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Related Concept Videos

Boundary Layer Characteristics01:18

Boundary Layer Characteristics

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When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...
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Steady, Laminar Flow Between Parallel Plates01:17

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Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
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Uniform Depth Channel Flow: Problem Solving01:18

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To calculate the flow rate for a trapezoidal channel, first, identify the bottom width, side slope, and flow depth of the channel. The cross-sectional area (A) corresponding to the depth of flow (y), channel bottom width (B), and side slope (θ) is determined by:Next, calculate the wetted perimeter, which includes the bottom width and the sloped side lengths in contact with the water. Using the values of the cross-sectional area and the wetted perimeter, determine the hydraulic radius by...
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Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...
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Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant...
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Application of the Linear Momentum Equation01:15

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The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
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Exploring the Effects of Atmospheric Forcings on Evaporation: Experimental Integration of the Atmospheric Boundary Layer and Shallow Subsurface
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A boundary-layer solution for flow at the soil-root interface.

Gerardo Severino1, Daniel M Tartakovsky

  • 1Division of Water Resources Management and Bio-System Engineering, University of Naples, Federico II via Universitá 100, 80055 , Portici, Naples, Italy, severino@unina.it.

Journal of Mathematical Biology
|July 11, 2014
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Summary
This summary is machine-generated.

This study models plant water uptake, explaining transpiration by analyzing root water absorption from soil. The findings provide a theoretical basis for understanding how plants absorb water and influence the hydrological cycle.

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Area of Science:

  • Hydrology
  • Plant Physiology
  • Soil Science

Background:

  • Transpiration is a critical yet under-quantified process in the hydrological cycle.
  • Understanding plant water uptake at the root scale is essential for accurate hydrological modeling.

Purpose of the Study:

  • To develop a first-principles, root-scale model for plant water uptake and transpiration.
  • To theoretically justify existing root-scale cylindrical flow models.

Main Methods:

  • Utilized the Richards equation for water flow in unsaturated porous media.
  • Employed Gardner's exponential constitutive relation for hydraulic conductivities.
  • Applied matched asymptotic expansion techniques to derive approximate solutions.

Main Results:

  • Derived approximate solutions for transpiration rate and plant capture zone size.
  • Identified a perturbation parameter relating root size to soil capillary length.
  • Defined a boundary layer at the soil-root interface with horizontal flow.

Conclusions:

  • The model provides a theoretical foundation for the standard root-scale cylindrical flow model.
  • The derived solutions are valid for roots larger than the soil's macroscopic capillary length.
  • The analysis clarifies kinematic constraints on water flow in the soil-root continuum.