ALBERT

Description: A boundary-layer model, based on computational results, describes a number of features of two-dimensional convection in a porous medium: the heat flux, velocity, length and temperature scales and the pattern of flow. The cell structure is different from that for convection in a viscous fluid. The model is valid for a limited range of the Rayleigh number. © 1976, Cambridge University Press. All rights reserved.

Description: The problem of the stability of a fluid with time-dependent heating has been investigated by Morton (1957), Lick (1965) and Foster (1965). Morton and Lick assumed that the rate of change of the temperature profile is small compared with the growth rate of the disturbances (quasi-static assumption). This assumption is invalid near the onset of instability (as defined by ∂/∂t = 0), and Foster has therefore used an initial-value approach.In this paper the range of validity of the quasi-static assumption is discussed, and results of a time-scaled analysis and calculations based on this are compared with the work of Foster; the agreement is found to be good. We restrict our attention to a semi-infinite fluid initially at a constant temperature; at time t = 0 a temperature difference ΔT is applied at the (lower) horizontal boundary (case (A) of Foster).

Description: In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N sim R^{frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Description: 1. Laboratory incubation studies with topsoil samples of the Kikuyu red loam coffee soil have shown that active nitrification of the natural soil nitrogen stops at a soil moisture level just below the permanent wilting percentage. Ammonification of natural nitrogen in this soil does not cease at this moisture level and ammonia nitrogen accumulates substantially, although the values found at the end of the 32-day incubation period, and the rate of ammonification are significantly lower as the moisture level is decreased from ⅚ to of the permanent wilting percentage.

Description: SUMMARYEwo milk yield data obtained by the lamb suckling technique from nutritional experiments were analysed statistically to obtain estimates of the several components of variation. Diurnal variation was studied. The fitting of a sinusoidal curve removed a significant amount of variation.There was a highly significant correlation between successive milk yields obtained at 4 h intervals. Number of lambs suckled and body weight of ewe at parturition had a significant effect on total daily milk yield.The variation within ewes after the removal of diurnal variation and between ewes after the removal of the effects of number of lambs suckled and body weight at parturition were computed. These sources of variation were combined in a general equation which enabled the prediction of the standard errors associated with daily milk production for a given sampling technique. The practical application of the predicted standard errors is discussed.

Description: SUMMARYSeventy-nine Finnish Landrace x Dorset Horn ewes in lamb to Suffolk rams were used in a comparative slaughter experiment to assess the effects of numbers of foetuses on the growth of the products of conception. The mean number of foetuses was 2·7, with a range from 1 to 5. The ewes were individually penned and given a standard diet with metabolizable energy concentration 7·7 MJ/kg and N concentration 21 g/kg, rationed at 2 kg/day during the first month and 1·25 kg/day during the second and third. Allowances beyond that time were on two scales and depended on the number of foetuses being carried as diagnosed by radiography. The ewes were slaughtered between 50 and 145 days of gestation. The gravid uterus was dissected into foetal, placental, foetal fluid and empty uterus components. Equations were fitted to the weights of each component to describe the effects of stage of gestation, litter size and ewe weight. For the mean weight per foetus (Y, kg) the preferred equation isIn (Y)= 2·419–17·574e-0.01976t–00079ft+0–0046w,where tis the time in days from conception, / is the number of foetuses and wis the weight (kg) of the ewe at mating. This is a version of the Gompertz equation, with additional terms to express the effects of / and w.The weights of the placenta and of the empty uterus were similarly fitted by versions of the Gompertz equation but the mean weight of fluids per foetus (Z, kg) or, rather, its natural logarithm was best described by a third degree polynomial, which isIn(Z) = –11·518 + 0–326t;–0·00316t2+0·0000102t3.None of the weights was significantly affected by the level of feeding in late pregnancy.Estimates of mean weights from the equations and of daily rates of gain in weight from the first differentials of the equations are tabulated against stage of gestation and litter size, and the forms of the weight, growth rate and specific growth-rate curves are illustrated graphically.The equation for foetal weight estimates that at the end of pregnancy the mean weight per foetus is reduced by a factor of 0–89 for each additional foetus being carried. The mathematical model implies that the differences originate in early pregnancy, when the factor is very close to unity, and that the mean weights gradually diverge. In the absence of direct evidence this would appear to be the simplest hypothesis, rather than the assumption in most of the earlier literature that the effect is entirely confined to the last 4 or 5 weeks of gestation.Just before parturition the total daily weight gain of quadruplet foetuses was about 250 g and was associated with a similar gain in weight of foetal fluids, the ratio of fluid weight to foetal weight appearing to increase with litter size. The ewes were clearly under considerable physical stress. It is suggested that this aspect must be closely considered when greater prolificacy is sought.

Description: SUMMARYThirty-six mature Finnish Landrace × Dorset Horn ewes, each suckling two lambs, were used in a comparative slaughter experiment to measure changes in body tissues during early lactation. Two levels of body fatness at lambing were established by giving ewes a complete diet containing 10 MJ metabolizable energy (ME) and 139 g crude protein (CP)/kg d.m. either close to requirements or ad libitum during the second half of pregnancy. In lactation half the ewes in each group were given a complete diet containing either 90 (diet A) or 60 (diet B) % milled hay ad libitum. These diets contained 7·9 and 9·2 MJ ME and 121 and 132 g CP/kg d.m. respectively.Ewes fed at the two levels in pregnancy contained 8·4 and 19·6 kg chemically determined fat 5 days after lambing but had similar amounts of body protein, ash and water. Over 6 weeks of lactation ewes given diet A lost 60 and 69% of these weights of fat respectively, while ewes given diet B gained 5% and lost 30% respectively. Up to 26 g of body protein was lost daily from ewes given diet A but none from ewes on diet B. During early lactation the weight of the empty digestive tract increased while the weights of most other body components, particularly the carcass, decreased. The ratio of body energy change to live-weight change varied from 24 to 90 MJ/kg. Thus live-weight change did not accurately reflect relative or absolute changes in body energy.Voluntary food intake was greater for ewes given the high-energy diet (B) than for those given diet A and was depressed in the fatter ewes. Differences in intake could be explained by the effects of body fatness and diet on the weight of gut contents. Milk yield was not significantly affected by body fat reserves but was higher on diet B than A. Fat content of milk was higher and protein content lower for ewes with the higher fat reserves at lambing.As the contribution of fat loss to energy available for milk synthesis increased there appeared to be a reduction in the energetic efficiency of milk synthesis. A number of possible reasons for this are discussed.

Description: SUMMARYThe efficacy of estimates of gut contents and total body water in increasing the precision with which the chemical composition of the body could be estimated in early lactation was evaluated in 36 Finnish Landrace × Dorset Horn ewes. The ewes were fed at two levels in pregnancy, and, in lactation, given diets of two metabolizable energy concentrations.The allometric relationships relating weight of chemical fat and protein to emptybody weight were not affected by treatment or stage of lactation. Inclusion of an index of gut contents, based on dry-matter intake, indigestibility and retention time of food residues, together with live weight in a regression equation predicting weight of body fat, only slightly increased the precision of estimate compared with equations using live weight alone.There was a close negative relationship between the proportions of water and fat in live weight. Inclusion of weight of body water with live weight in a regression equation predicting weight of body fat markedly increased the precision of estimate and the residual error (0·81 kg) was similar at different stages of lactation. However, when deuterium oxide space was used instead of body water there was only a small increase in precision of estimate and the residual error varied from 5·3 kg in early lactation to 2·1 kg in mid-lactation. The relationship between deuterium oxide space and body water was shown to be variable and altered by stage of lactation, and these differences were associated with differences in rate of water turnover in the animal's body.It is concluded that estimates of body water are unsuitable for estimating weight of body fat in early lactation.

Description: SUMMARYFrom 62 days of gestation to parturition, 20 Finnish Landrace x Dorset Horn ewes were each offered one of four diets with roughage to concentrate ratios of 20:80; 40:60; 60:40 and 80:20, at daily metabolizable energy and digestible crude protein intakes of 490 kJ and 3·55 g/kg W0·75 respectively. Plasma concentration of free fatty acids, glucose and urea were determined weekly, and nitrogen balance and digestibility trials were carried out at 70–80 and 130–140 days of gestation.On all treatments the concentration of plasma free fatty acids increased during pregnancy from approximately 200–600 μ-equiv./l and the concentration of glucose and urea decreased by approximately 25%.Digestibility coefficients for dry matter and organic matter increased from 58 to 68% and from 60 to 70% respectively as the proportion of concentrates in the diet increased and were not affected by stage of gestation. The apparent digestibility of nitrogen was not affected by the energy concentration of the diet.Between mid and late gestation there was a mean increase in daily nitrogen retention of 2·5 g and an improvement in the efficiency of nitrogen utilization of 19 percentage units.Nitrogen retention and the efficiency with which the apparently digested nitrogen intake was retained increased as the dietary energy concentration was increased. The mean daily increases in nitrogen retention were 0·0135 and 0·0039 g for each percentage unit increase in the concentrate portion of the diet at mid and late gestation respectively. The corresponding values for the improvement in the efficiency of nitrogen utilization were 0·13 and 0·10%.

Description: SummaryMeasurements of 21 bone lengths and breadths were made on radiographs of 215 foetuses of known gestational ages ranging from 50 to 145 days obtained from 80 Finnish Landrace x Dorset Horn ewes. Number of foetuses per ewe varied from 1 to 5, but the main statistical analyses were based on the 22 sets of twins, 34 of triplets and 11 of quadruplets. Equations were fitted to relate each of the linear measurements to foetal weight alone, to foetal age alone, to foetal age together with number of foetuses, and to foetal age together with foetal weight. It was found that there were significant differences between the twins, triplets, and quadruplets in the lengths their bones attained at any specified weight or at any specified age but not when both weight and age were fixed. The relationships to weight and age jointly were significantly closer than to either of them alone even after allowing for number of foetuses. The mathematical model that fitted best was a modified Gompertz equation of the formwhere ywas the measured length, w was the number of days prior to expected parturition, w was foetal weight, wu was an estimate of the expected foetal weight at time u, and P, Q, R and Dwere fitted constants.