Speed of Sound Data and Related Models for Mixtures of Natural Gas Constituents
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Che 253M Experiment No. 2 COMPRESSIBLE GAS FLOW
Rev. 8/15 AD/GW ChE 253M Experiment No. 2 COMPRESSIBLE GAS FLOW The objective of this experiment is to familiarize the student with methods for measurement of compressible gas flow and to study gas flow under subsonic and supersonic flow conditions. The experiment is divided into three distinct parts: (1) Calibration and determination of the critical pressure ratio for a critical flow nozzle under supersonic flow conditions (2) Calculation of the discharge coefficient and Reynolds number for an orifice under subsonic (non- choked) flow conditions and (3) Determination of the orifice constants and mass discharge from a pressurized tank in a dynamic bleed down experiment under (choked) flow conditions. The experimental set up consists of a 100 psig air source branched into two manifolds: the first used for parts (1) and (2) and the second for part (3). The first manifold contains a critical flow nozzle, a NIST-calibrated in-line digital mass flow meter, and an orifice meter, all connected in series with copper piping. The second manifold contains a strain-gauge pressure transducer and a stainless steel tank, which can be pressurized and subsequently bled via a number of attached orifices. A number of NIST-calibrated digital hand held manometers are also used for measuring pressure in all 3 parts of this experiment. Assorted pressure regulators, manual valves, and pressure gauges are present on both manifolds and you are expected to familiarize yourself with the process flow, and know how to operate them to carry out the experiment. A process flow diagram plus handouts outlining the theory of operation of these devices are attached. -
Laplace and the Speed of Sound
Laplace and the Speed of Sound By Bernard S. Finn * OR A CENTURY and a quarter after Isaac Newton initially posed the problem in the Principia, there was a very apparent discrepancy of almost 20 per cent between theoretical and experimental values of the speed of sound. To remedy such an intolerable situation, some, like New- ton, optimistically framed additional hypotheses to make up the difference; others, like J. L. Lagrange, pessimistically confessed the inability of con- temporary science to produce a reasonable explanation. A study of the development of various solutions to this problem provides some interesting insights into the history of science. This is especially true in the case of Pierre Simon, Marquis de Laplace, who got qualitatively to the nub of the matter immediately, but whose quantitative explanation performed some rather spectacular gyrations over the course of two decades and rested at times on both theoretical and experimental grounds which would later be called incorrect. Estimates of the speed of sound based on direct observation existed well before the Newtonian calculation. Francis Bacon suggested that one man stand in a tower and signal with a bell and a light. His companion, some distance away, would observe the time lapse between the two signals, and the speed of sound could be calculated.' We are probably safe in assuming that Bacon never carried out his own experiment. Marin Mersenne, and later Joshua Walker and Newton, obtained respectable results by deter- mining how far they had to stand from a wall in order to obtain an echo in a second or half second of time. -
Aspects of Flow for Current, Flow Rate Is Directly Proportional to Potential
Vacuum technology Aspects of flow For current, flow rate is directly proportional to potential difference and inversely proportional to resistance. I = V/R or I = V/R For a fluid flow, Q = (P1-P2)/R or P/R Using reciprocal of resistance, called conductance, we have, Q = C (P1-P2) There are two kinds of flow, volumetric flow and mass flow Volume flow rate, S = vA v – the average bulk velocity, A the cross sectional area S = V/t, V is the volume and t is the time. Mass flow rate is S x density. G = vA or V/t Mass flow rate is measured in units of throughput, such as torr.L/s Throughput = volume flow rate x pressure Throughput is equivalent to power. Torr.L/s (g/cm2)cm3/s g.cm/s J/s W It works out that, 1W = 7.5 torr.L/s Types of low 1. Laminar: Occurs when the ratio of mass flow to viscosity (Reynolds number) is low for a given diameter. This happens when Reynolds number is approximately below 2000. Q ~ P12-P22 2. Above 3000, flow becomes turbulent Q ~ (P12-P22)0.5 3. Choked flow occurs when there is a flow restriction between two pressure regions. Assume an orifice and the pressure difference between the two sections, such as 2:1. Assume that the pressure in the inlet chamber is constant. The flow relation is, Q ~ P1 4. Molecular flow: When pressure reduces, MFP becomes larger than the dimensions of the duct, collisions occur between the walls of the vessel. -
Introduction to Physical Chemistry – Lecture 5 Supplement: Derivation of the Speed of Sound in Air
Introduction to Physical Chemistry – Lecture 5 Supplement: Derivation of the Speed of Sound in Air I. LECTURE OVERVIEW We can combine the results of Lecture 5 with some basic techniques in fluid mechanics to derive the speed of sound in air. For the purposes of the derivation, we will assume that air is an ideal gas. II. DERIVATION OF THE SPEED OF SOUND IN AN IDEAL GAS Consider a sound wave that is produced in an ideal gas, say air. This sound may be produced by a variety of methods (clapping, explosions, speech, etc.). The central point to note is that the sound wave is defined by a local compression and then expansion of the gas as the wave FIG. 2: An imaginary cross-sectional tube running from one passes by. A sound wave has a well-defined velocity v, side of the sound wave to the other. whose value as a function of various properties of the gas (P , T , etc.) we wish to determine. Imagine that our cross-sectional area is the opening of So, consider a sound wave travelling with velocity v, a tube that exits behind the sound wave, where the air as illustrated in Figure 1. From the perspective of the density is ρ + dρ, and velocity is v + dv. Since there is sound wave, the sound wave is still, and the air ahead of no mass accumulation inside the tube, then applying the it is travelling with velocity v. We assume that the air principle of conservation of mass we have, has temperature T and P , and that, as it passes through the sound wave, its velocity changes to v + dv, and its ρAv = (ρ + dρ)A(v + dv) ⇒ temperature and pressure change slightly as well, to T + ρv = ρv + vdρ + ρdv + dvdρ ⇒ dT and P + dP , respectively (see Figure 1). -
The Physics of Sound 1
The Physics of Sound 1 The Physics of Sound Sound lies at the very center of speech communication. A sound wave is both the end product of the speech production mechanism and the primary source of raw material used by the listener to recover the speaker's message. Because of the central role played by sound in speech communication, it is important to have a good understanding of how sound is produced, modified, and measured. The purpose of this chapter will be to review some basic principles underlying the physics of sound, with a particular focus on two ideas that play an especially important role in both speech and hearing: the concept of the spectrum and acoustic filtering. The speech production mechanism is a kind of assembly line that operates by generating some relatively simple sounds consisting of various combinations of buzzes, hisses, and pops, and then filtering those sounds by making a number of fine adjustments to the tongue, lips, jaw, soft palate, and other articulators. We will also see that a crucial step at the receiving end occurs when the ear breaks this complex sound into its individual frequency components in much the same way that a prism breaks white light into components of different optical frequencies. Before getting into these ideas it is first necessary to cover the basic principles of vibration and sound propagation. Sound and Vibration A sound wave is an air pressure disturbance that results from vibration. The vibration can come from a tuning fork, a guitar string, the column of air in an organ pipe, the head (or rim) of a snare drum, steam escaping from a radiator, the reed on a clarinet, the diaphragm of a loudspeaker, the vocal cords, or virtually anything that vibrates in a frequency range that is audible to a listener (roughly 20 to 20,000 cycles per second for humans). -
FORMULAS for CALCULATING the SPEED of SOUND Revision G
FORMULAS FOR CALCULATING THE SPEED OF SOUND Revision G By Tom Irvine Email: [email protected] July 13, 2000 Introduction A sound wave is a longitudinal wave, which alternately pushes and pulls the material through which it propagates. The amplitude disturbance is thus parallel to the direction of propagation. Sound waves can propagate through the air, water, Earth, wood, metal rods, stretched strings, and any other physical substance. The purpose of this tutorial is to give formulas for calculating the speed of sound. Separate formulas are derived for a gas, liquid, and solid. General Formula for Fluids and Gases The speed of sound c is given by B c = (1) r o where B is the adiabatic bulk modulus, ro is the equilibrium mass density. Equation (1) is taken from equation (5.13) in Reference 1. The characteristics of the substance determine the appropriate formula for the bulk modulus. Gas or Fluid The bulk modulus is essentially a measure of stress divided by strain. The adiabatic bulk modulus B is defined in terms of hydrostatic pressure P and volume V as DP B = (2) - DV / V Equation (2) is taken from Table 2.1 in Reference 2. 1 An adiabatic process is one in which no energy transfer as heat occurs across the boundaries of the system. An alternate adiabatic bulk modulus equation is given in equation (5.5) in Reference 1. æ ¶P ö B = ro ç ÷ (3) è ¶r ø r o Note that æ ¶P ö P ç ÷ = g (4) è ¶r ø r where g is the ratio of specific heats. -
Mass Flow Rate and Isolation Characteristics of Injectors for Use with Self-Pressurizing Oxidizers in Hybrid Rockets
49th AIAA/ASME/SAE/ASEE Joint PropulsionConference AIAA 2013-3636 July 14 - 17, 2013, San Jose, CA Mass Flow Rate and Isolation Characteristics of Injectors for Use with Self-Pressurizing Oxidizers in Hybrid Rockets Benjamin S. Waxman*, Jonah E. Zimmerman†, Brian J. Cantwell‡ Stanford University, Stanford, CA 94305 and Gregory G. Zilliac§ NASA Ames Research Center, Moffet Field, CA 94035 Self-pressurizing rocket propellants are currently gaining popularity in the propulsion community, partic- ularly in hybrid rocket applications. Due to their high vapor pressure, these propellants can be driven out of a storage tank without the need for complicated pressurization systems or turbopumps, greatly minimizing the overall system complexity and mass. Nitrous oxide (N2O) is the most commonly used self pressurizing oxidizer in hybrid rockets because it has a vapor pressure of approximately 730 psi (5.03 MPa) at room temperature and is highly storable. However, it can be difficult to model the feed system with these propellants due to the presence of two-phase flow, especially in the injector. An experimental test apparatus was developed in order to study the performance of nitrous oxide injectors over a wide range of operating conditions. Mass flow rate characterization has been performed to determine the effects of injector geometry and propellant sub-cooling (pressurization). It has been shown that rounded and chamfered inlets provide nearly identical mass flow rate improvement in comparison to square edged orifices. A particular emphasis has been placed on identifying the critical flow regime, where the flow rate is independent of backpressure (similar to choking). For a simple orifice style injector, it has been demonstrated that critical flow occurs when the downstream pressure falls sufficiently below the vapor pressure, ensuring bulk vapor formation within the injector element. -
Speed of Sound in a System Approaching Thermodynamic Equilibrium
Proceedings of the DAE-BRNS Symp. on Nucl. Phys. 61 (2016) 842 Speed of Sound in a System Approaching Thermodynamic Equilibrium Arvind Khuntia1, Pragati Sahoo1, Prakhar Garg1, Raghunath Sahoo1∗, and Jean Cleymans2 1Discipline of Physics, School of Basic Science, Indian Institute of Technology Indore, Khandwa Road, Simrol, M.P. 453552, India 2UCT-CERN Research Centre and Department of Physics, University of Cape Town, Rondebosch 7701, South Africa Introduction uses Experimental high energy collisions at 1 fT (E) ≡ : (1) RHIC and LHC give an opportunity to study E−µ the space-time evolution of the created hot expq T ± 1 and dense matter known as QGP at high ini- tial energy density and temperature. As the where the function expq(x) is defined as initial pressure is very high, the system un- ( dergo expansion with decreasing temperature [1 + (q − 1)x]1=(q−1) if x > 0 exp (x) ≡ and energy density till the occurrence of the fi- q [1 + (1 − q)x]1=(1−q) if x ≤ 0 nal kinetic freeze-out. This change in pressure with energy density is related to the speed of (2) sound inside the system. The QGP formed and, in the limit where q ! 1 it re- in heavy ion collisions evolves from the initial duces to the standard exponential; QGP phase to a hadronic phase via a possi- limq!1 expq(x) ! exp(x). In the present con- ble mixed phase. The speed of sound reduces text we have taken µ = 0, therefore x ≡ E=T to zero on the phase boundary in a first or- is always positive. -
Physics 101: Lecture 18 Fluids II
PhysicsPhysics 101:101: LectureLecture 1818 FluidsFluids IIII Today’s lecture will cover Textbook Chapter 9 Physics 101: Lecture 18, Pg 1 ReviewReview StaticStatic FluidsFluids Pressure is force exerted by molecules “bouncing” off container P = F/A Gravity affects pressure P = P 0 + ρgd Archimedes’ principle: Buoyant force is “weight” of displaced fluid. F = ρ g V Today include moving fluids! A1v1 = A 2 v2 – continuity equation 2 2 P1+ρgy 1 + ½ ρv1 = P 2+ρgy 2 + ½ρv2 – Bernoulli’s equation Physics 101: Lecture 18, Pg 2 08 ArchimedesArchimedes ’’ PrinciplePrinciple Buoyant Force (F B) weight of fluid displaced FB = ρfluid Vdisplaced g Fg = mg = ρobject Vobject g object sinks if ρobject > ρfluid object floats if ρobject < ρfluid If object floats… FB = F g Therefore: ρfluid g Vdispl. = ρobject g Vobject Therefore: Vdispl./ Vobject = ρobject / ρfluid Physics 101: Lecture 18, Pg 3 10 PreflightPreflight 11 Suppose you float a large ice-cube in a glass of water, and that after you place the ice in the glass the level of the water is at the very brim. When the ice melts, the level of the water in the glass will: 1. Go up, causing the water to spill out of the glass. 2. Go down. 3. Stay the same. Physics 101: Lecture 18, Pg 4 12 PreflightPreflight 22 Which weighs more: 1. A large bathtub filled to the brim with water. 2. A large bathtub filled to the brim with water with a battle-ship floating in it. 3. They will weigh the same. Tub of water + ship Tub of water Overflowed water Physics 101: Lecture 18, Pg 5 15 ContinuityContinuity A four-lane highway merges down to a two-lane highway. -
Acoustics: the Study of Sound Waves
Acoustics: the study of sound waves Sound is the phenomenon we experience when our ears are excited by vibrations in the gas that surrounds us. As an object vibrates, it sets the surrounding air in motion, sending alternating waves of compression and rarefaction radiating outward from the object. Sound information is transmitted by the amplitude and frequency of the vibrations, where amplitude is experienced as loudness and frequency as pitch. The familiar movement of an instrument string is a transverse wave, where the movement is perpendicular to the direction of travel (See Figure 1). Sound waves are longitudinal waves of compression and rarefaction in which the air molecules move back and forth parallel to the direction of wave travel centered on an average position, resulting in no net movement of the molecules. When these waves strike another object, they cause that object to vibrate by exerting a force on them. Examples of transverse waves: vibrating strings water surface waves electromagnetic waves seismic S waves Examples of longitudinal waves: waves in springs sound waves tsunami waves seismic P waves Figure 1: Transverse and longitudinal waves The forces that alternatively compress and stretch the spring are similar to the forces that propagate through the air as gas molecules bounce together. (Springs are even used to simulate reverberation, particularly in guitar amplifiers.) Air molecules are in constant motion as a result of the thermal energy we think of as heat. (Room temperature is hundreds of degrees above absolute zero, the temperature at which all motion stops.) At rest, there is an average distance between molecules although they are all actively bouncing off each other. -
THERMODYNAMICS, HEAT TRANSFER, and FLUID FLOW, Module 3 Fluid Flow Blank Fluid Flow TABLE of CONTENTS
Department of Energy Fundamentals Handbook THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW, Module 3 Fluid Flow blank Fluid Flow TABLE OF CONTENTS TABLE OF CONTENTS LIST OF FIGURES .................................................. iv LIST OF TABLES ................................................... v REFERENCES ..................................................... vi OBJECTIVES ..................................................... vii CONTINUITY EQUATION ............................................ 1 Introduction .................................................. 1 Properties of Fluids ............................................. 2 Buoyancy .................................................... 2 Compressibility ................................................ 3 Relationship Between Depth and Pressure ............................. 3 Pascal’s Law .................................................. 7 Control Volume ............................................... 8 Volumetric Flow Rate ........................................... 9 Mass Flow Rate ............................................... 9 Conservation of Mass ........................................... 10 Steady-State Flow ............................................. 10 Continuity Equation ............................................ 11 Summary ................................................... 16 LAMINAR AND TURBULENT FLOW ................................... 17 Flow Regimes ................................................ 17 Laminar Flow ...............................................