# Components for Pneumatic Control Instruments

## 1st Edition

### The Static and Dynamic Characteristics of Pneumatic Resistances, Capacitances and Transmission Lines

**Authors:**L. A. Zalmanzon

**eBook ISBN:**9781483223995

**Imprint:**Pergamon

**Published Date:**1st January 1965

**Page Count:**338

## Description

Components for Pneumatic Control Instruments: The Static and Dynamic Characteristics of Pneumatic Resistances, Capacitances and Transmission Lines provides a list of problems necessitating a detailed study of the characteristics of restrictions and chambers. This book discusses the problems that arise during the development, improvement, and use of pneumatic instruments.

Organized into four chapters, this book begins with an overview of the theory and design of restrictions. This text then considers the main characteristics of restriction processes, giving the features of the restrictions used in different pneumatic control and regulating instruments. Other chapters deal with the static characteristics of pneumatic chambers with restrictions of various types. This book discusses as well problems of the dynamics of pneumatic chambers. The final chapter deals with the characteristics of log pneumatic lines and of systems with distribution parameters.

This book is a valuable resource for aircraft engineers and readers who wish to understand the problems of the theory and design of elements of pneumatic control and regulating instruments.

## Table of Contents

Introduction

Chapter I Theory of Restrictions

§1. Basic Data on Restrictions as Elements of Pneumatic Automatic Control Equipment and Pneumatic Measuring Instruments. Classification of Restrictions. Problems in the Theory and Design of Various Types of Restrictions

§2. General Methods of Calculating Restriction Processes. Characteristics of Turbulent-Flow Restrictions

(a) Notes on Restriction Processes

(b) Equations for Calculating the Characteristics of Turbulent-Flow Restrictions

(c) Explanation of Equations (I.10) and (I.12). Determination of the Flow Coefficient of the Restriction

(d) Further Notes on the Conditions in which Restrictions Come Into the Category of Turbulent-Flow Restrictions, and on the Conditions of Transition From Sub-to Supercritical Flow Regimes in Restrictions of this Type

§3. Characteristics of Laminar-Flow Restrictions

(a) Study of the Form of the Flow Characteristic

(b) Comparative Data Concerning the Flow Characteristics of Cylindrical Restrictions with a Channel of Circular Cross-Section and of Annular Restrictions. Adjustment Characteristics of Adjustable Annular Restrictions

(c) Effect of Eccentricity of Rod in Sleeve Opening on Air Flow Through an Annular Restriction

§4. Characteristics of Restrictions of the Mixed Category

(a) General Case of Flow of Gas Through a Cylindrical Restriction of Circular Cross-Section. Use in Determining the Characteristics of the Restriction of Data of the Gas Dynamic Theory of Flow in Pipes

(b) Characteristics of Restrictions with a Cylindrical Channel of Non-Circular Section, and of Restrictions with a Flow Cross-Section of Noncylindrical Shape (of the "Nozzle-Baffle" Type, Etc.)

(c) Effect of Air Temperature on Characteristics of Restrictions. Generalization of Conclusions Derived Earlier to Cases Where the Operating Medium is Not Air But Some Other Gas

(d) Further Notes on the Characteristics of Restrictions

Chapter II Pneumatic Chambers. Their Static Characteristics

§1. General Data on Pneumatic Chambers as Elements of Pneumatic Automatic Control Equipment and Measuring Devices. Problems in the Theory of Pneumatic Chambers

§2. Static Characteristics of Pneumatic Chambers in the Case of Turbulent-Flow Restrictions

(a) Basic Equations

(b) Graphs for Determining the Pressures in a Flow Chamber

(c) Principle of the Proportional Reduction of Absolute Air Pressures

(d) Characteristics of Variation in Terms of Gauge Pressures

(e) Theory of a Set of Pneumatic Restrictions

(f) Calculation of the Pressures in Flow Chambers in the Case of More Complex Combinations of Chambers

(g) Flow of Air Through a System of Flow Chambers at Small Pressure Drops

§3. Static Characteristics of Pneumatic Flow Chambers with Laminar-Flow Restrictions and with Different Combinations of Restrictions

(a) Characteristics of Flow Chambers with Laminar-Flow Restrictions. Proportional Reduction of the Gauge Pressures in a Chamber with a Laminar-Flow Restriction. Pneumatic Chamber as a Pressure Summator

(b) Relays with a Nozzle-Baffle Restriction as an Example of a Pneumatic Chamber with Restrictions of Various Types. Characteristics of Some Other Pneumatic Chambers with Restrictions of Various Types

(c) Determination of the Pressures in a Chamber When the Characteristics of the Restrictions are Given in the Form of Graphs

§4. Characteristics of Flow Chambers of Small Dimensions

(a) Data of the Experimental Investigation of Small Flow Chambers

(b) Basic Design Ratios for Small Flow Chambers

(c) Experimental Verification of Equation (II.59). Generalization of Characteristic of Variation in Magnitude of δp1max in Relation to f1, fch, P1, P0

(d) Calculation of the Quantity p1 Allowing for the Effect of Variation in the Air Density on the Characteristics of the Restrictions

(e) Investigation of the Shape of the Section of the Characteristic δP1max/P1=ᵩ(P1/P0) and of the Characteristics δP1/δP1max=ᵩ(l/dch) in the Range of Low P1/P0 Values

(f) Boundary Conditions Under Which a Small Chamber Can Still be Considered to be a Flow Chamber

(g) Investigation of the Characteristics of Chambers with Non-Coaxial Arrangement of the Restrictions

(h) Further Notes on the Characteristics of Small Flow Chambers

Chapter III Dynamics of Pneumatic Chambers

§1. Introductory Notes on the Investigation of the Dynamics of Pneumatic Chambers Used as Elements of Pneumatic Automatic Control Equipment

§2. Dynamics of Pneumatic Chambers with Turbulent-Flow Restrictions

(a) Derivation of the Differential Equation for the Process of Variation in the Pressures in a Flow Chamber

(b) Graphs for Determining the Coefficients of the Differential Equation of the Process of Variation in the Pressures in a Flow Chamber

(c) Derivation of the Differential Equation for a Flow Chamber Communicating with Several Chambers at the Inlet and Outlet. Closed Expressions of the Coefficients of this Equation

(d) Procedure for Determining the Numerical Values of the Coefficients of the Differential Equation for a Flow Chamber Communicating with Several Other Chambers

(e) Notes on the Conditions Under Which the Initial Combination of Outflow Regimes is Retained During the Transient Process, and on the Errors Introduced Through Linearization of the Equations. Allowing for Variation in the Flow Coefficients of the Restrictions

(f) The Dynamics of Blank Chambers with Turbulent-Flow Restrictions

§3. Dynamics of Flow and Blank Chambers with Laminar-Flow and Mixed-Category Restrictions

(a) Differential Equations of a Flow Chamber with Laminar-Flow Restrictions

(b) Characteristics of Filling and Emptying of Blank Chambers with Laminar-Flow Restrictions

(c) Notes on the Effects of the Mean Size of the Pressure and of the Range of Variation in the Pressures, on the Duration of the Transient Process in Pneumatic Chambers with Restrictions of Various Categories

(d) The Blank Chamber as a Harmonic Filter

(e) Procedure for Studying the Dynamics of Flow and Blank Chambers in Cases Where the Flow Characteristics of the Restrictions are Given in Graphs

(f) Further Notes on the Thermodynamic Conditions of Variation in the State of the Air During Filling and Emptying of Pneumatic Chambers. Estimating the Errors Involved in Assuming that the Non-Steady Processes of the Flow of Air Through the Restrictions and in the Chambers are Quasi-Static

Chapter IV Characteristics of Long Pneumatic Lines. Pneumatic Pipelines as Systems with Distributed Parameters

§1. General Information Concerning Long Pneumatic Lines Problems in the Design and Study of Long Pneumatic Lines

§2. Differential Equations for the Transmission of Air Pressure Changes in Long Pipelines

§3. Boundary Conditions. Equation of a Chamber Connected to a Long Line

§4. Solution of the Differential Equations for Pneumatic Pipelines Considered as Systems with Distributed Parameters

(a) Solution of the System of Differential Equations (IV.4) and (IV.5) by Operational Research Methods

(b) Two Special Cases

(c) Numerical Examples

(d) Relatively Short Pipelines as Systems with Distributed Parameters. Procedure for Solving Differential Equations of a Pipeline Under the Most General Boundary Conditions. the Case Where There is a Bypass Restriction at the Outlet from the Pipeline

(e) Solution of the Differential Equations of Pneumatic Pipelines as Systems with Distributed Parameters in the Form of Standing Waves. Solutions in this Form for Special Cases, Obtained by the Operational Research Method. Solution in the Form of Standing Waves for More General Cases, Where the Boundary Conditions are Given Graphically (Application of Pishinger's Graphical Method)

§5. Approximate Estimation of the Characteristics of Long Pneumatic Lines. Survey of Experimental Data on Long Pneumatic Lines. Analysis of the Effects of the Design Parameters and of the Range of Working Pressures, on the Characteristics of a Long Line

Appendix. Some Data From Aerodynamics

§1. Generalia. Classification of Gas Flows

§2. Basic Parameters of the State of Gases; Some Other Factors Encountered in Gas Dynamic Calculations

(a) Pressure

(b) Temperature

(c) Specific Gravity and Density

(d) Connexion Between Variations in Factors p, T and ρ in the Case of Isentropic Flows

(e) Velocity

(f) Plow

(g) Viscosity

(h) Numerical Values of Some Parameters for Air

§3. System of Initial Equations of Aerodynamics. Similarity Criteria of Gas Flows

(a) Equations of Motion

(b) Equation of Continuity

(c) Equation of the State of the Gas

(d) Equation of Conservation of Energy

(e) Some Additional Relations for the Case of Adiabatic Gas Flow, Following from the Equation of Conservation of Energy

(f) Similarity Criteria of Gas Flows

§4. Notes on Integration of the System of Basic Equations of Aerodynamics

(a) General Notes

(b) One-Dimensional Steady Flow of a Viscous Incompressible Liquid in a Cylindrical Channel of Circular Cross-Section and Along an Annular Gap. Poiseuille's Equation

(c) Approximate Solution of Navier-Stokes Equations by Means of Series

§5. Illustration of the Derivation of Some Equations of Aerodynamics to Which Reference is Made in the Main Text

(a) Saint Venant-Wantzel Equation for the Adiabatic Flow of Ideal Gas in a Nozzle From a Reservoir of Unbounded Capacity

(b) Equation of the Isothermal Flow of Gases in Pipes. Illustration of the Derivation of Equations (1.27) and (1.28) and of the Method Used to Plot the Curve M1'max=ᵩ[ξl/d], Given in Fig. 13 (c)

(c) Illustration of Equation (I.67) Used in Calculating Adiabatic Flow of Gases Along a Channel of a Restriction

(d) Notes on the Derivation of Equations (I.74) and (I.75) Used in Calculating the Flow of Air Along the Channel of a Restriction in the Presence of Heat Transfer

References

Subject Index

## Details

- No. of pages:
- 338

- Language:
- English

- Copyright:
- © Pergamon 1965

- Published:
- 1st January 1965

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483223995