# 338-0513/01 – Applied Fluid Mechanics (AplMT)

 Gurantor department Department of Hydromechanics and Hydraulic Equipment Credits 4 Subject guarantor doc. Dr. Ing. Lumír Hružík Subject version guarantor prof. RNDr. Milada Kozubková, CSc. Study level undergraduate or graduate Requirement Choice-compulsory Year 1 Semester winter Study language Czech Year of introduction 1999/2000 Year of cancellation 2012/2013 Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
HRU38 doc. Dr. Ing. Lumír Hružík
RAU01 Ing. Jana Jablonská, Ph.D.
KOZ30 prof. RNDr. Milada Kozubková, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Combined Credit and Examination 10+4

### Subject aims expressed by acquired skills and competences

The aim of the course is to acquaint students with the mathematical models, numerical methods and programs for the solution of unsteady flow in fluid systems. They will gain knowledge about the possibilities, advantages and limitations of using various mathematical models, numerical methods and programs, especially for circuits with long hydraulic circuits. Students gain experience in the field of experimental determination of dynamic properties of fluid systems. Will be evaluated transient and frequency response of long hydraulic lines. They will gain practical experience in numerical modeling of the dynamics of the hydraulic circuit with a long pipe in Matlab SimHydraulics.

### Teaching methods

Lectures
Tutorials
Experimental work in labs
Project work

### Summary

In the course of Applied Fluid Mechanics, students learn about mathematical models, numerical methods and programs for the solution of unsteady fluid flow. They will learn methods of experimental evaluation of dynamic properties of fluid systems. They will know the effects of various parameters on the dynamics of fluid systems. Will be evaluated transient and frequency response of the hydraulic lines.

### Compulsory literature:

[1] MATLAB User's Guide. The Mathworks, Inc., USA, www.mathworks.com [1] GOLDSTEIN, R. J. Fluid Mechanics Measurements. Washington : Hemisphere Publishing Corporation. 1983. 647 p. ISBN 0-89116-244-5.

### Recommended literature:

[1] MILLER, D. S. Internal Flow System, BHRA UK, 396 s., ISBN 0-947711-77-5 [2] EXNER, H. et al. Basic Principles and Components of Fluid Technology. Lohr am Main, Germany: Rexroth AG., 1991. 344 p. ISBN 3-8023-0266-4.

### E-learning

There are not other requirements.

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

The program of lectures 1 Overview of mathematical models, numerical methods and programs to solve the dynamics of fluid systems. Dimensional pipe model with lumped parameters - segmented pipeline, the program Matlab - SimHydraulics. 2 One-dimensional line model with continuously distributed parameters - quasistationary velocity profile, unsteady flow profile. 3 Method of characteristics and the method of Laplace transformation for solving of pipe with continuously distributed parameters. Flowmaster program, program circuit, program F-achar. 4 Modulus of elasticity for hydraulic lines: calculation relations, the effect of compressibility of fluid, pipe wall, the amount of air bubbles. Modulus of elasticity for mixture of liquid and gas. Experimental determination of the modulus of elasticity for fluid and hose. 5 Methods for determination of air content in the liquid. The speed of sound in the hydraulic line. Evaluation of wave runtime. Industrial tomograph. 6 Natural frequency of hydraulic system with long pipeline. The influence line modulus of elasticity, line length, boundary conditions and viscosity of the fluid on dynamics. Pulsating flow. 7 Experimental evaluation of the frequency and transient response of long pipe. Method of measurement and evaluation values, the frequency spectrum of the measured signal. 8 Simulation of transient and frequency characteristics of the circuit with a long pipe in the program SimHydraulics. Modeling of circuits with proportional distributors and linear hydraulic motors with mass load. 9 Influence of the accumulator in the pipe at pulsating flow. Comparison of numerical models and programs for modeling unsteady fluid flow in a long pipe. Program of exercises and seminars + individual students' work 1 Circuit for measuring the transient and frequency characteristics of the long pipeline. Structure, control of the proportional distributor in the medium Matlab. Used sensors, measuring instrument. Task of project Measurement and numerical simulation of frequency characteristics of the circuit with a long pipeline. 2 Measurement of transient response - hydraulic shock in the circuit with a long pipeline. Measuring the frequency response in a long pipeline with throttle valve at its end. 3 Evaluation of measured dynamic properties of long line. Modelling circuit with a long pipeline in medium Matlab SimHydraulics. Model of segmented pipeline, elements proportional distributor and throttle valve. 4 Modeling a circuit with a long pipeline in medium Matlab SimHydraulics. Numerical simulation of the dynamic properties of the circuit with a long pipeline in Matlab SimHydraulics - comparison of calculated pressure time profiles with experiment. 5 Simulation of influence of individual parameters (pipeline length, viscosity, amount of air bubbles) on the dynamics of the circuit – time profiles of pressure for simulated circuit. Task of project Measurement and numerical simulation of the circuit with a long pipeline and hydraulic motor with mass load. 6 Circuit with proportional distributor and linear hydraulic motor. Structure of the circuit, the measuring instrument, sensors. Measurement of pressure time profiles on the cylinder and position time profile. 7 Numerical modeling of circuit with linear hydraulic motor and proportional distributor. 8 Numerical modeling of circuit with linear hydraulic motor and proportional distributor. Comparison of simulated position and pressure profiles in time with the experiment. Effect of piston diameter size and weight on the response of pressure and position. 9 Numerical modeling of circuit with linear hydraulic motor and proportional distributor. Credit. List of questions to test 1st The mathematical model of the segmented pipeline with lumped parameters, structure and definition of R, H, D resistances. 2nd One-dimensional model of pipeline with continuously distributed parameters - quasistationary velocity profile. The equation of motion and the continuity equation. 3rd One-dimensional model of pipeline with continuously distributed parameters – nonstationary speed profile. 4th Method of characteristics for solving of pipeline with continuously distributed parameters. 5th Laplace transform method for solving of pipeline with continuously distributed parameters. 6th Modulus of elasticity of hydraulic line: calculation relations, the influence of fluid compressibility, elastic pipeline and the amount of air bubbles. Modulus of elasticity for mixture of liquid and gas. 7th Experimental determination of the modulus of elasticity for fluid and hose including the influence of air content. 8th Determination methods of the air amount in the liquid. 9th Experimental evaluation of hydraulic shock in the pipeline. Structure of circuit, measurement methodology, control of valves, sensors, measuring instrument. 10th Experimental determination of the speed of sound in the line. 11th The natural frequency of line - influence of pipeline length and boundary conditions. 12th Dynamic properties of hydraulic line - the influence of fluid modulus of elasticity, elasticity of line and the amount of air in the liquid. Effect of viscosity on the dynamics of the circuit with a long pipeline. 13th Circuits with hydraulic motor, mass load, long hydraulic line and proportional distributor. Influence of line parameters, dimensions of hydraulic motor and size of mass load. 14th Pulsating flow in line, pulsating number, the phase velocity of wave transmission. Amplitude and phase frequency characteristics of pipeline. 15th Experimental determination of the frequency characteristics of the pipeline pressure. Structure of circuit, measurement methodology, control of proportional distributor, sensors, measuring instrument. 16th The influence of the accumulator in the pipeline at the pulsating flow. 17th Unsteady flow simulation with software Flowmaster. Options, mathematical model, numerical method, entering the computational network. 18th Unsteady flow simulation with software Matlab SimHydraulics. Options, mathematical model, numerical method, entering the computational network – definition of throttle valve and proportional distributor. 19th Simulation of pipeline frequency characteristics with software Hydroobvod and software F-achar. Options, mathematical model, numerical method, entering the computational network. 20th Comparison of softwares Flowmaster, Matlab - SimHydraulics, Hydroobvod, F-achar for modeling of unsteady oil flow in a long pipeline.

### Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2010/2011 Summer semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 35 (35) 0
Project Project 35  0
Examination Examination 65 (65) 0
Oral Oral examination 65  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2012/2013 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2012/2013 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2011/2012 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2010/2011 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 2 Compulsory study plan
2008/2009 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2007/2008 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2006/2007 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2005/2006 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics P Czech Ostrava 1 Choice-compulsory study plan
2004/2005 (N2301) Mechanical Engineering (3909T001) Design and Process Engineering (16) Hydraulics and Pneumatics K Czech Ostrava 1 Choice-compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner