# 338-0513/04 – Applied Fluid Mechanics (AplMT)

 Gurantor department Department of Hydromechanics and Hydraulic Equipment Credits 4 Subject guarantor doc. Dr. Ing. Lumír Hružík Subject version guarantor doc. Dr. Ing. Lumír Hružík Study level undergraduate or graduate Requirement Compulsory Year 2 Semester summer Study language Czech Year of introduction 2020/2021 Year of cancellation Intended for the faculties FS Intended for study types Follow-up Master
Instruction secured by
BUR262 Ing. Adam Bureček, Ph.D.
HRU38 doc. Dr. Ing. Lumír Hružík
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
Part-time Credit and Examination 12+5

### 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 hydraulic systems with a long hydraulic pipeline. Students gain experience in the field of experimental determination of dynamic properties of fluid systems. Transient and frequency responses of long hydraulic pipelines will be evaluated. They will gain practical experience in numerical modeling of hydraulic system dynamics with a long hydraulic pipeline in Matlab Fluids.

### 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 solving unsteady fluid flow. They will learn experimental methods of dynamic properties evaluation in fluid systems. They will learn the effects of various parameters on the dynamics of fluid systems. Transient and frequency responses of hydraulic lines will be evaluated.

### Compulsory literature:

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

### Recommended literature:

MILLER, D. S. Internal Flow System, BHRA UK, 396 s., ISBN 0-947711-77-5 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.

### Way of continuous check of knowledge in the course of semester

Credit: during the semester will be enter 2 programs for which it is possible to get up to 35 points. Minimum for obtaining credit is 18 points, max. 35 points. Examination: oral exam - 2 questions, each for max 25 points, defense of programs for max. 15 points.

### E-learning

The following study materials are available on the department website: http://www.338.vsb.cz/studium/studijni-opory/

### 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 for solving fluid systems dynamics. One-dimensional pipeline model with lumped parameters - segmented pipeline, program Matlab - Fluids. 2. One-dimensional pipeline model with continuously distributed parameters - quasi-stationary velocity profile, unsteady velocity profile. 3. Method of characteristics and Laplace transform method for solving pipeline with continuously distributed parameters. Software Flowmaster, Circuit and F-achar. 4. Modulus of elasticity of hydraulic lines: calculation equations, the effect of fluid compressibility, pipe walls, amount of air bubbles. Bulk modulus for liquid and gas mixture. Experimental determination of liquid bulk modulus and hose modulus of elasticity. 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. Eigenfrequency of hydraulic system with a long pipeline. Influence of line elasticity module, line length, boundary conditions and liquid viscosity on dynamics. Pulsating flow. 7. Experimental evaluation of the frequency and transient response of long pipeline. Method of measurement and evaluation variables, the frequency spectrum of the measured signal. 8. Simulation of transient and frequency responses of the hydraulic system with a long pipeline in the software Fluids. Modeling of hydraulic systems with proportional directional control valves and hydraulic cylinders with a mass load. 9. Influence of accumulator in the pipeline during pulsating flow. Comparison of numerical models and software for modeling unsteady fluid flow in a long pipeline. Program of exercises and seminars 1. Hydraulic system for measurement of transient and frequency response of a long pipeline. Structure, control of the proportional directional control valve in the software Matlab. Used sensors, measuring device. Project assignment Measurement and numerical simulation of frequency responses of the hydraulic system with a long pipeline. 2. Transient responses measurements of hydraulic shock in a long pipeline. Frequency response measurement in the long pipeline with throttle valve at its end. 3. Evaluation of measured dynamic properties of a long pipeline. Numerical modeling of the hydraulic system with a long pipeline in software Matlab Fluids. Segmented pipeline model, proportional directional control valve and throttle valve. 4. Numerical modeling of the hydraulic system with a long pipeline in software Matlab Fluids. Numerical simulation of the dynamic properties of hydraulic system with a long pipeline in software Matlab Fluids - comparison of simulated time dependencies of pressure with an experiment. 5. Simulation of the influence of individual parameters (pipeline length, viscosity, amount of air bubbles) on dynamics of hydraulic system – time dependencies of pressure for the simulated hydraulic system. Project assignment Measurement and numerical simulation of long pipeline and hydraulic cylinder with mass load. 6. Hydraulic system with proportional directional control valve and hydraulic cylinder. Structure of hydraulic system, measuring device, sensors. Measurement of time dependencies of pressure and position of a hydraulic cylinder. 7. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve. 8. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve. Comparison of simulated time dependencies of position and pressure with experiment. Influence of piston diameter and mass load on time responses of pressure and position. 9. Numerical modeling of hydraulic system with a hydraulic cylinder and proportional directional control valve. Credit.

### Conditions for subject completion

Part-time form (validity from: 2021/2022 Winter semester)
Task nameType of taskMax. number of points
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 35  18
Examination Examination 65  30 3
Mandatory attendence participation: At least 50% účast.

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Conditions for subject completion and attendance at the exercises within ISP: Credit (exercise): Processing of 2 programs according to the trainer's instructions. Exam: Oral exam – 2 questions + defense of the programs.

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### Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0715A270035) Hydraulics and pneumatics K Czech Ostrava 2 Compulsory study plan
2024/2025 (N0715A270035) Hydraulics and pneumatics P Czech Ostrava 2 Compulsory study plan
2023/2024 (N0715A270035) Hydraulics and pneumatics K Czech Ostrava 2 Compulsory study plan
2023/2024 (N0715A270035) Hydraulics and pneumatics P Czech Ostrava 2 Compulsory study plan
2022/2023 (N0715A270035) Hydraulics and pneumatics P Czech Ostrava 2 Compulsory study plan
2022/2023 (N0715A270035) Hydraulics and pneumatics K Czech Ostrava 2 Compulsory study plan
2021/2022 (N0715A270035) Hydraulics and pneumatics P Czech Ostrava 2 Compulsory study plan
2021/2022 (N0715A270035) Hydraulics and pneumatics K Czech Ostrava 2 Compulsory study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner