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

  The standard linear regression assumptions issues

What is the residual standard error associated with the regression of alt_cur and CCbest?

  Solve differential equation of d2h dx20 using the galerkin

solve differential equation of d2h dx20 using the galerkin method and considering 0 le xle 3 given that h 0cm when x

  What real rate of return

Lew's market invested in a project that returned 16.67 percent during a period when inflation averaged 3.26 percent. What real rate of return did Lew's earn on its project?

  What fraction does the capacitance change

By what fraction does the amount of charge change ΔQ_new= Q_old (When the battery is connected, charges can keep moving and the charge may not stay to be the same.)

  Population experiences exponential growth

A bacterial population experiences exponential growth during a 4-day period. Assume that 200 colonies were present at the beginning of the 1st day, but by the beginning of the 3rd day, the population had grown to 335.

  Find the linearization of the system

MAST20029 Engineering Mathematics. Show that the system (*) has exactly two critical points, (4, 0) and (1, 3/2). Find the linearization of the system about the critical point (4, 0)

  Main reasons for regulations

In a study on speed control, it was found that the main reasons for regulations were to make traffic flow efficient and to minimize the risk of danger.

  Compute the derivative function

Problem 1: Compute the derivative function f'(x) algebraically.

  Find the volume of the solid formed when the shaded region

Find the volume of the solid formed when the shaded region is revolved about the indicated axis. Find the volume of the solid generated by revolving the region bounded by y = x (1 +x3)1/4 over 0 ≤ x ≤ 1 about the x-axis.

  Planning to save for retirement

You are planning to save for retirement over the next 24 years. To do this, you will invest $638 per month in a stock account and $228 per month in a bond account. The return of the stock account is expected to be 9 %, and the bond account will pa..

  Programming problem for optimization of an objective

This is liner programming problem for optimization of an objective function subject to some liner constraints. There are two profit maximization problems and two cost minimization problems.

  What if interest rates are non-zero

Show that if interest rates are zero and call option prices are a differentiable function of strike then the derivative of the prices with respect to strike must lie between -1 and 0. What if interest rates are non-zero?

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