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
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
Problem 1PE
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20dfe5a-a4c1-4793-9f05-a80ad59a67d4%2Fea174410-20e1-4574-b068-3048cf57eb7d%2F6pcda2_processed.png&w=3840&q=75)
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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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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