Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW

Size: px
Start display at page:

Download "Introduction. In general, gases are highly compressible and liquids have a very low compressibility. COMPRESSIBLE FLOW"

Transcription

1 COMRESSIBLE FLOW COMRESSIBLE FLOW Introduction he compressibility of a fluid is, basically, a measure of the change in density that will be produced in the fluid by a specific change in pressure and temperature. In general, gases are highly compressible and liquids have a very low compressibility. art one : Introduction of Compressible Flow

2 COMRESSIBLE FLOW Application ; Aircraft design Gas and steam turbines Reciprocating engines Natural gas transmission lines Combustion chambers Compressibility effect ; Supersonic the flow velocity is relatively high compared to the speed of sound in the gas. Subsonic art one : Introduction of Compressible Flow

3 COMRESSIBLE FLOW Fundamental assumptions. he gas is continuous.. he gas is perfect (obeys the perfect gas law) 3. Gravitational effects on the flow field are negligible. 4. Magnetic and electrical effects are negligible. 5. he effects of viscosity are negligible. Applied principles. Conservation of mass (continuity equation). Conservation of momentum (Newton s law) 3. Conservation of energy (first law of thermodynamics) 4. Equation of state art one : Introduction of Compressible Flow 3

4 COMRESSIBLE FLOW erfect gas law : R : ressure : Density R : Universal gas constant Rair : emperature J 87.04( ) kg K art one : Introduction of Compressible Flow 4

5 COMRESSIBLE FLOW Conservation laws : Conservation of mass Rate of increase of mass of fluid in control volume Rate mass enters control volume _ Rate mass leaves control volume Conservation of momentum : Net force on gas in control volume in direction considered Rate of increase of momentum in direction considered of fluid in control l _ Rate momentum leaves control volume in direction considered Rate momentum leaves control volume in direction considered art one : Introduction of Compressible Flow 5

6 COMRESSIBLE FLOW Conservation of energy : Rate of increase in internal energy and kinetic energy of gas in control volume Rate enthalpy and kinetic energy leave control volume _ Rate enthalpy and kinetic energy enter control volume Rate heat is transferred into control volume _ Rate work is done by gas in control volume art one : Introduction of Compressible Flow 6

7 COMRESSIBLE FLOW Definition : A control volume is a volume in space (geometric entity, independent of mass) through which fluid may flow Enthalpy H, is the sum of internal energy U and the product of pressure and volume appears. H U art one : Introduction of Compressible Flow 7

8 COMRESSIBLE FLOW COMRESSIBLE FLOW Introduction Many of the compressible flows that occur in engineering practice can be adequately modeled as a flow through a duct or streamtube whose cross-sectional area is changing relatively slowly in the flow direction. A duct is a solid walled channel, whereas a streamtube is defined by considering a closed curve drawn in a fluid flow. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 8

9 COMRESSIBLE FLOW Quasi-one-dimensional flow is flows in which the flow area is changing but in which the flow at any section can be treated as one-dimensional. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 9

10 COMRESSIBLE FLOW CONINUIY EQUAION he continuity equation is obtained by applying the principle of conservation of mass to flow through a control volume. One-dimensional flow is being considered. here is no mass transfer across the control volume. he only mass transfer occurs through the ends of the control volume. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 0

11 COMRESSIBLE FLOW Mass enters through the left hand face of the control volume be equal to the rate at which mass leaves through the right hand face of the control volume. m & & m We know that m& A We considered ; A A For the differentially short control volume indicated, art two : he Equation of Steady One-Dimensional Compressible Fluid Flow

12 COMRESSIBLE FLOW above equation gives ; A ( d)( d )( A da) Neglecting higher order terms, we found ; Ad Ad da 0 A Dividing this equation by then gives ; d d da A 0 his equation relates the fractional changes in density, velocity and area over a short length of the control volume. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow

13 COMRESSIBLE FLOW MOMENUM EQUAION (Euler s equation) he flow is steady flow. Gravitational forces are being neglected. he only forces acting on the control volume are the pressure forces and the frictional force exerted on the surface of the control volume. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 3

14 COMRESSIBLE FLOW he net force on the control volume in the x-direction is ; A ( p d)( A da) [( ( d)][( A da) A] df Note : dx is too small, dda have been neglected. Mean pressure on the curved surface can be taken as the average of the pressures acting on the two end surfaces. dfµ is the frictional force. Rearranging above equation, we found the net force on the control volume in the x-direction is ; Ad df art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 4

15 COMRESSIBLE FLOW Since the rate at which momentum crosses any section of the duct is equal to m&, we found that ; A[( d ) ] Ad he above equation can be written as ; Ad df Ad Frictional force is assumed to be negligible. he Euler s equation for steady flow through a duct becomes; d d art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 5

16 COMRESSIBLE FLOW Integrating Euler s equation ; d C (For compressible) And if density can be assumed constant, Euler s equation become ; C (For incompressible) art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 6

17 COMRESSIBLE FLOW SEADY FLOW ENERGY EQUAION For flow through the type of control volume considered as before, we found ; h h q w h enthalpy per mass velocity q heat transferred into the control volume per unit mass of fluid flowing through it w work done by the fluid per unit mass art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 7

18 COMRESSIBLE FLOW Assumption ; No work is done, w0 erfect gases is considered, h c p Steady flow energy equation ; cp cp q Applying this equation to the flow through the differentially short control volume gives ; c p dq c p ( d ) ( d ) art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 8

19 COMRESSIBLE FLOW Neglecting higher order terms gives ; c p d d dq his equation indicates that in compressible flows, changes in velocity will, in general, induce changes in temperature and that heat addition can cause velocity changes as well as temperature changes. If the flow is adiabatic i.e., if there is no heat transfer to of from the flow, it gives ; c p cp art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 9

20 COMRESSIBLE FLOW Steady flow energy equation for adiabatic flow becomes ; d c p d 0 his equation shows that in adiabatic flow, an increase in velocity is always accompanied by a decrease in temperature. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 0

21 COMRESSIBLE FLOW EQUAION OF SAE When applied between any two points in the flow ; When applied between the inlet and the exit of a differentially short control volume, this equation becomes ; d ( d)( d ) art two : he Equation of Steady One-Dimensional Compressible Fluid Flow

22 COMRESSIBLE FLOW Higher order terms are neglected and it gives ; d d d d d d 0 his equation shows how the changes in pressure, density and temperature are interrelated in compressible flow. art two : he Equation of Steady One-Dimensional Compressible Fluid Flow

23 COMRESSIBLE FLOW ENROY CONSIDERAIONS In studying compressible flows, another variable, the entropy, s, has to be introduced. he entropy basically places limitations on which flow processes are physically possible and which are physically excluded. he entropy change between any two points in the flow is given by ; s s c p ln R ln () Since R c p c v, this equation can be written; s c p s ln If there is no change in entropy, i.e., if the flow is art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 3

24 COMRESSIBLE FLOW isentropic, this equation requires that : hence, since the perfect gas law gives ; it follows that in isentropic flow : in isentropic flows, then is a constant. If equation () is applied between the inlet and the exit art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 4

25 COMRESSIBLE FLOW of a differentially short control volume, it gives ; ( d d s ds) s c p ln R ln neglecting small value, the above equation gives; ds c d d p R () which can be written as ; ds c p d d lastly, it is noted that in an isentropic flow, equation () gives; c p d R d using the perfect gas law ; art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 5

26 COMRESSIBLE FLOW c p d d (3) but the energy equation for isentropic flow, i.e., for flow with no heat transfer, it gives ; d c p d 0 which using equation (3) gives ; d d 0 art two : he Equation of Steady One-Dimensional Compressible Fluid Flow 6

27 COMRESSIBLE FLOW SOME FUNDAMENAL ASECS OF COMRESSIBLE FLOW Mach number gas velocity mach number, M speed of sound a a R M < : subsonic M : transonic M > : supersonic M >> : hypersonic art three : Mach Number 7

28 COMRESSIBLE FLOW Isentropic flow in a streamtube In order to illustrate the importance of the Mach number in determining the conditions under which compressibility must be taken in account, isentropic flow, i.e., frictionless adiabatic flow, through a streamtube will be first considered. From previous chapter, we know that ; d d and a the above equation can be written as : d d M a d () his equation shows that the magnitude of the fractional pressure change, induced by a given fractional velocity change, depends on the square of Mach number. art three : Mach Number 8

29 COMRESSIBLE FLOW Next, consider the energy equation. Since adiabatic flow is being considered ; d c p d R c p M d Since; R c v p c and R c p Above equation can be written as ; d ( ) M d () Lastly, consider the equation of state; d d d combining above equation with eq.() and eq.() art three : Mach Number 9

30 COMRESSIBLE FLOW d M ( ) M d d his equation indicates that: d M d (negative sign means, density decrease when velocity increased) at M0., at M0.33, d d d d % % At low mach number, density changes will be insignificant. art three : Mach Number 30

31 COMRESSIBLE FLOW Normally at M<0.3, the fluid is assumed incompressible. It should also be noted that above equation can we written as ; d d ( ) M Similarly, the temperature difference is neglected at lower value of Mach number. art three : Mach Number 3

32 COMRESSIBLE FLOW Mach waves Disturbances tend to propagated ahead of the body in motion to warn the gas of the approach of the body. his is due to pressure at the surface is higher than surrounding gas and pressure waves spread out from the body. he pressure waves spread out at the of sound Effect of the velocity of the body relative to the speed of sound (pressure wave velocity) on the flow field. art three : Mach Number 3

33 COMRESSIBLE FLOW Consider for subsonic flow M<, figure (). Speed of the body u and speed of sound a, where u<a. Body position at a, b, c and d at time interval t. Waves generated at time 0, t, t and 3t. Since u<a, a body moves slower than the waves and therefore a body will never overtake it. art three : Mach Number 33

34 COMRESSIBLE FLOW If u>a, then M>, the flow is supersonic, a body moves faster than the waves and will overtake it, (figure ()). he waves lie within a cone which has its vertex at the body at the time considered. On gas within this cone aware of the presence of the body. ertex angle α is called Mach angle, where ; a sin α u M he cone is therefore termed a conical Mach wave. art three : Mach Number 34

35 COMRESSIBLE FLOW art three : Mach Number 35

36 COMRESSIBLE FLOW art three : Mach Number 36

37 COMRESSIBLE FLOW ONE-DIMENSIONAL ISENROIC FLOW INRODUCION An adiabatic flow (a flow in which there is no heat exchange) in which viscous losses are negligible, i.e., it is an adiabatic frictionless flow. Although no real flow is entirely isentropic, there are many flows of great practical importance in which the major portion of the flow can be assumed to be isentropic. art four : One-Dimensional Isentropic Flow 37

38 COMRESSIBLE FLOW For example, in internal duct flows there are many important cases where the effects of viscosity and heat transfer are restricted to thin layers adjacent to the walls, i.e., are only important in the wall boundary layers, and the rest of the flow can be assumed to be isentropic. Even when non-isentropic effects become important, it is often possible to calculate the flow by assuming it to be isentropic and to then apply an empirical correction factor to the solution so obtained to account for the non-isentropic effect, for example, in the design nozzle. art four : One-Dimensional Isentropic Flow 38

39 COMRESSIBLE FLOW GOERNING EQUAION By definition, the entropy remains constant in an isentropic flow. c (c:constant) (4.) From equation (4.) art four : One-Dimensional Isentropic Flow 39

40 COMRESSIBLE FLOW Hence, since the general equation of state gives ; or It follows that in isentropic flow ; Recalling that R a, that ; a a eq.(4.5) he steady flow adiabatic energy equation is next applied between the point and point. his gives ; c c p p art four : One-Dimensional Isentropic Flow 40

41 COMRESSIBLE FLOW It can be written as ; ) ( ) ( c p c p From ; M c R R c p p So, it follows that ; ) ( M ) ( M eq.(4.6) his equation applies in adiabatic flow. If friction effects are also negligible, i.e., if the flow is isentropic, eq.(4.6) cam be used in conjunction with the isentropic state relations given in eq.(4.5) to obtain ; art four : One-Dimensional Isentropic Flow 4

42 COMRESSIBLE FLOW ) ( ) ( M M and ) ( ) ( M M Lastly, it is called that the continuity equation gives ; A A which can be rearranged to give ; A A art four : One-Dimensional Isentropic Flow 4

43 COMRESSIBLE FLOW SAGNAION CONDIIONS Stagnation conditions are those that would exist if the flow at any point in fluid stream was isentropically brought to rest. If the entire flow is essentially isentropic and if the velocity is essentially zero at some point in the flow, then the stagnation conditions will be those existing at the zero velocity point. art four : One-Dimensional Isentropic Flow 43

44 COMRESSIBLE FLOW However, even when the flow is non-isentropic, the concept of the stagnation conditions is still useful, the stagnation conditions at a point the being the conditions that would exist if the local flow were brought to rest isentropically. If the equations derived in the previous section are applied between a point in the flow where the pressure, density, temperature and Mach number are,,, M respectively, then if the stagnation conditions are denoted by the subscript 0, the stagnation pressure, density and temperature will, since the Mach number is zero at the point where the stagnation conditions exist, be given by ; art four : One-Dimensional Isentropic Flow 44

45 COMRESSIBLE FLOW 0 M 0 M 0 M ( for the particular case of 4. ) art four : One-Dimensional Isentropic Flow 45

46 COMRESSIBLE FLOW CRIICAL CONDIIONS he critical conditions are those that would exist if the flow was isentropically accelerated or decelerated until the Mach number was unity, (M ) hese critical conditions are usually denoted by an asterisk. By setting M, we found ; * M * M a a * M art four : One-Dimensional Isentropic Flow 46

47 COMRESSIBLE FLOW * M By setting M 0, we found ; 0 * 0 * a a 0 * 0 * For the case of air flow ; *, *, * art four : One-Dimensional Isentropic Flow 47

48 COMRESSIBLE FLOW MAXIMUM DISCHARGE ELOCIY Also known as maximum escape velocity, is the velocity that would be generated if a gas was adiabatically expanded until its temperature has dropped to absolute zero. Using the adiabatic energy equation gives the maximum discharge velocity as : 0 ˆ c c p his can be rearranged to give ; 0 ) ( ˆ c c p ) ( ˆ 0 a a art four : One-Dimensional Isentropic Flow 48

49 ONE-DIMENSIONAL ISENROIC FLOW SUMMARY OF MAJOR EQUAIONS ISENROIC FLOW RELAIONS a a ) ( ) ( M M ) ( ) ( M M ) ( ) ( M M ) ( ) ( ) ( M M M M A A A A

50 SAGNAION CONDIIONS 0 ) ( M 0 ) ( M 0 ) ( M CRIICAL CONDIIONS * M * M * M

51 RELAIONSHI BEWEEN CRIICAL AND SAGNAION CONDIIONS 0 * 0 * 0 * 0 * a a

52 able Some typical values for the speed of sound at 0 ºC Source: Compressible Fluid Flow, he McGraw-Hill Companies, Inc. atrick, H.O. and William, E.C. Gas Molar mass Speed of sound at 0 ºC (m/s) Air Argon (Ar) Carbon dioxide (CO ) Freon (CCl F ) Helium (He) Hydrogen (H ) Xenon (Xe)

53 able Isentropic flow tables for air with.4 Source: Compressible Fluid Flow, he McGraw-Hill Companies, Inc. atrick, H.O. and William, E.C. M o / o / o / a o / a A / A* θ

54 M o / o / o / a o / a A / A* θ

55 M o / o / o / a o / a A / A* θ

56 able 3 Approximate properties of the standard atmosphere Source: Compressible Fluid Flow, he McGraw-Hill Companies, Inc. atrick, H.O. and William, E.C. H a v ( m ) ( K ) ( a 0 5 ) ( kg/m 3 ) ( m/s ) ( m /s 0-5 )

57 H a v ( m ) ( K ) ( a 0 5 ) ( kg/m 3 ) ( m/s ) ( m /s 0-5 )

58 utorial for compressible flow. An air stream enters a variable area channel at a velocity of 30m/s with a pressure of 0ka and a temperature of 0ºC. At a certain point in the channel, the velocity is found to be 50m/s. Using Bernoulli s equation (i.e., p /constant), which assunmes incompressible flow, find the pressure at this point. In this calculation use the density evaluated at the inlet conditions. If the temperature of the air is assumed to remain constant, evaluate the air density at the point in the flow where the velocity is 50m/s. Compare this density with the density a the inlet to the channel. On the basis of this comparison, do you think that the use of Bernoulli s equation is justified.. wo kilograms of air at an initial temperature and pressure of 30ºC and 00ka undergoes an isentropic process, the final temperature attained being 850ºC. Find the final pressure, the initial and final densities and the initial and final volumes. 3. wo air streams are mixed in a chamber. One stream enters the chamber through a 5cm diameter pipe at velocity of 00m/s with a pressure of 50ka and a temperature of 30ºC. he other stream enters the chamber through a.5cm diameter pipe at a velocity of 50m/s with a pressure of 75ka and a temperature of 30ºC. he air leaves the chamber through a 9cm diameter pipe at a pressure of 90ka and a temperature of 30ºC. Assuming that the flow is steady, find the velocity in the exit pipe. 4. he jet engine fitted to a small aircraft uses 35kg/s of air when the aircraft is flying at a speed of 800km/h. he jet efflux velocity is 590m/s. If the pressure on the engine discharge plane is assumed to be equal to the ambient pressure and if effects of the mass of the fuel used are ignored, find the thrust developed by the engine. 5. he engine of a small jet aircraft develops a thrust of 8kN when the aircraft is flying at a speed of 900km/h at an altitude where the ambient pressure is 50ka. he air flow rate through the engine is 75kg/s and the engine uses fuel at a rate of 3kg/s. he pressure on the engine discharge plane is 55ka and the area of the engine exit is 0.m. Find the jet efflux velocity.

59 6. A solid fuelled rocket is fitted with a convergent-divergent nozzle with an exit plane diameter of 30cm. he pressure and velocity on this nozzle exit plane are 75Kpa and 750m/s respectively and the mass flow rate through the nozzle is 350kg/s. Find the thrust developed by this engine when the ambient pressure is (a) 00ka and (b) 0ka. 7. In a hydrogen powered rocket, hydrogen enters a nozzle at a very low velocity with a temperature and pressure of 000ºC and 6.8Mpa respectively. he pressure on the exit plane of the nozzle is equal to the ambient pressure which is 0ka. If the required thrust is 0MN, what hydrogen mass flow rate required? he flow though the nozzle can be assumed to be isentropic and the specific heat ratio of the hydrogen can be assumed to be Carbon dioxide flows through a constant area duct. At inlet to the duct, the velocity is 0m/s and the temperature and pressure are 00ºC and 700ka respectively. Heat is added to the flow in the duct and at the exit of the duct the velocity is 40m/s and the temperature is 450ºC. Find the amount of heat being added to the carbon dioxide per unit mass of gas and the mass flow rate through the duct per unit cross-sectional area of the duct. Assume that for carbon dioxide, Air enters a heat exchanger with a velocity of 0m/s and a temperature and pressure of 5ºC and.5mpa. Heat is removed from the air in the heat exchanger and the air leaves with a velocity 30m/s at a temperature and pressure 80ºC and.45ma. Find the heat removed per kilogram of air flowing through the heat exchanger and the density of the air at the inlet and the exit to the heat exchanger.

60 utorial for compressible flow. Air enters a tank at a velocity of 00m/s and leaves the tank at a velocity of 00m/s. lf the flow is adiabatic find the difference between the temperature of the air at exit and the temperature of the air at inlet. Air at a temperature of 5 C is flowing at a velocity of 500m/s. A shock wave occurs in the flow reducing the velocity to 300m/s. Assuming the flow through the shock wave to be adiabatic, find the temperature of the air behind the shock wave. 3. Air being released from a tire through the valve is found to have a temperature of 5 C. Assuming that the air in the tire is at the ambient temperature of 30 C, find the velocity of the air at the exit of the valve. he process can be assumed to be adiabatic. 4. Gas with a molecular weight of 4 and a specific heat ratio of.67 flows through a variable area duct. At some point in the now the velocity is 80m/s and the temperature is 0 C. At some other point in the flow the temperature is minus 0 C. Find the velocity at this point in the flow assuming that the flow is adiabatic. 5. At a section of a circular duct through which air is flowing the pressure is 50ka, the temperature is 35 C, the velocity is 50m/s, and the diameter is 0.m. If, at this section, the duct diameter is increasing at a rate of 0.m/m, find dp/dx, d/dx and d/dx 6. Consider an isothermal air flow through a duct. At a certain section of the duct the velocity, temperature,and pressure are 00m/s, 5 C,and 0ka respectively. lf the velocity is decreasing at this section at a rate of 30 percent per meter, find dp/dx, ds/dx and d/dx. 7. Consider adiabatic air flow through a variable area duct, At a certain section of the duct the flow area is 0.m, the pressure is 0ka, the temperature is 5 C and the duct area is changing at a rate of 0.m /m. lot the variations of dp/dx, d/dx and d/dx with the velocity at the section for velocities between 50m/s and 300m/s.

61 utorial 3 for compressible flow. he velocity of an air flow changes by one percent. Assuming that the flow is isentropic,plot the percentage changes in pressure, temperature, and density induced by this change in velocity with flow Mach number for Mach numbers between 0. and.. Calculate the speed of sound at 88 K in hydrogen, helium and nitrogen. Under what conditions will the speed of sound in hydrogen be equal to that in helium? 3. Find the speed of sound in carbon dioxide at temperatures of 0ºC and 600ºC. 4. A very weak pressure wave, i.e, a sound wave, across which the pressure rise is 30a moves through air which has a temperature of 30 C and a pressure of 0ka. Find the density change, the temperature change, and the velocity change across this wave. 5. An airplane can fly at a speed or800km/h at sea-level where the temperature is 5 C. lf the airplane flies at the same Mach number at an altitude where the temperature is -44 C, find the speed at which the airplane is flying at this altitude. 6. he test section of a supersonic wind tunnel is square in cross-section with a side length of.m. he Mach number in the test section is 3.5, the temperature is - 00 C, and the pressure is 0ka. Find the mass flow rate of air through the test section. 7. A gas with a molar mass of 44 and a specific heat ratio.67 flows through a channel at supersonic speed. he temperature of the gas in the channel is 0 C. A photograph of the flow reveals weak waves originating at imperfections in the wall running across the flow at an angle to 45 to the flow direction. Find the Mach number and the velocity in the flow. 8. An observer at sea level does not hear an aircraft that is flying at an altitude of 7000m until it is a distance of 3km from the observer. Estimate the Mach number at which the aircraft is flying. In arriving at the answer, assume that the average temperature of the air between sea level and 7000m is -0 C. 9. An observer on the ground finds that an airplane flying horizontally at an altitude of 500m has traveled 6 km from the overhead position before the sound of the airplane is first heard. Assuming that, overall, the aircraft creates a small disturbance, estimate the speed at which the airplane is flying. he average air temperature between the ground and the altitude at which the airplane is flying is 0 C. Explain the assumptions you have made in arriving at the answer.

62 utorial 4 for compressible flow. A gas with a molar mass of 4 and a specific heat ratio of.67 flows through a variable area duct. At some point in the flow the velocity is 00m/s and the temperature is 0ºC. Find the Mach number at this point in the flow. At some other point in the flow the temperature is -0ºC. Find the velocity and Mach number at this point in the flow assuming that the flow is isentropic.. he exhaust gases from a rocket engine have a molar mass of 4. hey can be assumed to behave as a perfect gas with a specific heat ratio of.5. hese gases are accelerated through a nozzle. At some point in the nozzle where the crosssectional area of the nozzle is 0.7m, the pressure is 000ka, the temperature is 500 C and the velocity is 00 m/s, Find the mass flow rate through the nozzle and the stagnation pressure and temperature. Also find the highest velocity that could be generated by expanding this flow. lf the pressure at some other point in the nozzle is 00ka, find the temperature and velocity at this point in the flow assuming the flow to be one-dimensional and isentropic. 3. lf Concorde is flying at a Mach number of., at an altitude of 0000m in the standard atmosphere, find the stagnation pressure and temperature for the flow over the aircraft. 4. If a gas is flowing at 300m/s and has a pressure and temperature of 90ka and 0 C, find the maximum possible velocity that could be generated by expansion of this gas if the gas is air and if it is helium.

4 Compressible Fluid Dynamics

4 Compressible Fluid Dynamics 4 Compressible Fluid Dynamics 4. Compressible flow definitions Compressible flow describes the behaviour of fluids that experience significant variations in density under the application of external pressures.

More information

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us

Please welcome for any correction or misprint in the entire manuscript and your valuable suggestions kindly mail us Problems of Practices Of Fluid Mechanics Compressible Fluid Flow Prepared By Brij Bhooshan Asst. Professor B. S. A. College of Engg. And Technology Mathura, Uttar Pradesh, (India) Supported By: Purvi Bhooshan

More information

IX. COMPRESSIBLE FLOW. ρ = P

IX. COMPRESSIBLE FLOW. ρ = P IX. COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity.

More information

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives

Chapter 17. For the most part, we have limited our consideration so COMPRESSIBLE FLOW. Objectives Chapter 17 COMPRESSIBLE FLOW For the most part, we have limited our consideration so far to flows for which density variations and thus compressibility effects are negligible. In this chapter we lift this

More information

One-Dimensional Isentropic Flow

One-Dimensional Isentropic Flow Cairo University Second Year Faculty of Engineering Gas Dynamics AER 201B Aerospace Department Sheet (1) 2011-2012 One-Dimensional Isentropic Flow 1. Assuming the flow of a perfect gas in an adiabatic,

More information

Applied Gas Dynamics Flow With Friction and Heat Transfer

Applied Gas Dynamics Flow With Friction and Heat Transfer Applied Gas Dynamics Flow With Friction and Heat Transfer Ethirajan Rathakrishnan Applied Gas Dynamics, John Wiley & Sons (Asia) Pte Ltd c 2010 Ethirajan Rathakrishnan 1 / 121 Introduction So far, we have

More information

Review of Fundamentals - Fluid Mechanics

Review of Fundamentals - Fluid Mechanics Review of Fundamentals - Fluid Mechanics Introduction Properties of Compressible Fluid Flow Basics of One-Dimensional Gas Dynamics Nozzle Operating Characteristics Characteristics of Shock Wave A gas turbine

More information

UOT Mechanical Department / Aeronautical Branch

UOT Mechanical Department / Aeronautical Branch Chapter One/Introduction to Compressible Flow Chapter One/Introduction to Compressible Flow 1.1. Introduction In general flow can be subdivided into: i. Ideal and real flow. For ideal (inviscid) flow viscous

More information

Richard Nakka's Experimental Rocketry Web Site

Richard Nakka's Experimental Rocketry Web Site Página 1 de 7 Richard Nakka's Experimental Rocketry Web Site Solid Rocket Motor Theory -- Nozzle Theory Nozzle Theory The rocket nozzle can surely be described as the epitome of elegant simplicity. The

More information

AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics

AEROSPACE ENGINEERING DEPARTMENT. Second Year - Second Term ( ) Fluid Mechanics & Gas Dynamics AEROSPACE ENGINEERING DEPARTMENT Second Year - Second Term (2008-2009) Fluid Mechanics & Gas Dynamics Similitude,Dimensional Analysis &Modeling (1) [7.2R*] Some common variables in fluid mechanics include:

More information

SOME FUNDAMENTAL ASPECTS OF COMPRESSIBLE FLOW

SOME FUNDAMENTAL ASPECTS OF COMPRESSIBLE FLOW SOE FUNDAENAL ASECS OF CORESSIBLE FLOW ah number gas veloity mah number, speed of sound a a R < : subsoni : transoni > : supersoni >> : hypersoni art three : ah Number 7 Isentropi flow in a streamtube

More information

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303

Introduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303 Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum

More information

GAS DYNAMICS AND JET PROPULSION

GAS DYNAMICS AND JET PROPULSION GAS DYNAMICS AND JE PROPULSION 1. What is the basic difference between compressible and incompressible fluid flow? Compressible Incompressible 1. Fluid velocities are appreciable 1. Fluid velocities are

More information

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald

Introduction to Fluid Mechanics. Chapter 13 Compressible Flow. Fox, Pritchard, & McDonald Introduction to Fluid Mechanics Chapter 13 Compressible Flow Main Topics Basic Equations for One-Dimensional Compressible Flow Isentropic Flow of an Ideal Gas Area Variation Flow in a Constant Area Duct

More information

Chapter Four fluid flow mass, energy, Bernoulli and momentum

Chapter Four fluid flow mass, energy, Bernoulli and momentum 4-1Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (4-1). Figure (4-1): the differential control volume and differential control volume (Total mass entering

More information

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)

Introduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD) Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The

More information

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow

SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow SPC 407 Sheet 5 - Solution Compressible Flow Rayleigh Flow 1. Consider subsonic Rayleigh flow of air with a Mach number of 0.92. Heat is now transferred to the fluid and the Mach number increases to 0.95.

More information

Gas Dynamics and Jet Propulsion

Gas Dynamics and Jet Propulsion Gas Dynamics and Jet Propulsion (For B.E. Mechanical Engineering Students) (As per Anna University and Leading Universities New Revised Syllabus) Prof. K. Pandian Dr. A.Anderson, M.E., Ph.D., Professor

More information

Chapter 5. Mass and Energy Analysis of Control Volumes. by Asst. Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn

Chapter 5. Mass and Energy Analysis of Control Volumes. by Asst. Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Chapter 5 Mass and Energy Analysis of Control Volumes by Asst. Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Reference: Cengel, Yunus A. and Michael A. Boles, Thermodynamics:

More information

Compressible Flow. Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist

Compressible Flow. Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist Compressible Flow Professor Ugur GUVEN Aerospace Engineer Spacecraft Propulsion Specialist What is Compressible Flow? Compressible Flow is a type of flow in which the density can not be treated as constant.

More information

1 One-dimensional analysis

1 One-dimensional analysis One-dimensional analysis. Introduction The simplest models for gas liquid flow systems are ones for which the velocity is uniform over a cross-section and unidirectional. This includes flows in a long

More information

Thermal Energy Final Exam Fall 2002

Thermal Energy Final Exam Fall 2002 16.050 Thermal Energy Final Exam Fall 2002 Do all eight problems. All problems count the same. 1. A system undergoes a reversible cycle while exchanging heat with three thermal reservoirs, as shown below.

More information

Chapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh

Chapter Two. Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency. Laith Batarseh Chapter Two Basic Thermodynamics, Fluid Mechanics: Definitions of Efficiency Laith Batarseh The equation of continuity Most analyses in this book are limited to one-dimensional steady flows where the velocity

More information

Figure 1. Mach cone that arises upon supersonic flow around an object

Figure 1. Mach cone that arises upon supersonic flow around an object UNIT I BASIC CONCEPTS AND ISENTROPIC FLOWS Introduction The purpose of this applet is to simulate the operation of a converging-diverging nozzle, perhaps the most important and basic piece of engineering

More information

Chapter 5. Mass and Energy Analysis of Control Volumes

Chapter 5. Mass and Energy Analysis of Control Volumes Chapter 5 Mass and Energy Analysis of Control Volumes Conservation Principles for Control volumes The conservation of mass and the conservation of energy principles for open systems (or control volumes)

More information

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass

2013/5/22. ( + ) ( ) = = momentum outflow rate. ( x) FPressure. 9.3 Nozzles. δ q= heat added into the fluid per unit mass 9.3 Nozzles (b) omentum conservation : (i) Governing Equations Consider: nonadiabatic ternal (body) force ists variable flow area continuously varying flows δq f ternal force per unit volume +d δffdx dx

More information

vector H. If O is the point about which moments are desired, the angular moment about O is given:

vector H. If O is the point about which moments are desired, the angular moment about O is given: The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment

More information

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature

1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature CHAPTER 11 1. For an ideal gas, internal energy is considered to be a function of only. YOUR ANSWER: Temperature 2.In Equation 11.7 the subscript p on the partial derivative refers to differentiation at

More information

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)

Aerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved) Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation

More information

5/6/ :41 PM. Chapter 6. Using Entropy. Dr. Mohammad Abuhaiba, PE

5/6/ :41 PM. Chapter 6. Using Entropy. Dr. Mohammad Abuhaiba, PE Chapter 6 Using Entropy 1 2 Chapter Objective Means are introduced for analyzing systems from the 2 nd law perspective as they undergo processes that are not necessarily cycles. Objective: introduce entropy

More information

Chapter 7. Entropy. by Asst.Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn

Chapter 7. Entropy. by Asst.Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Chapter 7 Entropy by Asst.Prof. Dr.Woranee Paengjuntuek and Asst. Prof. Dr.Worarattana Pattaraprakorn Reference: Cengel, Yunus A. and Michael A. Boles, Thermodynamics: An Engineering Approach, 5th ed.,

More information

CLASS Fourth Units (Second part)

CLASS Fourth Units (Second part) CLASS Fourth Units (Second part) Energy analysis of closed systems Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. MOVING BOUNDARY WORK Moving boundary work (P

More information

EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE

EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE Equatorial Journal of Engineering (2018) 9-13 Journal Homepage: www.erjournals.com ISSN: 0184-7937 EVALUATION OF THE BEHAVIOUR OF STEAM EXPANDED IN A SET OF NOZZLES, IN A GIVEN TEMPERATURE Kingsley Ejikeme

More information

Notes #4a MAE 533, Fluid Mechanics

Notes #4a MAE 533, Fluid Mechanics Notes #4a MAE 533, Fluid Mechanics S. H. Lam lam@princeton.edu http://www.princeton.edu/ lam October 23, 1998 1 The One-dimensional Continuity Equation The one-dimensional steady flow continuity equation

More information

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS

UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS UNIT 1 COMPRESSIBLE FLOW FUNDAMENTALS 1) State the difference between compressible fluid and incompressible fluid? 2) Define stagnation pressure? 3) Express the stagnation enthalpy in terms of static enthalpy

More information

CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES

CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Thermodynamics: An Engineering Approach 8th Edition in SI Units Yunus A. Çengel, Michael A. Boles McGraw-Hill, 2015 CHAPTER 5 MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES Lecture slides by Dr. Fawzi Elfghi

More information

Isentropic Flow. Gas Dynamics

Isentropic Flow. Gas Dynamics Isentropic Flow Agenda Introduction Derivation Stagnation properties IF in a converging and converging-diverging nozzle Application Introduction Consider a gas in horizontal sealed cylinder with a piston

More information

5 ENERGY EQUATION OF FLUID MOTION

5 ENERGY EQUATION OF FLUID MOTION 5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws

More information

the pitot static measurement equal to a constant C which is to take into account the effect of viscosity and so on.

the pitot static measurement equal to a constant C which is to take into account the effect of viscosity and so on. Mechanical Measurements and Metrology Prof. S. P. Venkateshan Department of Mechanical Engineering Indian Institute of Technology, Madras Module -2 Lecture - 27 Measurement of Fluid Velocity We have been

More information

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.

In which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0. bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,

More information

6.1 According to Handbook of Chemistry and Physics the composition of air is

6.1 According to Handbook of Chemistry and Physics the composition of air is 6. Compressible flow 6.1 According to Handbook of Chemistry and Physics the composition of air is From this, compute the gas constant R for air. 6. The figure shows a, Pitot-static tube used for velocity

More information

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering

Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Jet Aircraft Propulsion Prof. Bhaskar Roy Prof. A.M. Pradeep Department of Aerospace Engineering Indian Institute of Technology, IIT Bombay Module No. # 01 Lecture No. # 08 Cycle Components and Component

More information

Civil aeroengines for subsonic cruise have convergent nozzles (page 83):

Civil aeroengines for subsonic cruise have convergent nozzles (page 83): 120 Civil aeroengines for subsonic cruise have convergent nozzles (page 83): Choked convergent nozzle must be sonic at the exit A N. Consequently, the pressure (p 19 ) at the nozzle exit will be above

More information

Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation

Objectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved

More information

Thermodynamics: An Engineering Approach Seventh Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, Chapter 7 ENTROPY

Thermodynamics: An Engineering Approach Seventh Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, Chapter 7 ENTROPY Thermodynamics: An Engineering Approach Seventh Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011 Chapter 7 ENTROPY Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction

More information

High Speed Aerodynamics. Copyright 2009 Narayanan Komerath

High Speed Aerodynamics. Copyright 2009 Narayanan Komerath Welcome to High Speed Aerodynamics 1 Lift, drag and pitching moment? Linearized Potential Flow Transformations Compressible Boundary Layer WHAT IS HIGH SPEED AERODYNAMICS? Airfoil section? Thin airfoil

More information

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW

Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Fluid Mechanics - Course 123 COMPRESSIBLE FLOW Flow of compressible fluids in a p~pe involves not only change of pressure in the downstream direction but also a change of both density of the fluid and

More information

Tutorial Materials for ME 131B Fluid Mechanics (Compressible Flow & Turbomachinery) Calvin Lui Department of Mechanical Engineering Stanford University Stanford, CA 94305 March 1998 Acknowledgments This

More information

ENTROPY. Chapter 7. Mehmet Kanoglu. Thermodynamics: An Engineering Approach, 6 th Edition. Yunus A. Cengel, Michael A. Boles.

ENTROPY. Chapter 7. Mehmet Kanoglu. Thermodynamics: An Engineering Approach, 6 th Edition. Yunus A. Cengel, Michael A. Boles. Thermodynamics: An Engineering Approach, 6 th Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2008 Chapter 7 ENTROPY Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc. Permission required

More information

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations

SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations SPC 407 Sheet 2 - Solution Compressible Flow - Governing Equations 1. Is it possible to accelerate a gas to a supersonic velocity in a converging nozzle? Explain. No, it is not possible. The only way to

More information

Shock and Expansion Waves

Shock and Expansion Waves Chapter For the solution of the Euler equations to represent adequately a given large-reynolds-number flow, we need to consider in general the existence of discontinuity surfaces, across which the fluid

More information

Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow

Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow Section 2: Lecture 1 Integral Form of the Conservation Equations for Compressible Flow Anderson: Chapter 2 pp. 41-54 1 Equation of State: Section 1 Review p = R g T " > R g = R u M w - R u = 8314.4126

More information

Unified Quiz: Thermodynamics

Unified Quiz: Thermodynamics Unified Quiz: Thermodynamics October 14, 2005 Calculators allowed. No books or notes allowed. A list of equations is provided. Put your ID number on each page of the exam. Read all questions carefully.

More information

Chapter 4 DYNAMICS OF FLUID FLOW

Chapter 4 DYNAMICS OF FLUID FLOW Faculty Of Engineering at Shobra nd Year Civil - 016 Chapter 4 DYNAMICS OF FLUID FLOW 4-1 Types of Energy 4- Euler s Equation 4-3 Bernoulli s Equation 4-4 Total Energy Line (TEL) and Hydraulic Grade Line

More information

Propulsion Thermodynamics

Propulsion Thermodynamics Chapter 1 Propulsion Thermodynamics 1.1 Introduction The Figure below shows a cross-section of a Pratt and Whitney JT9D-7 high bypass ratio turbofan engine. The engine is depicted without any inlet, nacelle

More information

Rocket Thermodynamics

Rocket Thermodynamics Rocket Thermodynamics PROFESSOR CHRIS CHATWIN LECTURE FOR SATELLITE AND SPACE SYSTEMS MSC UNIVERSITY OF SUSSEX SCHOOL OF ENGINEERING & INFORMATICS 25 TH APRIL 2017 Thermodynamics of Chemical Rockets ΣForce

More information

first law of ThermodyNamics

first law of ThermodyNamics first law of ThermodyNamics First law of thermodynamics - Principle of conservation of energy - Energy can be neither created nor destroyed Basic statement When any closed system is taken through a cycle,

More information

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1

P 1 P * 1 T P * 1 T 1 T * 1. s 1 P 1 ME 131B Fluid Mechanics Solutions to Week Three Problem Session: Isentropic Flow II (1/26/98) 1. From an energy view point, (a) a nozzle is a device that converts static enthalpy into kinetic energy. (b)

More information

Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011.

Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011. Thermodynamics: An Engineering Approach Seventh Edition in SI Units Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011 Chapter 7 ENTROPY Mehmet Kanoglu University of Gaziantep Copyright The McGraw-Hill

More information

Mass of fluid leaving per unit time

Mass of fluid leaving per unit time 5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.

More information

Lesson 6 Review of fundamentals: Fluid flow

Lesson 6 Review of fundamentals: Fluid flow Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass

More information

2 Navier-Stokes Equations

2 Navier-Stokes Equations 1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1

More information

Chapter 5 Control Volume Approach and Continuity Equation

Chapter 5 Control Volume Approach and Continuity Equation Chapter 5 Control Volume Approach and Continuity Equation Lagrangian and Eulerian Approach To evaluate the pressure and velocities at arbitrary locations in a flow field. The flow into a sudden contraction,

More information

Chapter 3 Bernoulli Equation

Chapter 3 Bernoulli Equation 1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around

More information

Steady waves in compressible flow

Steady waves in compressible flow Chapter Steady waves in compressible flow. Oblique shock waves Figure. shows an oblique shock wave produced when a supersonic flow is deflected by an angle. Figure.: Flow geometry near a plane oblique

More information

Contents. Preface... xvii

Contents. Preface... xvii Contents Preface... xvii CHAPTER 1 Idealized Flow Machines...1 1.1 Conservation Equations... 1 1.1.1 Conservation of mass... 2 1.1.2 Conservation of momentum... 3 1.1.3 Conservation of energy... 3 1.2

More information

First Law of Thermodynamics

First Law of Thermodynamics CH2303 Chemical Engineering Thermodynamics I Unit II First Law of Thermodynamics Dr. M. Subramanian 07-July-2011 Associate Professor Department of Chemical Engineering Sri Sivasubramaniya Nadar College

More information

2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B.

2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False A. True B. CHAPTER 03 1. Write Newton's second law of motion. YOUR ANSWER: F = ma 2.The lines that are tangent to the velocity vectors throughout the flow field are called steady flow lines. True or False 3.Streamwise

More information

Two mark questions and answers UNIT I BASIC CONCEPT AND FIRST LAW SVCET

Two mark questions and answers UNIT I BASIC CONCEPT AND FIRST LAW SVCET Two mark questions and answers UNIT I BASIC CONCEPT AND FIRST LAW 1. What do you understand by pure substance? A pure substance is defined as one that is homogeneous and invariable in chemical composition

More information

MODELING & SIMULATION OF ROCKET NOZZLE

MODELING & SIMULATION OF ROCKET NOZZLE MODELING & SIMULATION OF ROCKET NOZZLE Nirmith Kumar Mishra, Dr S Srinivas Prasad, Mr Ayub Padania Department of Aerospace Engineering MLR Institute of Technology Hyderabad, T.S Abstract This project develops

More information

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD

CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.

More information

AE301 Aerodynamics I UNIT A: Fundamental Concepts

AE301 Aerodynamics I UNIT A: Fundamental Concepts AE301 Aerodynamics I UNIT A: Fundamental Concets ROAD MAP... A-1: Engineering Fundamentals Reiew A-: Standard Atmoshere A-3: Goerning Equations of Aerodynamics A-4: Airseed Measurements A-5: Aerodynamic

More information

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.

William В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C. William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory

More information

Brown Hills College of Engineering & Technology

Brown Hills College of Engineering & Technology UNIT 4 Flow Through Nozzles Velocity and heat drop, Mass discharge through a nozzle, Critical pressure ratio and its significance, Effect of friction, Nozzle efficiency, Supersaturated flow, Design pressure

More information

Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras

Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras Rocket Propulsion Prof. K. Ramamurthi Department of Mechanical Engineering Indian Institute of Technology, Madras Lecture 11 Area Ratio of Nozzles: Under Expansion and Over Expansion (Refer Slide Time:

More information

Engineering Thermodynamics. Chapter 1. Introductory Concepts and Definition

Engineering Thermodynamics. Chapter 1. Introductory Concepts and Definition 1.1 Introduction Chapter 1 Introductory Concepts and Definition Thermodynamics may be defined as follows : Thermodynamics is an axiomatic science which deals with the relations among heat, work and properties

More information

Introduction to Turbomachinery

Introduction to Turbomachinery 1. Coordinate System Introduction to Turbomachinery Since there are stationary and rotating blades in turbomachines, they tend to form a cylindrical form, represented in three directions; 1. Axial 2. Radial

More information

Compressible Potential Flow: The Full Potential Equation. Copyright 2009 Narayanan Komerath

Compressible Potential Flow: The Full Potential Equation. Copyright 2009 Narayanan Komerath Compressible Potential Flow: The Full Potential Equation 1 Introduction Recall that for incompressible flow conditions, velocity is not large enough to cause density changes, so density is known. Thus

More information

Thin airfoil theory. Chapter Compressible potential flow The full potential equation

Thin airfoil theory. Chapter Compressible potential flow The full potential equation hapter 4 Thin airfoil theory 4. ompressible potential flow 4.. The full potential equation In compressible flow, both the lift and drag of a thin airfoil can be determined to a reasonable level of accuracy

More information

Flow Characteristic Through Convergent-Divergent Nozzle

Flow Characteristic Through Convergent-Divergent Nozzle 2018 IJSRST Volume 4 Issue 2 Print ISSN: 2395-6011 Online ISSN: 2395-602X Themed Section: Science and Technology Flow Characteristic Through Convergent-Divergent Nozzle S. Sathyapriya 1, R. Swathi 2, P.

More information

equation 4.1 INTRODUCTION

equation 4.1 INTRODUCTION 4 The momentum equation 4.1 INTRODUCTION It is often important to determine the force produced on a solid body by fluid flowing steadily over or through it. For example, there is the force exerted on a

More information

Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Introduction to Fluid Machines, and Compressible Flow Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 09 Introduction to Reaction Type of Hydraulic

More information

Section 4.1: Introduction to Jet Propulsion. MAE Propulsion Systems II

Section 4.1: Introduction to Jet Propulsion. MAE Propulsion Systems II Section 4.1: Introduction to Jet Propulsion Jet Propulsion Basics Squeeze Bang Blow Suck Credit: USAF Test Pilot School 2 Basic Types of Jet Engines Ramjet High Speed, Supersonic Propulsion, Passive Compression/Expansion

More information

Introduction to Aerospace Engineering

Introduction to Aerospace Engineering Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility

More information

The Turbofan cycle. Chapter Turbofan thrust

The Turbofan cycle. Chapter Turbofan thrust Chapter 5 The Turbofan cycle 5. Turbofan thrust Figure 5. illustrates two generic turbofan engine designs. The upper figure shows a modern high bypass ratio engine designed for long distance cruise at

More information

GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey

GAS DYNAMICS. M. Halük Aksel. O. Cahit Eralp. and. Middle East Technical University Ankara, Turkey GAS DYNAMICS M. Halük Aksel and O. Cahit Eralp Middle East Technical University Ankara, Turkey PRENTICE HALL f r \ New York London Toronto Sydney Tokyo Singapore; \ Contents Preface xi Nomenclature xiii

More information

Multistage Rocket Performance Project Two

Multistage Rocket Performance Project Two 41 Multistage Rocket Performance Project Two Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078 Project Two in MAE 3293 Compressible Flow December

More information

Compressible Fluid Flow

Compressible Fluid Flow Compressible Fluid Flow For B.E/B.Tech Engineering Students As Per Revised Syllabus of Leading Universities in India Including Dr. APJ Abdul Kalam Technological University, Kerala Dr. S. Ramachandran,

More information

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

More information

Therefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V

Therefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control

More information

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions.

1. (20 pts total 2pts each) - Circle the most correct answer for the following questions. ME 50 Gas Dynamics Spring 009 Final Exam NME:. (0 pts total pts each) - Circle the most correct answer for the following questions. i. normal shock propagated into still air travels with a speed (a) equal

More information

Fanno Flow. Gas Dynamics

Fanno Flow. Gas Dynamics Fanno Flow Simple frictional flow ( Fanno Flow Adiabatic frictional flow in a constant-area duct * he Flow of a compressible fluid in a duct is Always accompanied by :- ariation in the cross sectional

More information

Chapter 5: The First Law of Thermodynamics: Closed Systems

Chapter 5: The First Law of Thermodynamics: Closed Systems Chapter 5: The First Law of Thermodynamics: Closed Systems The first law of thermodynamics can be simply stated as follows: during an interaction between a system and its surroundings, the amount of energy

More information

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30

SPC Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 SPC 307 - Aerodynamics Course Assignment Due Date Monday 28 May 2018 at 11:30 1. The maximum velocity at which an aircraft can cruise occurs when the thrust available with the engines operating with the

More information

ENT 254: Applied Thermodynamics

ENT 254: Applied Thermodynamics ENT 54: Applied Thermodynamics Mr. Azizul bin Mohamad Mechanical Engineering Program School of Mechatronic Engineering Universiti Malaysia Perlis (UniMAP) azizul@unimap.edu.my 019-4747351 04-9798679 Chapter

More information

Flight Vehicle Terminology

Flight Vehicle Terminology Flight Vehicle Terminology 1.0 Axes Systems There are 3 axes systems which can be used in Aeronautics, Aerodynamics & Flight Mechanics: Ground Axes G(x 0, y 0, z 0 ) Body Axes G(x, y, z) Aerodynamic Axes

More information

AOE 3114 Compressible Aerodynamics

AOE 3114 Compressible Aerodynamics AOE 114 Compressible Aerodynamics Primary Learning Objectives The student will be able to: 1. Identify common situations in which compressibility becomes important in internal and external aerodynamics

More information

THE FIRST LAW APPLIED TO STEADY FLOW PROCESSES

THE FIRST LAW APPLIED TO STEADY FLOW PROCESSES Chapter 10 THE FIRST LAW APPLIED TO STEADY FLOW PROCESSES It is not the sun to overtake the moon, nor doth the night outstrip theday.theyfloateachinanorbit. The Holy Qur-ān In many engineering applications,

More information

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area

Lecture-2. One-dimensional Compressible Fluid Flow in Variable Area Lecture-2 One-dimensional Compressible Fluid Flow in Variable Area Summary of Results(Cont..) In isoenergetic-isentropic flow, an increase in velocity always corresponds to a Mach number increase and vice

More information

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory?

for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? 1. 5% short answers for what specific application did Henri Pitot develop the Pitot tube? what was the name of NACA s (now NASA) first research laboratory? in what country (per Anderson) was the first

More information