Computer simulation of the hydraulic milking method

1992 ◽  
Vol 59 (3) ◽  
pp. 253-264
Author(s):  
M. Clare Butler ◽  
Robert J. Grindal
Keyword(s):  
Differential Equation ◽  
Flow Rate ◽  
Equations Of Motion ◽  
Flow Rates ◽  
Air Inlet ◽  
Wall Movement ◽  
Linear Differential ◽  
Milking Machine ◽  
The Relationship ◽  
Return Valve

SummaryA mathematical model of the interactions within a milking machine teatcup has been developed, which describes the relationship between liner wall movement, pressures and flow rate when milking without an air inlet. It is based on equations of motion for a column of incompressible fluid and requires a second-order, non-linear differential equation to be solved. Incorporating a non-return valve allows hydraulic milking to be modelled, and the comparison between predicted and measured pressures, flow rates and liner wall movement when milking hydraulically is shown. The model can be used to optimize milking conditions to reduce vacuum peaks, improve liner opening and thus maximize flow rate.

Interaction between CO2 concentration and flow rate on peripheral airway resistance

1991 ◽  
Vol 70 (6) ◽  
pp. 2514-2521 ◽  
Author(s):  
A. Kaise ◽  
A. N. Freed ◽  
W. Mitzner
Keyword(s):  
Flow Rate ◽  
Airway Resistance ◽  
Co2 Concentration ◽  
Low Flow ◽  
Flow Rates ◽  
Peripheral Airway ◽  
Residual Capacity ◽  
Local Ventilation ◽  
End Tidal ◽  
The Relationship

In the present study, we investigated the interaction between CO2 concentration and rate of delivered flow on peripheral airway resistance (Rp) in the intact canine lung. Dogs were anesthetized, intubated, paralyzed, and mechanically ventilated with room air to maintain end-tidal CO2 between 4.8 and 5.2%. Using a wedged bronchoscope technique, we measured Rp at functional residual capacity. The relationship between CO2 concentration and Rp was measured at flow rates of 100 and 400 ml/min with 5, 3, 2, 1, and 0% CO2 in air. Measurements were made at the end of a 3-min exposure to each gas. At low flow rates (100 ml/min) responses to hypocapnia were small, whereas at high flow rates (400 ml/min) responses were large. The PC50 (defined as the CO2 concentration required to produce a 50% increase in Rp above baseline Rp established on 5% CO2) at 400 ml/min (1.73%) was significantly larger than that at 100 ml/min (0.38%). We also directly measured the relationship between Rp and flow rate with 5% CO2 (normocapnia) or 1% CO2 (hypocapnia) delivered into the wedged segment. Increases in normocapnic flow caused small but significant decreases in Rp. In contrast, increases in hypocapnic flow from 100 to 400 ml/min caused a 108% increase in Rp. Thus the response to hypocapnia is augmented by increasing flow rate. This interaction can be explained by a simple model that considers the effect of local ventilation-perfusion ratio and gas mixing on the local CO2 concentration at the site of peripheral airway contraction.

scholarly journals Relation between Small Functions with Differential Polynomials Generated by Solutions of Linear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Zhigang Huang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Entire Functions ◽  
Linear Differential Equations ◽  
Differential Polynomials ◽  
Small Functions ◽  
Linear Differential ◽  
The Relationship ◽  
Growth Of Solutions

This paper is devoted to studying the growth of solutions of second-order nonhomogeneous linear differential equation with meromorphic coefficients. We also discuss the relationship between small functions and differential polynomialsL(f)=d2f″+d1f′+d0fgenerated by solutions of the above equation, whered0(z),d1(z),andd2(z)are entire functions that are not all equal to zero.

Notes on the Riccati Equation

2005 ◽  
Vol 70 (7) ◽  
pp. 941-950 ◽  
Author(s):  
Eugene S. Kryachko
Keyword(s):  
Differential Equation ◽  
Normal Form ◽  
Riccati Equation ◽  
Second Order ◽  
Order Linear Differential Equation ◽  
Riccati Transformation ◽  
Rational Solutions ◽  
Order Polynomial ◽  
Linear Differential ◽  
The Relationship

The relationship between the Riccati and Schrödinger equations is discussed. It is shown that the transformation converting the Riccati equation into its normal form is expressed in terms of the roots of its algebraic part treated as a second-order polynomial. Together with the well-known Riccati transformation, a new transformation which also links the Riccati equation to the second-order linear differential equation is introduced. The latter is actually the Riccati transformation applied to an "inverse" Riccati equation. Two specific forms of the Riccati equation admitting the explicit particular rational solutions are obtained.

Assessment of the impact of water parameters on the flow rate of ceramic pot filters in a long-term experiment

2015 ◽  
Vol 15 (6) ◽  
pp. 1425-1432 ◽  
Author(s):  
C. Salvinelli ◽  
A. C. Elmore
Keyword(s):  
Flow Rate ◽  
Water Production ◽  
Premature Failure ◽  
Initial Flow ◽  
Flow Rates ◽  
Treated Water ◽  
Long Term Study ◽  
The Impact ◽  
The Relationship

Poor water quality is a major contributing factor to disease in developing countries. Silver-coated ceramic pot filters (CPFs) are a relatively common form of household water treatment system (HWTS) representing an effective and sustainable technology for poor communities. Water production seems to be the major limiting factor of the CPF's lifetime and sustainability since low flow rates do not produce an adequate daily volume of treated water. This paper describes a long-term study of CPF flow rates under controlled conditions using three different water sources. The relationship between water characteristics and flow rate was assessed with the intent of identifying the principal parameters that impact CPF water production. The study concluded that turbidity seems to be the principal indicator in determining CPF lifetime in terms of quantity of treated water. There is no evidence that biological activity also contributes to premature failure of CPFs and the data did not indicate that chemical precipitation is responsible for the filter clogging. Manufacturers commonly conduct initial flow rate tests using clear water as a measure of quality assurance. However, the relationship between initial flow rate and average flow rate during the lifetime of the CPF should be further studied.

scholarly journals Oscillator with a Sum of Noninteger-Order Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
L. Cveticanin ◽  
T. Pogány
Keyword(s):  
Differential Equation ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Equations Of Motion ◽  
Dominant Term ◽  
Advantages And Disadvantages ◽  
Polynomial Type ◽  
Polynomial Nonlinearity ◽  
Non Linear ◽  
Linear Differential

Free and self-excited vibrations of conservative oscillators with polynomial nonlinearity are considered. Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. For the case when only one nonlinear term exists, the exact analytical solution of the differential equation is determined as a cosine-Ateb function. Based on this solution, the asymptotic averaging procedure for solving the perturbed strong non-linear differential equation is developed. The method does not require the existence of the small parameter in the system. Special attention is given to the case when the dominant term is a linear one and to the case when it is of any non-linear order. Exact solutions of the averaged differential equations of motion are obtained. The obtained results are compared with “exact” numerical solutions and previously obtained analytical approximate ones. Advantages and disadvantages of the suggested procedure are discussed.

scholarly journals At what flow rate does aortic valve gradient become severely elevated? Implications for guideline recommendations on aortic valve area cutoffs

2021 ◽  
Author(s):  
Wilbert Aronow ◽  
Ayesha Salahuddin ◽  
Daniel Spevack
Keyword(s):  
Aortic Valve ◽  
Linear Regression ◽  
Aortic Stenosis ◽  
Flow Rate ◽  
Aortic Valve Area ◽  
Flow Rates ◽  
Wide Range ◽  
The Relationship ◽  
Valve Area

IntroductionSince many patients with AVA < 1.0 cm2 do not manifest a mAVG > 40 mmHg, we sought to determine the AVA at which mAVG tends to exceed 40 mmHg in a sample of subjects with varied transvalvular flow rates.Material and methodsWe selected 200 subjects with an AVA< 1.0 cm2. The sample was selected to include subjects with a varied mean systolic flow (MSF) rates. Linear regression was performed to determine the relationship between MSF and mAVG. Since this relationship varied by AVA, the regression was stratified by AVA (critical <0.6 cm2, severe 0.6-0.79 cm2 , moderately severe 0.8-0.99 cm2)ResultsThe study sample was 79 ± 12 years-old and was 60% female. The MSF rate at which mAVG tended to exceed 40 mmHg was 120 ml/s for critical AVA, 183 ml/s for severe AVA and 257 ml/s for moderately severe AVA. Those with moderately severe AVA rarely (8%) had a mAVG > 40 mmHg at a wide range of MSF. In contrast, those with severe AVA typically (75%) had mAVG > 40 mmHg when MSF was normal (>200 ml/s). Those with critical AVA frequently (44%) had mAVG > 40 mmHg, even when MSF was reduced.ConclusionsAVA > 0.8 cm2 was rarely associated with mAVG > 40 mmHg, even when transvalvular flow rate was normal. Consideration should therefore be given to either raising the cutoff AVA or lowering the mAVG at which aortic stenosis is considered severe.

STUDIES ON THE RELATIONSHIP BETWEEN WATER MOVEMENT AND WATER CHEMISTRY IN MIRES

1966 ◽  
Vol 44 (6) ◽  
pp. 747-758 ◽  
Author(s):  
J. H. Sparling
Keyword(s):  
Water Chemistry ◽  
Oxygen Concentration ◽  
Flow Rate ◽  
Water Surface ◽  
Water Movement ◽  
Simple Diffusion ◽  
Flow Rates ◽  
Acidic Conditions ◽  
The Relationship ◽  
Iron And Manganese

Fifty-four sites were selected in a number of mires in Ontario, and rates of water movement were measured on a number of occasions. The rates of water movement ranged from less than 0.1 cm sec−1 to over 8 cm sec−1. The oxygen concentration of the mire waters increased with increasing flow rate, approaching saturation at rates over 1 cm sec−1. From a model it was shown that at a flow rate of less than 0.3–0.4 cm sec−1 the diffusion of oxygen into the water would be similar to simple diffusion into a stationary water surface, and because of the respiration of roots and microorganisms in the peat, the oxygen would tend to be depleted. Above flow rates of 0.4 cm sec−1 the water is agitated, and is continually replenished with oxygen from the atmosphere. Reduced states of iron and manganese were shown to be in solution at concentrations greater than 0.1 mg/1 only at low rates of water flow. The pH was also shown to increase with faster rates of water movement, the increase depending on the base status of the mire. Aluminium is in solution only in situations of low water movement where more acidic conditions are prevalent.

The Thermal Stability of Fuels at 480 °C (900 °F): Effect of Test Time, Flow Rate, and Additives

1995 ◽  
Author(s):  
Tim Edwards ◽  
John Krieger
Keyword(s):  
Deposition Rate ◽  
Flow Rate ◽  
Test Time ◽  
Fuel Quality ◽  
Time Curve ◽  
Flow Rates ◽  
Time Flow ◽  
Aircraft Fuel ◽  
Small Flow ◽  
The Relationship

The thermal oxidative stability of several aircraft fuels at high temperatures has been evaluated in a flowing test device. The fuels studied include Jet A, JPTS, and JP-7. The tests evaluated solid deposition under various conditions, typically at maximum fuel temperatures of ∼480 °C (900 °F) at a pressure of 69 atm. Under these conditions, the dissolved oxygen in the fuel is completely consumed and the thermal-oxidative reactions are driven to completion. At test times up to 50 hours, both surface and bulk (filter) deposition was usually an approximately linear function of test time, after an initial induction time of low deposition which varied from 0 to ∼20 hours depending upon fuel quality. In tests with flow rates from 12 to 200 mL/min (1–21 lb/hr), the deposition rate (expressed in ppm) was fairly constant. These data give some guidance for extrapolating results from small flow-rate bench-scale tests to higher flow rates more realistic to aircraft fuel systems, for conditions where the oxygen is completely consumed. For conditions where the oxygen is not completely consumed, the relationship between surface and suspended bulk deposits can become quite complex. Two dispersant additives widely examined in the JP-8+100 program were studied, with the additive significantly decreasing the slope of the deposition-vs-time curve (the deposition rate) for Jet A fuels.

Lymphatic pump function curves in awake sheep

1996 ◽  
Vol 270 (2) ◽  
pp. R486-R488 ◽  
Author(s):  
R. E. Drake ◽  
S. Dhother ◽  
V. M. Oppenlander ◽  
J. C. Gabel
Keyword(s):  
Pressure Gradient ◽  
Mathematical Models ◽  
Flow Rate ◽  
Lymphatic Vessels ◽  
Ringer Solution ◽  
Nonlinear Flow ◽  
Flow Rates ◽  
Passive Flow ◽  
Lymphatic Pumping ◽  
The Relationship

We determined the relationship between flow rate and inflow pressure for intestinal lymphatic vessels in six sheep. First we anesthetized the sheep and cannulated both ends of a 6- to 10-cm-long segment of intestinal lymphatic. We allowed the sheep to recover from the anesthesia for 2-24 h. To determine the flow rate-inflow pressure relationship, we recorded the inflow pressure and infused Ringer solution into the lymphatic at rates from 34 to 510 microliters/min. The flow rate-pressure relationship was not linear and it had two regions. For flow rates less than approximately 150 microliters/min, inflow pressure was greater than outflow pressure. Thus the lymphatic pumped fluid against a pressure gradient. For flow rates > 150 microliters/min, inflow pressure was greater than outflow pressure, and we attributed most of the flow to the favorable inflow-outflow pressure gradient (passive flow). When we used verapamil to inhibit lymphatic pumping, we found no flow for inflow pressure less than outflow pressure, and flow increased linearly for inflow pressure greater than outflow pressure. Our data for actively pumping lymphatic vessels are consistent with the flow vs. pressure relationships derived from mathematical models of the lymphatic pump. Furthermore, our data with verapamil confirm that active lymphatic pumping was responsible for the nonlinear flow vs. pressure relationship for the lymphatic vessels.

scholarly journals Salivary secretion and chewing: stimulatory effects from artificial and natural foods

2004 ◽  
Vol 12 (2) ◽  
pp. 159-163 ◽  
Author(s):  
Maria Beatriz Duarte Gavião ◽  
Andries Van der Bilt
Keyword(s):  
Flow Rate ◽  
Healthy Subjects ◽  
Salivary Secretion ◽  
Physical Characteristics ◽  
Mechanical Failure ◽  
Flow Rates ◽  
Saliva Secretion ◽  
Natural Foods ◽  
Yield Force ◽  
The Relationship

The aim of the present study was to determine the relationship between the flow rate of saliva and characteristics of the food. Therefore, we determined the rate of saliva secretion in 16 healthy subjects in rest and while chewing natural and artificial foods (toast with and without margarine, three sizes of breakfast cake, and Parafilm). We also determined the chewing rate, number of chewing cycles until swallowing, and time until swallowing. The physical characteristics of the foods were quantified from force-deformation experiments. The results showed that the average at which mechanical failure occurred (yield force) was 1.86 ± 0.24 N for the breakfast cake and 16.3 ± 1.3 N for the melba toast. The flow rates obtained without stimulation and with Parafilm were significantly lower (P < 0.001) than the flow rates obtained from chewing food. No differences in flow rate occurred between the natural foods. The flow rates of the saliva as obtained without stimulation, with Parafilm stimulation, and with chewing on the various foods were significantly correlated (P < 0.05). There were no significant differences in chewing rate among the foods. The number of chewing cycles and the time until swallowing significantly depended on the type or volume of the food.

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