades. No translocation was found from a younger frond to an older frond, nor was there transport upward from a blade on a frond lacking the apical region.     

Chemical structure and antioxidant activity of a new exopolysaccharide produced from Micrococcus luteus

An exopolysaccharide (EPS) reaching a maximum of 13 g/L was isolated from Micrococcus luteus by ethanol precipitation. The crude EPS was purified by chromatography on DEAE-cellulose and Sephacryl S-200, affording a polysaccharide active fraction (AEP) with a molecular weight of ∼137 kDa. AEP was investigated by a combination of chemical and chromatographic methods including FTIR, HPLC, periodate oxidation, methylation and GC–MS. Data obtained indicated that AEP was composed of mannose, arabinose, glucose and glucuronic acid in a molar ratio of 3.6:2.7:2.1:1.0, respectively. The main backbone consists of mannose units linked with (1→6)-glycosidic bonds and arabinose units linked with (1→5)-glycosidic bonds. There is a side chain consisting of mannose units linked with (1→6)-glycosidic bonds at C3, when all glucose and most of glucuronic acid are found in the side chain. The in vitro antioxidant assay showed that AEP possesses DPPH radical-scavenging activity, with an EC₅₀ value of 180 μg/mL.     

Power input measurements in a production scale bioreactor

Summary Power input measurements are carried out in a production bioreactor with a liquid volume up to 25 m³. The results show that the cavity formation principle is applicable to reactors at this scale. It can also be observed that empirical correlations are not useful to predict gassed power input accurately. It is found that at gas flow rates for normal production conditions (N_Q =0.1), the gassed power input is about 30–40 % of the non gassed power input.Nomenclature C_p specific heat J/kgK - D impeller diameter m - D_b1 impeller blade diameter m - d baffle diameter m - Fr Froude number - - g gravitation m/s² - h impeller clearance m - H liquid height m - N stirrer speed s^-1 - N_p power number - - N_Q gas flow (aeration) number - - N_Q ^* critical gasflow number for 3 cavity formation - - P_o ungassed power consumption W - P_g gassed power consumption W - Q gas flow rate (273 K, 10⁵ N/m²) m³/s - Re Reynolds number - - T tankdiameter m temperature K - t time s - V liquid volume m³ - ^Vtip impeller tip speed m/s - V_s impeller correlated superficial gas flow rate m/s - W impeller blade width m - density kg/m³     

LAS测算森林冠层上方温度结构参数的可行性

利用位于河南省济源市的华北低丘山地30年生栓皮栎-侧柏-刺槐人工混交林2010年4月至8月每月连续7d,LAS直接测算的森林冠层上方湍流结构参数,与经过湍流谱方法计算处理的三维超声风速/温度仪的观测数据比较,分析LAS测算低丘山地森林冠层温度湍流结构的可行性。结果表明:水平风速和温度湍流谱都有明显的惯性区出现(斜率-2/3);LAS直接测算的湍流温度结构参数与利用该惯性区的数据计算的结果具有较好的一致性,说明在起伏非均匀下垫面上,采用LAS观测湍流结构的变化情况具有较好的可行性。     

Polyester Biosynthesis Characteristics of Pseudomonas citronellolis Grown on Various Carbon Sources, Including 3-Methyl-Branched Substrates

Forty-two different carbon sources were tested for the polyester synthesis of a citronellol-utilizing bacterium, Pseudomonas citronellolis (ATCC 13674). These included linear C₂ to C₁₀ monocarboxylic acids, C₃ to C₁₀ dicarboxylic acids, saccharides, α,ω-diols, hydrocarbons, and 3-methyl-branched substrates such as 3,7-dimethyl-6-octen-1-ol (citronellol), 3-methyl-n-valerate, 3-methyl-1-butanol, and 3-methyladipate. Isolated polymers were characterized by gas chromatography, infrared spectroscopy, ¹H- or ¹³C-nuclear magnetic resonance spectroscopy, ¹H-¹³C heteronuclear correlation spectroscopy (¹H-¹³C COSY), ¹H-¹H homonuclear COSY, and differential scanning calorimetry. Polyesters from nine monocarboxylic acids and two related carbon sources could be metabolically divided into three groups. The first group of C₂ to C₄ carbon sources resulted in copolyesters composed of 61 to 70 mol% 3-hydroxydecanoate, 23 to 33 mol% 3-hydroxyoctanoate, 3.6 to 9.0 mol% 3-hydroxy-5-cis-dodecenoate, and 1.8 to 2.6 mol% 3-hydroxy-7-cis-tetradecenoate. Carbon sources in group II (C₇ to C₁₀) produced copolyesters composed of 3-hydroxyacid monomer units with the same number of carbon atoms as the substrate (major constituent) and monomer units with either two less or two more carbons. Negligible amounts of 3-hydroxy-5-cis-dodecenoate and 3-hydroxy-7-cis-tetradecenoate were detected in copolyesters from this group. Copolyesters from group III (C₅ and C₆) had a monomer unit distribution that could be said to be between those of groups I and II. In addition, a novel copolyester, poly(3-hydroxy-7-methyl-6-octenoate-co-3-hydroxy-5-methylhexanoate), was synthesized when grown on citronellol. The ¹H-¹³C heteronuclear COSY spectrum for monomer unit II revealed that both methylene and isopropyl groups, proximately connected in series to a single chiral center, had magnetically diastereotopic natures.     

Photosynthesis in the Higher Plant Vicia faba: V. Role of Malate as a Precursor of the Tricarboxylic Acid Cycle

In the higher plant Vicia faba, anomalous labeling patterns in the organic acids and related amino acids of the tricarboxylic acid cycle which result from photosynthetic ¹⁴CO₂ fixation (in conjunction with an enzyme localization pattern unique to plant mitochondria) suggest that the tricarboxylic acid cycle functions primarily as a pathway leading to glutamic acid biosynthesis during autotrophic growth. The distribution of isotope in citrate indicates little recycling of oxaloacetate for the resynthesis of citrate. Rather, malate appears to provide both the C₂ and C₄ fragments for the synthesis of citrate, and [³H]formate and ¹⁴CO₂-labeling patterns implicate serine as the ultimate C₃ precursor of malate.     

Conformational characteristics of polypeptides containing isolated L-proline residues with cis peptide bonds

The conformational characteristics of the peptide sequence X-l-Pro, where X  Gly or l-Ala and the peptide bond joining X and l-Pro is cis, are evaluated. Semi-empirical potential functions are used to estimate the contributions to the conformational energy made by the non-bonded van der Waals' and electrostatic interactions and the intrinsic torsional potentials about the NC^a and C^aC′ bonds. Rotations φ₁ and ψ₁ about the NC^a and C^aC′ bonds in residue X and rotation ψ₂ about the C^aC′ bond in l-Pro are permitted, while the angle of rotation φ₂ about the NC^a bond in l-Pro is fixed at 120 ° by the pyrrolidine ring. The presence of the cis peptide bond connecting X and l-Pro renders the backbone rotations φ₁, ψ₁ in X dependent upon the rotation ψ₂ about the C^aC′ bond in l-Pro. (Interdependence of rotations in neighboring residues joined by a cis peptide bond was previously observed in l-alanine oligomers.) The number of energetically allowed conformations for the Gly and l-Ala residues preceding a cis peptide bond l-Pro residue are found to be substantially reduced from those permitted when the peptide bond is trans or when l-Pro is replaced by an amino acid residue. On the other hand, ψ₂ = 100 to 160 ° (cis′) and 300 to 0 ° (trans′) are found to be the lowest energy conformations of the l-Pro residue irrespective of the cis or trans conformation of the X-l-Pro peptide bond.     

Luminescence and energy transfer in Ce3+, Mn2+‐doped K2AEP2O7 (AE = Ca,Sr) phosphor

Pyrophosphates K₂AEP₂O₇ (AE = Ca, Sr) prepared by the classical solid‐state technique and activated with Ce³⁺ are described. Intense emission was observed in K₂AEP₂O₇ (AE = Ca, Sr). The effect of Mn²⁺ co‐doping was studied. The broad emission peak of Mn²⁺ was observed at 534 nm in K₂SrP₂O₇:Ce³⁺ and at 539 nm in K₂CaP₂O₇:Ce³⁺, Mn²⁺. Mn²⁺ emission was greatly enhanced by addition of the sensitizer Ce³⁺ due to efficient energy transfer from Ce³⁺ to Mn²⁺. Copyright © 2015 John Wiley & Sons, Ltd.     

Structures of some botryococcenes: branched hydrocarbons from the b-race of the green alga Botryococcus braunii

Nine branched hydrocarbons of the botryococcene type (C_nH_2n-10 30 ? n ? 37) have been isolated from the green alga Botryococcus braunii. Hydrocarbon mixtures were recovered from wild algae collected in fresh water lakes or from the same strains growing in laboratory; they were further separated by reversed-phase, and in some cases by normal phase, HPLC. From chemical investigations, GC/MS analyses, ¹H and ¹³C NMR spectroscopy, the structures of four new botryococcenes (one C₃₃H₅₆, two C₃₄H₅₈ and one C₃₇H₆₄) were elucidated.     

Determination of the drag coefficient of a toroidal plasma vortex in air

Forces acting on toroidal vortices in an unbounded medium (plasma vortices in air and vortex rings in air and water) are investigated. A solution to the equations describing such votrices is obtained. It is shown that this solution satisfactorily agrees with experiment. Based on the experimental results and the solution obtained, the drag coefficient C _x of such vortices is found. For the same Reynolds numbers, the value of C _x may be much less than the drag coefficient of a drop-shaped axisymmetric body (0.045), which is known to be the best streamlined object.     

The relationship between absorption of sulfur dioxide (SO2) and inhibition of photosynthesis in several plants

Photosynthetic rate, transpiration rate and SO₂ absorption rate were simultaneously measured under exposure to SO₂ (0.1–1.0 μl l ^?1) for 5 or 8 hr in six species belonging to C₄ or C₃ plants (Zea mays, Sorghum vulgare, Amaranthus tricolor, Oryza sativa, Avena sativa andHelianthus annuus). Distinct interspecific differences were found as to the extent of inhibition of photosynthetic rate. Calculation of diffusive resistance to H₂O(r) and SO₂(r′) showed that the ratio of r′/r was 1.9 irrespective of species and coincided well with the theoretical value based on molecular diffusion. Thus it was made clear that the absorption of SO₂ was dependent upon the gas exchange capacity of leaf blade. Using the ratio of r′/r the rate of SO₂ absorption could be calculated from transpiration rate and was compared with the inhibition rate of photosynthesis. In three C₄ species, the inhibition of photosynthesis increased linearly with the amount of SO₂ absorbed during a 5-hour period. The pattern of inhibition of photosynthesis inA. sativa andH. annuus among C₃ species was similar to that of C₄ species until the amount of SO₂ absorbed reached 60 mg-SO₂ m^?2 above which the inhibition abruptly increased. The inhibition of photosynthesis inO. sativa was exceptionally severe even with only a small amount of SO₂ absorbed.     

The equivalent circuit of single crab muscle fibers as determined by impedance measurements with intracellular electrodes

The input impedance of muscle fibers of the crab was determined with microelectrodes over the frequency range 1 cps to 10 kc/sec. Care was taken to analyze, reduce, and correct for capacitive artifact. One dimensional cable theory was used to determine the properties of the equivalent circuit of the membrane admittance, and the errors introduced by the neglect of the three dimensional spread of current are discussed. In seven fibers the equivalent circuit of an element of the membrane admittance must contain a DC path and two capacitances, each in series with a resistance. In two fibers, the element of membrane admittance could be described by one capacitance in parallel with a resistance. In several fibers there was evidence for a third very large capacitance. The values of the elements of the equivalent circuit depend on which of several equivalent circuits is chosen. The circuit (with a minimum number of elements) that was considered most reasonably consistent with the anatomy of the fiber has two branches in parallel: one branch having a resistance R_e in series with a capacitance C_e; the other branch having a resistance R_b in series with a parallel combination of a resistance R_m and a capacitance C_m. The average circuit values (seven fibers) for this model, treating the fiber as a cylinder of sarcolemma without infoldings or tubular invaginations, are R_e = 21 ohm cm²; C_e = 47 µf/cm²; R_b = 10.2 ohm cm²; R_m = 173 ohm cm²; C_m = 9.0 µf/cm². The relation of this equivalent circuit and another with a nonminimum number of circuit elements to the fine structure of crab muscle is discussed. In the above equivalent circuit R_m and C_m are attributed to the sarcolemma; R_e and C_e, to the sarcotubular system; and R_b, to the amorphous material found around crab fibers. Estimates of actual surface area of the sarcolemma and sarcotubular system permit the average circuit values to be expressed in terms of unit membrane area. The values so expressed are consistent with the dielectric properties of predominantly lipid membranes.     

The vicissitudes of microorganism and vegetation recorded by lipid biomarkers in the Antarctic penguin habitat and their implications for climate change

Lipid biomarkers of microorganism and vegetation preserved in penguin droppings record historical changes in the West Antarctic climate and environment. n-Alkanes, fatty acids and coprostanols have been determined in sediment core AD6 from penguin droppings in Ardley Island, West Antarctica, using GC or GC/MS/SIM. For n-alkanes, the main carbon number was nC₂₃ with single-peak pattern, ΣC₂₁⁻/ΣC₂₂⁺ value was from 0.27 to 0.61, the carbon preference index (CPI) was from 2.97 to 6.12 with significant odd–even predominance (OEP), and these indicate that the vegetation was dominated by mosses and lichens. For fatty acids, the main carbon numbers were nC_16:0 and nC_24:0 with double-peak pattern, ΣC₂₁⁻/ΣC₂₂⁺ value was from 0.35 to 0.77, and the relative abundance ratio of even:odd carbon (CPI_A) was from 2.88 to 6.40 with significant OEP. Bacteria invasion index ((iC_15:0 + aC_15:0)/nC_15:0 for fatty acids) showed high contribution of bacteria during 1977–1982, 1948–1953 and 1920–1925, indicating enhanced microbial activities. Meanwhile, CPI_A values decreased and extreme microbes contributed fatty acids with low carbon number to penguin dropping strata. Furthermore, the concentration of cholestanol and ratio of cholestanol/cholesterol in penguin dropping strata changed correspondingly, indicating that the microbial degradation played a major role in the increasing ratio of cholestanol/cholesterol during the sedimentation process. The down-core profiles of n-alkanes, fatty acids and coprostanols in penguin dropping strata indicate that extreme microorganism and bacteria play important roles in the relatively simple Antarctic ecological system associated with climate conditions.     

Comparing real-time quantitative polymerase chain reaction analysis methods for precision,linearity, and accuracy of estimating amplification efficiency

New methods are used to compare seven qPCR analysis methods for their performance in estimating the quantification cycle (C_q) and amplification efficiency (E) for a large test data set (94 samples for each of 4 dilutions) from a recent study. Precision and linearity are assessed using chi-square (χ²), which is the minimized quantity in least-squares (LS) fitting, equivalent to the variance in unweighted LS, and commonly used to define statistical efficiency. All methods yield C_qs that vary strongly in precision with the starting concentration N₀, requiring weighted LS for proper calibration fitting of C_q vs log(N₀). Then χ² for cubic calibration fits compares the inherent precision of the C_qs, while increases in χ² for quadratic and linear fits show the significance of nonlinearity. Nonlinearity is further manifested in unphysical estimates of E from the same C_q data, results which also challenge a tenet of all qPCR analysis methods — that E is constant throughout the baseline region. Constant-threshold (C_t) methods underperform the other methods when the data vary considerably in scale, as these data do.     

Degree of C(4) Photosynthesis in C(4) and C(3)-C(4)Flaveria Species and Their Hybrids : I. CO(2) Assimilation and Metabolism and Activities of Phosphoenolpyruvate Carboxylase and NADP-Malic Enzyme

The degree of C₄ photosynthesis was assessed in four hybrids among C₄, C₄-like, and C₃-C₄ species in the genus Flaveria using ¹⁴C labeling, CO₂ exchange, ¹³C discrimination, and C₄ enzyme activities. The hybrids incorporated from 57 to 88% of the ¹⁴C assimilated in a 10-s exposure into C₄ acids compared with 26% for the C₃-C₄ species Flaveria linearis, 91% for the C₄ species Flaveria trinervia, and 87% for the C₄-like Flaveria brownii. Those plants with high percentages of ¹⁴C initially fixed into C₄ acids also metabolized the C₄ acids quickly, and the percentage of ¹⁴C in 3-phosphoglyceric acid plus sugar phosphates increased for at least a 30-s exposure to ¹²CO₂. This indicated a high degree of coordination between the carbon accumulation and reduction phases of the C₄ and C₃ cycles. Synthesis and metabolism of C₄ acids by the species and their hybrids were highly and linearly correlated with discrimination against ¹³C. The relationship of ¹³C discrimination or ¹⁴C metabolism to O₂ inhibition of photosynthesis was curvilinear, changing more rapidly at C₄-like values of ¹⁴C metabolism and ¹³C discrimination. Incorporation of initial ¹⁴C into C₄ acids showed a biphasic increase with increased activities of phosphoenolpyruvate carboxylase and NADP-malic enzyme (steep at low activities), but turnover of C₄ acids was linearly related to NADP-malic enzyme activity. Several other traits were closely related to the in vitro activity of NADP-malic enzyme but not phosphoenolpyruvate carboxylase. The data indicate that the hybrids have variable degrees of C₄ photosynthesis but that the carbon accumulation and reduction portions of the C₄ and C₃ cycles are well coordinated.