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1-059-ContainerShapeFallingWater-ModelingScenario

Author(s): Brian Winkel

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

Keywords: containers Torricelli's Law shape discharge coefficient

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Abstract

Resource Image We examine many different physical situations to determine the time it takes a fixed volume of water to flow out of different shape containers through the same size exit hole at the bottom of the container.

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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

We consider the question. For a fixed volume of water, say V = 1000 cm3 and fixed exit hole at the bottom of a container does the shape of the column matter in determining the time of complete draining of the water from the container?

We examine many different containers, each holding 1000 cm3  of water and each with an exit hole for the water to fall out of the container of radius r = 0.25 cm. If alpha is the effective area (percentage due to friction at the opening called the discharge or contraction coefficient) for water flowing through the exit hole then alpha = 0.70.

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Authors

Author(s): Brian Winkel

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

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