Darcy–Weisbach equation | EPFL Graph Search

In fluid dynamics, the Darcy–Weisbach equation is an empirical equation that relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach. Currently, there is no formula more accurate or universally applicable than the Darcy-Weisbach supplemented by the Moody diagram or Colebrook equation. The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy–Weisbach friction factor, friction factor, resistance coefficient, or flow coefficient. Pressure-loss equation In a cylindrical pipe of uniform diameter D, flowing full, the pressure loss due to viscous effects Δp is proportional to length L and can be characterized by the Darcy–Weisbach equation: :\frac{\Delta p}{L} =f_\mathrm{D} \cdot \frac{\rho }{2} \cdot

Experimental study on tsunamis generated by landslides

Christophe Ancey, Ivan Maeder, Zhenzhu Meng

Tsunami generated by landslides is one of the major threats to populations in coastal areas. A recent example is the 2017 Nuugaatsiaq tsunami. The village in Greenland was partially swept by a tsunami created by a landslide that fell into the Karrat Fjord. We carried out laboratory experiments to understand how the wave characteristics are related to the landslide features. Emphasis was put on slide-water interactions and efficiency of momentum transfers between the two media. We manufactured granular slides made of differently sized particles using plasticine clay, whose density is close to that of real-world materials. The granular mixture could be shaped, which made it possible to study how the leading edge’s shape affected momentum transfer. The mixture was initially placed in a reservoir upstream of a chute, which entered into a water basin. The angle of chute and water depth were kept constant in all our experiments, whereas the material properties and volume were varied systematically. Wave amplitudes and heights were determined from the free-surface variations, which were recorded using a high-speed camera. The velocity field within the water basin was measured using Particle image velocimetry (PIV). To compare the waves generated by slides exhibiting different properties, empirical equations for prediction of wave characteristics were used. We discuss the differences between experimental results and predictions based on empirical equations. Among other things, we found that the lower the material’s permeability, the larger the wave amplitude.

2020

Improve the Model Stability of Dam's Displacement Prediction Using a Numerical-Statistical Combined Model

Yating Hu, Zhenzhu Meng, Chenfei Shao

In most studies of dam's displacement prediction based on monitoring data, emphasis was given on improving the prediction accuracy, while the model stability was merely considered. This study proposed a numerical-statistical combined model which aims to improve the model stability. The displacement was modelled within three modules: recoverable displacement (i.e., displacement induced by the external load including the water pressure and temperature), non-recoverable displacement (i.e., displacement due to the inherent variations of the materials such as the creep and fatigue of the concrete), and measurement errors (i.e., instrument error and human error). To reduce the random errors and increase the model stability, we used the numerical simulation to constrain the coefficients of explanatory variables for the recoverable displacement. The non-recoverable displacement was estimated by empirical equations, and the measurement errors were given by Gaussian distributions. The randomness of coefficients in the model among all monitoring points are constrained further by random coefficient model. We adopted the root mean square error (RMSE) at varying time and the change ratio of the coefficients (CRC) to evaluate the model stability. Results indicated that the proposed model not only has better prediction accuracy but also has better model stability compared with the statistical model and coordinates-included statistical model proposed in previous studies.

2020

Experimental study of impulse waves generated by viscoplastic fluid

Zhenzhu Meng

Landslide-generated waves, also called impulse waves, occur as a result of the intrusion of landslides (such as rock falls, debris flows, and avalanches) into bodies of water (such as lakes, reservoirs, and seas). The objective of this thesis was to study the momentum transfer from the slide material to the body of water, in order to develop a better understanding of how the slide material's properties affect the wave generation and to discover alternative modeling approaches to existing empirical equations. Previous experimental studies have usually used blocks and granular materials to mimic natural landslides. However, many landslides in real worlds have been idealized as viscoplastic fluids in theoretical and numerical studies. No studies have used viscoplastic material in experimental studies of landslide-generated waves. The originality of this thesis lies in the use of a viscoplastic material called Carbopol Ultrez 10, an artificial aqueous micro-gel whose rheological behavior can be described using the Herschel-Bulkley model. Carbopol's cohesive and deformable properties are different to both block and granular slides. Further, Carbopol is transparent and can easily be seeded with micro-seeding particles, so its velocity field can be measured using particle image velocimetry (PIV). As a comparison of Carbopol, I also used a granular material named polymer-water balls whose density is close to that of Carbopol. The investigations of this thesis are as follows: I conducted two series of experiments. First, I observed waves generated by Carbopol, water balls, and mixtures of them using high-speed cameras, to investigate the role of slide material's properties in wave prediction. Second, I conducted PIV experiments with Carbopol to investigate the internal dynamic of slide-water interaction. (1) I developed a theoretical model that combined the momentum conservation of twophase flow in a control volume (Zitti et al., 2016) and viscoplastic theory (Ancey et al., 2012). With the experimental results obtained from PIV measurements, I analyzed the drag force and hydrostatic force that act on stopping the sliding mass, and validated the theoretical model. (2) I developed empirical equations using the dimensionless groups that emerged from the governing equations to quantify the wave characteristics (for example, maximum wave amplitude and height) as functions of the slide parameters. Using empirical equations, I compared the characteristics of waves generated by cohesive Carbopol and cohesionless water balls, and discussed the effect of slide cohesion on wave generation. (3) Taking advantage of a purely data-driven approach that strictly relies on the dataset and does not need any physical constraints in advance, I applied an artificial neural network method to predict wave characteristics under complex configurations, such as dealing with an experimental dataset with several different slide materials (Carbopol, water balls, and mixtures of them). (4) Using a panel data model called random coefficient model, I predicted the time series data of wave characteristics from the time series data of slide parameters on impact. Given the slide parameters on impact by the viscoplastic theory, the temporal wave characteristics were quantified from the parameters of the slide material at the initial stage (at rest on the slope and then starting to move).

EPFL2020

Experimental study of impulse waves generated by viscoplastic fluid

Zhenzhu Meng

EPFL2020