scholarly journals Discharge coefficient of broad-crested weirs as a function of the relative weir height for different weir lengths

2020 ◽  
Vol 2020 (2) ◽  
pp. 63-68 ◽  
Author(s):  
Volodymyr Zhuk ◽  
◽  
Ivan Matlai ◽  
Ihor Popadiuk ◽  
Lesiia Vovk ◽  
...  
Keyword(s):  
Water Management ◽  
Power Law ◽  
Flow Rate ◽  
Discharge Coefficient ◽  
Relative Length ◽  
Engineering Practice ◽  
Relative Height ◽  
Empirical Power ◽  
Friction Resistance ◽  
Weir Height

Broad-crested weirs (BCW) are often used in hydraulic engineering and water management. The most complex factor that affects the discharge capacity of BCW is the discharge coefficient. In Ukrainian engineering practice, the flow rate of BCW is defined as a function of the relative height of the spillway wall, while in the most common European methods – as a function of the relative length of the weir. The experimental dependences of the discharge coefficient of rectangular sharp-edged BCW with vertical inlet and outlet walls with the ratio of the weir length and height d/Р = 2; 4 are obtained. A comparison of the obtained results with the values of the discharge coefficient of the same BCW using the methods of Kumin and Hager indicates that this coefficient depends on both the height of the wall and the length of the weir. The corresponding empirical power law dependences are obtained. At the same values of the relative height of the wall, the discharge coefficient for the weir with the ratio d/Р = 4 is significantly lower comparing the weir with d/Р = 2, that can be explained by the more significant effect of friction resistance for the weir with longer threshold.

Flow Features Analysis of Throttle Notches of Proportional Direct Valve

2011 ◽  
Vol 189-193 ◽  
pp. 2285-2288
Author(s):  
Wen Hua Jia ◽  
Chen Bo Yin ◽  
Guo Jin Jiang
Keyword(s):  
Fluid Flow ◽  
Dynamic Behavior ◽  
Flow Rate ◽  
Discharge Coefficient ◽  
3D Models ◽  
Operating Conditions ◽  
Flow Models ◽  
Flow Features ◽  
Rate Discharge ◽  
Spool Valve

Flow features, specially, flow rate, discharge coefficient and efflux angle under different operating conditions are numerically simulated, and the effects of shapes and the number of notches on them are analyzed. To simulate flow features, 3D models are developed as commercially available fluid flow models. Most construction machineries in different conditions require different actions. Thus, in order to be capable of different actions and exhibit good dynamic behavior, flow features should be achieved in designing an optimized proportional directional spool valve.

scholarly journals Power Laws in Economics: An Introduction

2016 ◽  
Vol 30 (1) ◽  
pp. 185-206 ◽  
Author(s):  
Xavier Gabaix
Keyword(s):  
Stock Market ◽  
Power Law ◽  
Power Laws ◽  
Economic Fluctuations ◽  
Formal Definition ◽  
Empirical Power

Many of the insights of economics seem to be qualitative, with many fewer reliable quantitative laws. However a series of power laws in economics do count as true and nontrivial quantitative laws—and they are not only established empirically, but also understood theoretically. I will start by providing several illustrations of empirical power laws having to do with patterns involving cities, firms, and the stock market. I summarize some of the theoretical explanations that have been proposed. I suggest that power laws help us explain many economic phenomena, including aggregate economic fluctuations. I hope to clarify why power laws are so special, and to demonstrate their utility. In conclusion, I list some power-law-related economic enigmas that demand further exploration. A formal definition may be useful.

Scaling Formulae for the Wellbore Hydraulics Similitude with Drill Pipe Rotation and Eccentricity

2021 ◽  
Author(s):  
Thad Nosar ◽  
Pooya Khodaparast ◽  
Wei Zhang ◽  
Amin Mehrabian
Keyword(s):  
Power Law ◽  
Flow Rate ◽  
Annular Flow ◽  
Rotation Speed ◽  
Drilling Fluid ◽  
Drill Pipe ◽  
Flow Loop ◽  
Annular Flows ◽  
Fluid Rheology ◽  
Pipe Rotation

Abstract Equivalent circulation density of the fluid circulation system in drilling rigs is determined by the frictional pressure losses in the wellbore annulus. Flow loop experiments are commonly used to simulate the annular wellbore hydraulics in the laboratory. However, proper scaling of the experiment design parameters including the drill pipe rotation and eccentricity has been a weak link in the literature. Our study uses the similarity laws and dimensional analysis to obtain a complete set of scaling formulae that would relate the pressure loss gradients of annular flows at the laboratory and wellbore scales while considering the effects of inner pipe rotation and eccentricity. Dimensional analysis is conducted for commonly encountered types of drilling fluid rheology, namely, Newtonian, power-law, and yield power-law. Appropriate dimensionless groups of the involved variables are developed to characterize fluid flow in an eccentric annulus with a rotating inner pipe. Characteristic shear strain rate at the pipe walls is obtained from the characteristic velocity and length scale of the considered annular flow. The relation between lab-scale and wellbore scale variables are obtained by imposing the geometric, kinematic, and dynamic similarities between the laboratory flow loop and wellbore annular flows. The outcomes of the considered scaling scheme is expressed in terms of closed-form formulae that would determine the flow rate and inner pipe rotation speed of the laboratory experiments in terms of the wellbore flow rate and drill pipe rotation speed, as well as other parameters of the problem, in such a way that the resulting Fanning friction factors of the laboratory and wellbore-scale annular flows become identical. Findings suggest that the appropriate value for lab flow rate and pipe rotation speed are linearly related to those of the field condition for all fluid types. The length ratio, density ratio, consistency index ratio, and power index determine the proportionality constant. Attaining complete similarity between the similitude and wellbore-scale annular flow may require the fluid rheology of the lab experiments to be different from the drilling fluid. The expressions of lab flow rate and rotational speed for the yield power-law fluid are identical to those of the power-law fluid case, provided that the yield stress of the lab fluid is constrained to a proper value.

scholarly journals Determination of mass flow characteristics of supersonic axisymmetric nozzle diaphragms in modeling variable duties of low-consumption turbines

2020 ◽  
pp. 39-43
Author(s):  
Р.Р. Симашов ◽  
С.В. Чехранов
Keyword(s):  
Mass Flow ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Relative Length ◽  
Axisymmetric Nozzle ◽  
Relative Flow Rate ◽  
Wide Range ◽  
Mass Flow Rates ◽  
Subsonic Part ◽  
Low Consumption

В работе приводятся обобщающие зависимости коэффициентов расхода сопловых аппаратов со сверхзвуковыми осесимметричными соплами в широком диапазоне изменения определяющих геометрических и режимных параметров. Предложена двухпараметрическая функция, учитывающая влияние расположения сопел в сопловом аппарате и степени конфузорности дозвуковой части осесимметричного сопла на коэффициент расхода. Показано слабое влияние на коэффициент расхода относительного радиуса закругления стенки в узкой части сопла и относительной длины дозвуковой части сопла в области их оптимальных значений определенных по минимуму потерь кинетической энергии. Переменные режимы работы сопла учитываются зависимостью относительного коэффициента расхода в функции от числа Рейнольдса в критическом сечении сопла. Полученные в работе эмпирические зависимости позволяют использовать их при моделировании переменных режимов и многорежимной оптимизации малорасходных турбин. The research presents generalizing dependences of mass flow rates in supersonic axisymmetric nozzle diaphragms n a wide range of variation of the governing geometric and operating parameters. A two-parameter function is proposed that takes into account the influence of the location of the nozzles in the nozzle apparatus and the degree of compression of the flow of the subsonic part of the nozzle on the mass flow rate. It is shown that the relative radius of rounding of the nozzle wall in the vicinity of the throat section and the relative length of the subsonic part of the nozzle in the region of their optimal values determined by the minimum of kinetic energy losses have a weak effect on the flow rate. Variable duties of nozzle operation are taken into account by the dependence of the relative flow rate as a function of the Reynolds number in the throat of the nozzle. The empirical dependencies obtained in this work make it possible to use them in modeling variable modes and multi-mode optimization of low-consumption turbines.

scholarly journals Analysis of metrological characteristics of elbow flowmeter under rotating state

2021 ◽  
Vol 12 ◽  
pp. 24
Author(s):  
Yu Wang ◽  
Ruiwei Li ◽  
Lin Luo ◽  
Lin Ruan
Keyword(s):  
Flow Rate ◽  
Measurement Accuracy ◽  
Discharge Coefficient ◽  
Water Flow Rate ◽  
Internal Flow ◽  
Metrological Characteristics ◽  
Centrifugal Acceleration ◽  
Flow Rate Measurement ◽  
Fitting Method ◽  
Cfd Method

The application of elbow flowmeter in rotary equipments is beneficial to reduce the pipeline complexity. However, the intervention of centrifugal acceleration will lead to the change of metrological characteristics of elbow flowmeter. Based on the analysis of the differential pressure formation mechanism of the environmental acceleration on the elbow flowmeter, the calculation formula of the flow rate measurement with the elbow flowmeter in the rotating state is derived, and the fitting method of the discharge coefficient is put forward. The CFD method was used to analyze the internal flow field of the elbow flowmeter under rotating state, summarize the pressure distribution characteristics of the pipe wall, and verify the feasibility of the discharge coefficient fitting strategy by simulation. The results show that for the elbow flowmeters with diameters of 10 mm and 15 mm and the radius to diameter ratio of 1.5, as long as the water flow rate is between 1.5 m/s and 5 m/s, the measurement accuracy can be guaranteed to be above 4%.

Influence of convective conditions on the peristaltic mechanism of power-law fluid through a slippery elastic porous tube with different waveforms

2019 ◽  
Vol 16 (2) ◽  
pp. 340-358 ◽  
Author(s):  
Manjunatha Gudekote ◽  
Rajashekhar Choudhari ◽  
Hanumesh Vaidya ◽  
Prasad K.V. ◽  
Viharika J.U.
Keyword(s):  
Power Law ◽  
Flow Rate ◽  
Velocity Slip ◽  
Elastic Tube ◽  
Slip Parameter ◽  
Convective Conditions ◽  
Power Law Fluid ◽  
Porous Tube ◽  
Content Type ◽  
Similarity Transformations

Purpose The purpose of this paper is to emphasize the peristaltic mechanism of power-law fluid in an elastic porous tube under the influence of slip and convective conditions. The effects of different waveforms on the peristaltic mechanism are taken into account. Design/methodology/approach The governing equations are rendered dimensionless using the suitable similarity transformations. The analytical solutions are obtained by using the long wavelength and small Reynold’s number approximations. The expressions for velocity, flow rate, temperature and streamlines are obtained and analyzed graphically. Furthermore, an application to flow through an artery is determined by using a tensile expression given by Rubinow and Keller. Findings The principal findings from the present model are as follows. The axial velocity increases with an expansion in the estimation of velocity slip parameter and fluid behavior index, and it diminishes for a larger value of the porous parameter. The magnitude of temperature diminishes with an expansion in the Biot number. The flux is maximum for trapezoidal wave and minimum for the triangular wave when compared with other considered waveforms. The flow rate in an elastic tube increases with an expansion in the porous parameter, and it diminishes with an increment in the slip parameter. The volume of tapered bolus enhances with increasing values of the porous parameter. Originality/value The current study finds the application in designing the heart-lung machine and dialysis machine. The investigation further gives a superior comprehension of the peristaltic system associated with the gastrointestinal tract and the stream of blood in small or microvessels.

Aerodynamic Loss Characteristics of a Turbine Blade With Trailing Edge Coolant Ejection: Part 1—Effect of Cut-Back Length, Spanwise Rib Spacing, Free-Stream Reynolds Number, and Chordwise Rib Length on Discharge Coefficients

2000 ◽  
Vol 123 (2) ◽  
pp. 238-248 ◽  
Author(s):  
Oguz Uzol ◽  
Cengiz Camci ◽  
Boris Glezer
Keyword(s):  
Reynolds Number ◽  
Mass Flow Rate ◽  
Flow Rate ◽  
Discharge Coefficient ◽  
Free Stream ◽  
Cooling System ◽  
Trailing Edge ◽  
Discharge Coefficients ◽  
Reynolds Number Dependency ◽  
Spanwise Rib

The internal fluid mechanics losses generated between the blade plenum chamber and a reference point located just downstream of the trailing edge are investigated for a turbine blade trailing edge cooling system. The discharge coefficient Cd is presented as a function of the free-stream Reynolds number, cut-back length, spanwise rib spacing, and chordwise rib length. The results are presented in a wide range of coolant to free-stream mass flow rate ratios. The losses from the cooling system show strong free-stream Reynolds number dependency, especially at low ejection rates, when they are correlated against the coolant to free-stream pressure ratio. However, when Cd is correlated against a coolant to free-stream mass flow rate ratio, the Reynolds number dependency is eliminated. The current data clearly show that internal viscous losses due to varying rib lengths do not differ significantly. The interaction of the external wall jet in the cutback region with the free-stream fluid is also a strong contributor to the losses. Since the discharge coefficients do not have Reynolds number dependency at high ejection rates, Cd experiments can be performed at a low free-stream Reynolds number. Running a discharge coefficient experiment at low Reynolds number (or even in still air) will sufficiently define the high blowing rate portion of the curve. This approach is extremely time efficient and economical in finding the worst possible Cd value for a given trailing edge coolant system.

Numerical Argumentation of any Factors for Effecting Flow Property of a Power-Law Gel Propellant in a Converging Injector

2012 ◽  
Vol 170-173 ◽  
pp. 2601-2608
Author(s):  
Xue Li Xia ◽  
Hong Fu Qiang ◽  
Wang Guang
Keyword(s):  
Pressure Drop ◽  
Power Law ◽  
Flow Rate ◽  
Apparent Viscosity ◽  
Volumetric Flow Rate ◽  
Flow Property ◽  
Newtonian Viscosity ◽  
Convergence Angle ◽  
The Mean ◽  
Injector Design

To evaluate the effect of a converging injector geometry, volumetric flow rate and gallant content on the pressure drop, the velocity and viscosity fields, the governing equations of the steady, incompressible, isothermal, laminar flow of a Power-Law, shear-thinning gel propellant in a converging injector were formulated, discretized and solved. A SIMPLEC numerical algorithm was applied for the solution of the flow field. The results indicate that the mean apparent viscosity decreases with increasing the volumetric flow rate and increasing the gallant content results in an increase in the viscosity. The results indicate also that the convergence angle can produce additional decrease in the mean apparent viscosity of the fluid. The mean apparent viscosity decreases significantly with increasing the convergence angle of the injector, and its value is limited by the Newtonian viscosity η∞. The effect of the convergence angle on the mean apparent viscosity is more significant than the effect of the volumetric flow rate and the gallant content on the mean apparent viscosity. Additional decreasing the viscosity results in increasing the pressure drop with increasing convergence angle. It is important to injector design that the viscosity decreasing and the pressure drop increasing are took into account together.

Hydraulic Circulation Test and CFD Analysis of Prestressed Cementing Unit Earth Anchor

2014 ◽  
Vol 1006-1007 ◽  
pp. 156-159
Author(s):  
Ding Li
Keyword(s):  
Flow Rate ◽  
Discharge Coefficient ◽  
Drilling Fluid ◽  
Critical Value ◽  
Thermal Recovery ◽  
Differential Pressure ◽  
Cfd Analysis ◽  
Fluid Flow Rate ◽  
Casing Pipe ◽  
Opening And Closing

In the process of thickened oil thermal recovery, the pre-stress cementing needs to be anchored at the bottom of the casing pipe. And the reliable opening and closing of anchor flukes directly influence the anchoring. In allusion to the problems of how to get the critical value of drilling fluid flow rate of when the anchor flukes begin to open, completely open, begin to close and completely close, whether different nozzles can open or close reliably, getting the corresponding differential pressure and discharge coefficient of the different nozzles, this paper conducts a study from both theory and experiment to obtain the relevant parameters. By simulating the anchor in actual work and dealing with the data, we conclude that: (1) The fluke can open smoothly when the flow rate reaches a certain flow and it can also close smoothly when the flow rate declines. (2) The critical flow rate of the flukes, when two kinds of anchors are with different nozzles, has been acquired. (3) Corresponding differential pressure and discharge coefficient of the different nozzles in different flow rate have been ascertained.

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