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Related Concept Videos

Uniform Depth Channel Flow: Problem Solving01:18

Uniform Depth Channel Flow: Problem Solving

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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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Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2 in the liquid.
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Pipe Flowrate Measurement: Problem Solving01:28

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A spray tank system is engineered to uniformly distribute a pest-control liquid across plants by using a pressurized mechanism. The tank, pressurized to 150 kPa, holds the pesticide at a height of 0.80 meters. Liquid flows from the tank through a 1.9 meter pipe with a diameter of 0.015 meters, angled at 0.698 radians, ultimately reaching a 0.007 meter nozzle that sprays the pesticide. Accurate calculation of the system's flow rate is crucial to ensure uniform application, and this is achieved...
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Uniform Depth Channel Flow01:27

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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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Steady Flow of a Fluid Stream01:27

Steady Flow of a Fluid Stream

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Consider a control volume, such as a pipe with solid boundaries, through which fluid flows and changes direction due to the impulse exerted by the resulting force from the pipe walls. In steady flow, the mass of fluid entering the control volume at a given time, t, with velocity v1, is equal to the mass leaving after infinitesimal time dt, with velocity v2.
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Bernoulli's Equation for Flow Along a Streamline01:30

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Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
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Improved Parameter Resolution with Markov Chain Monte Carlo Simulation of Different Aquifer Tests.

Ground water·2020
Same author

Derivation of the Theis (1935) equation by substitution.

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Related Experiment Video

Updated: Nov 26, 2025

Fabrication, Operation and Flow Visualization in Surface-acoustic-wave-driven Acoustic-counterflow Microfluidics
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Flowing Well-Time-Domain Solution and Inverse Problem Revisited.

Tomas Perina1

  • 1APTIM Environmental & Decommissioning, 420 Exchange, Suite 150, Irvine, CA, 92602.

Ground Water
|December 14, 2020
PubMed
Summary

A new analytical solution for groundwater flow to wells improves aquifer property estimation. Analyzing both flow rate and drawdown data simultaneously provides more accurate results than flow data alone.

Area of Science:

  • Hydrogeology
  • Aquifer Mechanics
  • Mathematical Modeling

Background:

  • Theis (1935) equation is a cornerstone for analyzing transient groundwater flow.
  • Existing analytical solutions for flowing wells have limitations in computational efficiency and accuracy.
  • Accurate estimation of aquifer properties is crucial for sustainable groundwater management.

Purpose of the Study:

  • To derive a time-domain analytical solution for groundwater flow to a fully penetrating flowing well.
  • To confirm the approximate solution by Mishra and Guyonnet (1992).
  • To introduce a computationally effective alternative to existing solutions.

Main Methods:

  • Utilized a substitution technique, similar to that used for the Theis (1935) equation.
  • Developed an exponential integral-based flowing well function.

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  • Applied the derived solution to analyze field test data, including simultaneous fitting of flow and drawdown measurements.

    • Main Results:

    • Confirmed the approximate solution by Mishra and Guyonnet (1992).
    • The exponential integral-based flowing well function offers a computationally effective alternative.
    • Simultaneous fitting of flow and drawdown data yielded more accurate and better-resolved aquifer property estimates compared to flow data alone.

    Conclusions:

    • The derived analytical solution provides a robust method for analyzing groundwater flow to wells.
    • Simultaneous analysis of flow rate and drawdown significantly enhances the reliability of aquifer characterization.
    • This approach offers practical benefits for hydrogeological investigations and groundwater resource assessment.