Solve the differential equation using euler method

Assignment Help Engineering Mathematics
Reference no: EM131226703

1. The particle equation of motion considering only drag is

m(dup/dt) = ½CD(πdp2/4)ρf(uf - up)[uf - up]  

which can be reduced to

dup/dt = (18μ/ρpdp2)(CDRer/24)(uf - up)

Rer = (ρfdp|uf - up|/μ)

a) Create a spreadsheet to solve the differential equation using Euler's method. Assume CD = 24/Rer + 0.44.

b) Use the spreadsheet to examine the particle motion for the following conditions:

Fluid density = 1000 kg/m3, fluid viscosity = 0.001 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 0.01 m/s, initial particle velocity = 0 with a time step of 1e-5 s. Plot particle velocity for the time range from 0 to 4e-3 s.

c) Compare solution of part b with the exact solution for Stoke's flow.

up = uf(1 - e-t/τ_v)

τv = ρpdp2/18μ

d) Use the spreadsheet to examine the particle motion for the following conditions: Fluid density = 1000 kg/m3, fluid viscosity = 0.001 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 2 m/s, initial particle velocity = 0 with a time step of le-5 s. Plot particle velocity for the time range from 0 to 4e-3 s.

e) Use the spreadsheet to examine the particle motion for the following conditions: Fluid density = 1.2 kg/m3, fluid viscosity = 1.8e-5 Pa s, particle density = 2650 kg/m3, particle diameter = 100 microns, fluid velocity = 10 m/s, initial particle velocity = 0 with a time step of le-3 s. Plot particle velocity for the time range from 0 to 0.3 s.

Reference no: EM131226703

Questions Cloud

Identify the characters in one of the given story : Identify the characters in one of the following stories. - Describe each character in the story as protagonist or secondary (or as antagonist, if there is one), as static or dynamic, as flat, round, or stereotypical.
Briefly explain the concept of dispositions : Most trait theories focus on broad dispositions as the determinants of behavior. Briefly explain the concept of "dispositions." How do dispositions most significantly contribute to the construct of personality? Why is this contribution significant..
Evaluating critical the originality of your ideas : If you don't identify a problem, you don't have a paper that meets the learning outcome. How you address the problem or challenge's causes, implications and possible solutions, will form the basis of your critical thinking grade. The recommendatio..
Provide information regarding stress management : There are many sites available on the web that provide information regarding stress management. Explore the internet and share with us any sites that offered helpful hints regarding stress management that you were able to find.
Solve the differential equation using euler method : Particle-Laden Flows ME 4863-01 Homework. Create a spreadsheet to solve the differential equation using Euler's method. Assume CD = 24/Rer + 0.44. Use the spreadsheet to examine the particle motion for the following conditions
Promotions and transfers of employees : Fiji Airways has embarked on promotions and transfers of employees within the company to mitigate its potential labour shortage. Discuss the advantages offilling positions with current employees rather than recruiting from externalsources. Illustr..
What is the load factor of the hash table : Find the average number of key comparisons in a successful search in the hash table. You can assume that a search for each of the nine keys is equally likely - What is the load factor of the hash table?
Describe the ethical model being used by the company : Describe the motivational practices used by the organization to promote better strategy execution. Include some illustrative examples in your response.
Improve employees performance : Question: Besides giving employees feedback, what other steps a manager can take to improve employees' performance? Discuss your answer.

Reviews

Write a Review

Engineering Mathematics Questions & Answers

  What is the most common height

Use your frequency distribution to construct a histogram. Label your histogram using midpoints. Your histogram should be labeled so that an outsider can completely understand it.

  Calculate the eigenvalues and eigenvectors of matrix

Hand calculate the eigenvalues and eigenvectors of matrix A - Outline the steps on how you can use Simulink to demonstrate the linearity and the time invariance of the system.

  Determine what happens to the turtle population

Differential equation to determine what happens to the turtle population in the long run -remote island satisfies the differential equation

  Find the total balance

Now, use the model you developed to find the total balance after 5 years if a person starts with an initial deposit of $500 on the first day of a given month and deposits $100 on the first day of every subsequent month.

  Solve by simplex method

XYZ Co. can manufacture three types of stereo cases. Profit is $80 for type 1, $200 for type 2, and $200 for type 3. Each case must be processed through two machines according to the following requirements.

  Compute the fourier transform

Math 054 Partial Differential Equations - HW Assignment 9. Compute the Fourier transform Fk(α) for k = 1, 2, ... and sketch the graphs of fk(x) and Fk(α) for k = 1, 2, 3. Relate the changes in fk(x) as k varies to the corresponding changes in Fk(α)

  State the null and alternative hypotheses

In a recent survey, we found that 70% of students in a sample of 100 believe that their online education courses are as good as or superior to courses that use traditional, face-to-face instruction. State the null and alternative hypotheses.

  Maximum number of families

Suppose further that tribe B uses twice as much water as tribe A. What is the maximum number of families of each tribe that can coexist in the valley.

  Dimensions for the base and height

Your iron works has contracted to design and build a 500-cubic foot, square based, open topped, rectangular steel holding tank for a paper company.

  What is amount of the excess quantity supplied or demanded

If the present rental rate of one-bedroom apartments is $1,000 per month, through what mechanism will the rental rate adjust to the equilibrium rental rate of $800?

  How will the prices of call options on a and b struck

Asset B will be worth 110 with probability 0.5 and 90 otherwise. Asset C is worth 1 both today and tomorrow. How will the prices of call options on A and B struck at 100 compare?

  Dimensions for the cheapest box

U-Pack-Em sells cardboard boxes for the do-it-yourself mover. Their most popular size has a volume of 2 cubic feet. As shown in the figure below, the top and bottom are made using four flaps.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd