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Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

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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 cross-section...
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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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Uniform Distribution01:19

Uniform Distribution

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The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.
Two essential properties of this distribution are
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Uniform Circular Motion01:14

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Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. For example, any point on a propeller spinning at a constant rate is undergoing uniform circular motion. The second, minute, and hour hands of a watch also undergo uniform circular motion. It is hard to believe that points on these rotating objects are actually accelerating, even though the rotation rate is constant. To understand this, we must analyze the motion in terms of...
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Light Acquisition02:16

Light Acquisition

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In order to produce glucose, plants need to capture sufficient light energy. Many modern plants have evolved leaves specialized for light acquisition. Leaves can be only millimeters in width or tens of meters wide, depending on the environment. Due to competition for sunlight, evolution has driven the evolution of increasingly larger leaves and taller plants, to avoid shading by their neighbors with contaminant elaboration of root architecture and mechanisms to transport water and nutrients.
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Related Experiment Video

Updated: Apr 3, 2026

Measuring Spatially- and Directionally-varying Light Scattering from Biological Material
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Measuring Spatially- and Directionally-varying Light Scattering from Biological Material

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Virtual source simultaneous dual-surface method for uniform illumination.

Hang Zhang, Zeyu Su, Yufei Ma

    Journal of the Optical Society of America. A, Optics, Image Science, and Vision
    |September 15, 2015
    PubMed
    Summary
    This summary is machine-generated.

    A new virtual light source method enables dual-surface lens design for uniform illumination. This optical design achieves high uniformity, validated by simulation and experiment for LED light sources.

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    Area of Science:

    • Optics
    • Optical Engineering
    • Illumination Design

    Background:

    • Achieving uniform illumination is critical in various optical systems.
    • Designing freeform optical surfaces for uniform light distribution presents significant challenges.

    Purpose of the Study:

    • To introduce a novel simultaneous dual-surface design method for uniform illumination.
    • To develop a method applicable to extended light sources using virtual light sources and optimization algorithms.

    Main Methods:

    • The method combines the equal optical path length condition and a tailored design approach.
    • A negative feedback algorithm is employed for optimization with extended light sources.
    • A solid lens for circular uniform irradiance distribution was designed using this method.

    Main Results:

    • Optical simulations and experiments confirmed the design's effectiveness.
    • The designed lens achieved a uniformity higher than 0.9 with an LED light source.
    • Experimental irradiance maps closely matched simulation results and the desired uniform distribution.

    Conclusions:

    • The presented dual-surface design method effectively achieves uniform illumination.
    • The method shows potential for designing complex freeform optics with multiple surfaces.
    • Topological invariance of rays suggests broad applicability in advanced optical design.