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1-140-LeakyBucket-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: flow Torricelli's Law leaky bucket

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Abstract

Resource Image We seek to model the height of water in a cylindrical tank (bucket) in which water flows out the bottom of the tank through a small bore hole while we are pouring water into the tank at the top of the tank at a constant (or varying) rate.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

The tank is a right circular cylinder of radius 4 cm and height 13 cm and the initial height of the water in the tank is 10 cm.

Water is flowing out of the tank through a small bore hole of radius rC cm. Water is coming into the tank at a steady rate of F cm3/s.

First we need to determine the governing equations or model for the height of a column of liquid in a cone with a hole in the bottom from which the liquid leaks out. We refer to Torricelli' s Law development

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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