scholarly journals Laminar pipe flow with time-dependent viscosity

2010 ◽  
Vol 13 (4) ◽  
pp. 729-740 ◽  
Author(s):  
Alan E. Vardy ◽  
James M. B. Brown
Keyword(s):  
General Solution ◽  
Hankel Transform ◽  
Temporal Variations ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Newtonian Viscosity ◽  
Transform Method ◽  
Dependent Viscosity ◽  
Laminar Pipe Flow ◽  
Selection Of

A general solution is obtained for laminar flow in axisymmetric pipes, allowing for prescribed timedependent viscosity and time-dependent pressure gradients. In both cases, the only restriction on the prescribed time dependence is that it must vary continuously; it is not necessary for rates of change to be continuous. The general solution is obtained using the Finite Hankel Transform method. This makes it possible to allow explicitly for time-dependent viscosity, but it does not permit the spatial dependence of viscosity. This contrasts with Laplace transforms, which allow spatial, but not general, temporal variations. The general solution is used to study a selection of particular flows chosen to illustrate distinct forms of physical behaviour and to demonstrate the ease with which solutions are obtained. The methodology is also applied to the simple case of constant (Newtonian) viscosity. In this case, it yields the same solutions as previously published methods, but it does so in a much simpler manner.

scholarly journals Unraveling the time-dependent relevance of input model uncertainties for a lumped hydrologic model of a pre-alpine karst system

2021 ◽  
Author(s):  
Daniel Bittner ◽  
Beatrice Richieri ◽  
Gabriele Chiogna
Keyword(s):  
Groundwater Recharge ◽  
Temporal Variations ◽  
Hydrologic Model ◽  
Time Dependent ◽  
Model Parameters ◽  
Lumped Parameter ◽  
Hydrodynamic Processes ◽  
Input Model ◽  
Karst Model ◽  
Input Uncertainties

AbstractUncertainties in hydrologic model outputs can arise for many reasons such as structural, parametric and input uncertainty. Identification of the sources of uncertainties and the quantification of their impacts on model results are important to appropriately reproduce hydrodynamic processes in karst aquifers and to support decision-making. The present study investigates the time-dependent relevance of model input uncertainties, defined as the conceptual uncertainties affecting the representation and parameterization of processes relevant for groundwater recharge, i.e. interception, evapotranspiration and snow dynamic, on the lumped karst model LuKARS. A total of nine different models are applied, three to compute interception (DVWK, Gash and Liu), three to compute evapotranspiration (Thornthwaite, Hamon and Oudin) and three to compute snow processes (Martinec, Girons Lopez and Magnusson). All the input model combinations are tested for the case study of the Kerschbaum spring in Austria. The model parameters are kept constant for all combinations. While parametric uncertainties computed for the same model in previous studies do not show pronounced temporal variations, the results of the present work show that input uncertainties are seasonally varying. Moreover, the input uncertainties of evapotranspiration and snowmelt are higher than the interception uncertainties. The results show that the importance of a specific process for groundwater recharge can be estimated from the respective input uncertainties. These findings have practical implications as they can guide researchers to obtain relevant field data to improve the representation of different processes in lumped parameter models and to support model calibration.

scholarly journals Critical Assessment Of The Issues In The Application Of Hilbert Transform To Compute The Logarithmic Decrement

2015 ◽  
Vol 60 (2) ◽  
pp. 1105-1108
Author(s):  
M. Majewski ◽  
L.B. Magalas
Keyword(s):  
Internal Friction ◽  
Hilbert Transform ◽  
Computing Methods ◽  
Critical Assessment ◽  
Logarithmic Decrement ◽  
High Dispersion ◽  
Mechanical Spectroscopy ◽  
Transform Method ◽  
Twin Method ◽  
Selection Of

Abstract The parametric OMI (Optimization in Multiple Intervals), the Yoshida-Magalas (YM) and a novel Hilbert-twin (H-twin) methods are advocated for computing the logarithmic decrement in the field of internal friction and mechanical spectroscopy of solids. It is shown that dispersion in experimental points results mainly from the selection of the computing methods, the number of oscillations, and noise. It is demonstrated that conventional Hilbert transform method suffers from high dispersion in internal friction values. It is unequivocally demonstrated that the Hilbert-twin method, which yields a ‘true envelope’ for exponentially damped harmonic oscillations is superior to conventional Hilbert transform method. The ‘true envelope’ of free decaying strain signals calculated from the Hilbert-twin method yields excellent estimation of the logarithmic decrement in metals, alloys, and solids.

scholarly journals Influence of Microcapsule Size and Shell Polarity on the Time-Dependent Viscosity of Geopolymer Paste

2018 ◽  
Vol 57 (29) ◽  
pp. 9457-9464 ◽  
Author(s):  
Vinh Duy Cao ◽  
Shima Pilehvar ◽  
Carlos Salas-Bringas ◽  
Anna M. Szczotok ◽  
Nu Bich Duyen Do ◽  
...  
Keyword(s):  
Time Dependent ◽  
Dependent Viscosity ◽  
Geopolymer Paste

scholarly journals Transient Analysis of Grout Penetration With Time-Dependent Viscosity Inside 3D Fractured Rock Mass by Unified Pipe-Network Method

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1122 ◽  
Author(s):  
Zizheng Sun ◽  
Xiao Yan ◽  
Rentai Liu ◽  
Zhenhao Xu ◽  
Shucai Li ◽  
...  
Keyword(s):  
Rock Mass ◽  
Large Scale ◽  
High Efficiency ◽  
Fractured Rock ◽  
Time Dependent ◽  
Pipe Network ◽  
Fractured Rock Mass ◽  
Network Method ◽  
The Stability ◽  
Dependent Viscosity

Grouting is widely used for mitigating the seepage of underground water and enhancing the stability of fractured rock mass. After injection, the viscosity of the grout gradually increases until solidification. Conventional multifield analysis models ignoring such effects greatly overestimate the penetration region of the grout and the stability of the grouted rock structures. Based on the 3D unified pipe-network method (UPM), we propose a novel numerical model considering the time-dependent viscosity of the grout, therein being a quasi-implicit approach of high efficiency. The proposed model is verified by comparing with analytical results and a time-wise method. Several large-scale 3D examples of fractured rock mass are considered in the numerical studies, demonstrating the effectiveness and robustness of the proposed method. The influence of the time-dependent viscosity, fracture properties, and grouting operation methods are discussed for the grout penetration process.

Time-Dependent Laminar Flow in Curved Channels

1970 ◽  
Vol 37 (3) ◽  
pp. 838-843 ◽  
Author(s):  
R. J. Nunge
Keyword(s):  
Laminar Flow ◽  
Pressure Gradient ◽  
Constant Pressure ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Straight Channel ◽  
Curvature Ratio ◽  
Curved Channels ◽  
Developing Flow ◽  
Time Required

The velocity distribution for time-dependent laminar flow in curved channels is derived. The analysis applies to flows with pressure gradients which are arbitrary functions of time. Numerical results are obtained for developing flow due to a constant pressure gradient. Developing flow in a straight channel is also discussed and it is found that the curvature ratio has only a small effect on the time required to reach the fully developed state.

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