Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Noncompartmental Analysis: Mean Residence Time01:05

Noncompartmental Analysis: Mean Residence Time

According to statistical moment theory, mean residence time (MRT) is an important measure in pharmacokinetics. MRT can be defined as the expected mean of a probability density function distribution. It provides valuable insights into drug disposition in the body.
After the administration of a drug through intravenous bolus injection, the drug molecules are distributed throughout the body and remain there for varying periods. The MRT represents the average time these drug molecules stay in the...
Application of the Energy Equation01:04

Application of the Energy Equation

The application of the energy equation to centrifugal pumps is a fundamental principle in fluid dynamics and engineering. In this scenario, the energy equation is used to calculate the flow rate of a centrifugal pump responsible for transferring water between two reservoirs at different elevations. The pump applies an energy input of 7500 joules per second, and the vertical difference between the lower and upper reservoirs is 10 meters. Additionally, the head loss due to friction and other...
Typical Model Studies01:30

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
Design Example: Creating a Hydraulic Model of a Dam Spillway01:21

Design Example: Creating a Hydraulic Model of a Dam Spillway

Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
Fundamental Theorem of Calculus I: Problem Solving01:22

Fundamental Theorem of Calculus I: Problem Solving

In many engineering and environmental applications, accumulated quantities are determined from rates that vary over time. A common example arises in water management, where a supply system pumps water into a storage tank at a rate that changes with time. Accurately determining how much water has entered the tank over a given period is essential for maintaining proper pressure, scheduling operations, and ensuring system safety.The flow rate of water into the tank is described by a time-dependent...
Indefinite Integrals01:25

Indefinite Integrals

The water inflow rate into a storage tank is not constant but increases over time. Initially, the pump delivers water at a rate of 5 L/min. However, the inflow rate increases by 2 L/min for each additional minute due to rising pressure or system adjustments. This scenario can be described mathematically by a linear function:It is necessary to integrate the inflow rate function to measure the total volume of water added to the tank over time. The total water volume V(t) is obtained by performing...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Time-lapse in vivo dynamics of human corneal immune cells reveals a density-diffusivity relationship.

The ocular surface·2026
Same author

Likelihood-free parameter inference for spatiotemporal stochastic biological models using neural posterior estimation.

Journal of theoretical biology·2026
Same author

Continuum models describing probabilistic motion of tagged agents in exclusion processes.

Physical review. E·2026
Same author

Parameter-wise predictions and sensitivity analysis for random walk models in the life sciences.

Journal of theoretical biology·2025
Same author

Adsorptive Removal of PFAS from Aqueous Solutions Using GAC, PAC and Ball-Milled Colloidal Activated Carbon: Characterizing Efficiency, Kinetics, and Mechanisms.

ACS ES&T water·2025
Same author

Inference and prediction for stochastic models of biological populations undergoing migration and proliferation.

Journal of the Royal Society, Interface·2025

Related Experiment Video

Updated: Jul 29, 2026

Measuring Carbon-based Contaminant Mineralization Using Combined CO2 Flux and Radiocarbon Analyses
11:19

Measuring Carbon-based Contaminant Mineralization Using Combined CO2 Flux and Radiocarbon Analyses

Published on: October 21, 2016

Analytical model for computing residence times near a pumping well.

Matthew J Simpson1, T Prabhakar Clement, Francis E Yeomans

  • 1Centre for Water Research, The University of Western Australia, Nedlands, WA-6907, Australia.

Ground Water
|May 30, 2003
PubMed
Summary

A new analytical solution accurately calculates fluid residence time in unconfined aquifers near pumping wells. This method, based on radial flow, offers a reliable alternative to complex numerical simulations for groundwater studies.

More Related Videos

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Multi-Stream Perfusion Bioreactor Integrated with Outlet Fractionation for Dynamic Cell Culture
10:00

Multi-Stream Perfusion Bioreactor Integrated with Outlet Fractionation for Dynamic Cell Culture

Published on: July 20, 2022

Related Experiment Videos

Last Updated: Jul 29, 2026

Measuring Carbon-based Contaminant Mineralization Using Combined CO2 Flux and Radiocarbon Analyses
11:19

Measuring Carbon-based Contaminant Mineralization Using Combined CO2 Flux and Radiocarbon Analyses

Published on: October 21, 2016

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump
09:04

A Modeling and Simulation Method for Preliminary Design of an Electro-Variable Displacement Pump

Published on: June 1, 2022

Multi-Stream Perfusion Bioreactor Integrated with Outlet Fractionation for Dynamic Cell Culture
10:00

Multi-Stream Perfusion Bioreactor Integrated with Outlet Fractionation for Dynamic Cell Culture

Published on: July 20, 2022

Area of Science:

  • Hydrogeology
  • Groundwater Hydrology
  • Fluid Dynamics

Background:

  • Calculating fluid residence time is crucial for understanding contaminant transport and aquifer management.
  • Existing methods often rely on complex numerical simulations, which can be computationally intensive.
  • The Dupuit-Forchheimer flow model provides a simplified yet effective framework for analyzing groundwater flow.

Purpose of the Study:

  • To develop an analytical solution for determining fluid residence time in unconfined aquifers.
  • To provide a computationally efficient alternative to numerical methods for groundwater flow analysis.
  • To validate the proposed analytical solution against established numerical approximations.

Main Methods:

  • Derivation of an analytical solution based on a radial, steady-state, Dupuit-Forchheimer flow model.
  • Development of a series expansion for computing the imaginary error function.
  • Comparison of analytical solution results with numerical simulation data for validation.

Main Results:

  • An accurate analytical solution for fluid residence time in unconfined aquifers was successfully developed.
  • The proposed series expansion for the imaginary error function proved effective.
  • The analytical solution demonstrated favorable agreement with numerical results, confirming its validity.

Conclusions:

  • The developed analytical solution offers a reliable and efficient tool for estimating fluid residence time in groundwater systems.
  • This method can aid in better groundwater resource management and contaminant transport predictions.
  • The study highlights the utility of analytical approaches in hydrogeological modeling.