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1.13 Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area, dV dt a -KA

1.13 Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area, dV dt a -KA

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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### 1.13 Evaporation of a Spherical Droplet **Problem Statement:** Consider a spherical droplet of liquid evaporating at a rate proportional to its surface area. This relationship is described by the differential equation: \[ \frac{dV}{dt} = -kA \] where: - \( V \) = volume (mm\(^3\)) - \( t \) = time (min) - \( k \) = evaporation rate (mm/min) - \( A \) = surface area (mm\(^2\)) **Task:** Use Euler’s method to compute the volume of the droplet over a time interval from \( t = 0 \) to 10 minutes, utilizing a step size of 0.25 minutes. Assume: - \( k = 0.1 \) mm/min - The initial radius of the droplet is 3 mm. **Objective:** Assess the validity of your computational results by: 1. Determining the radius of your final computed volume. 2. Verifying consistency with the defined evaporation rate.
Transcribed Image Text:### 1.13 Evaporation of a Spherical Droplet **Problem Statement:** Consider a spherical droplet of liquid evaporating at a rate proportional to its surface area. This relationship is described by the differential equation: \[ \frac{dV}{dt} = -kA \] where: - \( V \) = volume (mm\(^3\)) - \( t \) = time (min) - \( k \) = evaporation rate (mm/min) - \( A \) = surface area (mm\(^2\)) **Task:** Use Euler’s method to compute the volume of the droplet over a time interval from \( t = 0 \) to 10 minutes, utilizing a step size of 0.25 minutes. Assume: - \( k = 0.1 \) mm/min - The initial radius of the droplet is 3 mm. **Objective:** Assess the validity of your computational results by: 1. Determining the radius of your final computed volume. 2. Verifying consistency with the defined evaporation rate.
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1. Classify the governing equation for the spherical droplet problem. (A ___ order, _____ differential equation, in (variables) ___ and ___). 2. For the spherical droplet problem, generate an overlay of the droplet radius vs. time (a) as inferred from your computed volume and (b) using the k value given in the problem. Make sure the traces have different colors and have markers at 0, 10, 20 and 30 minutes.
Transcribed Image Text:1. Classify the governing equation for the spherical droplet problem. (A ___ order, _____ differential equation, in (variables) ___ and ___). 2. For the spherical droplet problem, generate an overlay of the droplet radius vs. time (a) as inferred from your computed volume and (b) using the k value given in the problem. Make sure the traces have different colors and have markers at 0, 10, 20 and 30 minutes.
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