GOVERNMENT ENGINEERING COLLEGE VALSAD SUB : FLUID MECHANICS DEPT. : CIVIL (3 rd sem)

GROUP-14 1.Sidharth Shah Shiraz Solanki Deepak Someshwar SUBMITTED TO : PROF. KULDEEP PATEL

INTRODUCTION  Compressible fluid flow :- In this fluid flow, the density of the fluid does not remain constant during the process of flow.  Example:- # Flow of gases through nozzles and orifices. # Flow of gases in compressors. # The flight of projectiles and aeroplanes moving at high altitude with high velocity. # Water hammer and acoustics.

 Incompressible fluid flow :- In this fluid flow, the density of the flowing fluid is constant during the process of flow. All real fluid flow are compressible fluid flow. But in some cases, i.e. Flow of liquids witch undergo only small changes in density even over wide range of velocity and pressure changes. Hence liquid flow can be assumed incompressible fluid flow.

BASIC GAS EQUATIONS  Bernoulli’s (energy) Equation  Momentum Equation  Continuity Equation

 Continuity Equation:- For one dimensional compressible flow, the mass flow rate(kg/sec) given by m = AV where = mass density kg/ A = cross section area of duct V = velocity of fluid, m/s

 According to law of conservation mass mass flow rate = constant   AV = constant differentiating the above equation dividing by  AV, Continuity Equation in differential form.

 Bernoulli’s(energy) equation:- We know the Euler equation constant constant For Incompressible fluid flow, the But in compressible fluid flow Bernoulli’s equations are different for iso- thermal and adiabatic process.

 Bernoulli’s equation for isothermal process:- in case of isothermal process, P  = constant suppose, P  = C  = P/C putting in energy equ.

 Dividing by g, (K=constant) Bernoulli’s equation for compressible flow undergoing isothermal process.

 Bernoulli’s equation for adiabatic process. In case of an adiabatic process, constant Suppose, C  Putting in Bernoulli’s equation.



 dividing by g, ( K=constant) Bernoulli’s equation for compressible flow undergoing adiabatic process.

Momentum equation:- The momentum per second known as momentum flux. The momentum flux = mass flow rate  velocity of fluid = mass per second  velocity =  AV  V =  A The rate of change of momentum in the X- direction = mass per second  change of velocity =  AV = net force in the direction of x

Mach Number (M) Mach Number is defined as “ratio of velocity of fluid to velocity of sound in fluid”. The Mach Number is dimensionless number. We know that, M =

MACH CONE :- When M>1, propagation sphere always legs behind the projectile,if we draw a tangent to a different circle of propagated pressure wave on both sides of circle, we gets a cone with vertex at E. This cone is known as Mach cone.

Area velocity relationship for compressible flow :- We know that continuity equation for compressible flow.  AV=constant, The above equation say that with change of area A,the velocity V and density are changed. Differentiating above equation, we get

Thus this is the area velocity relationship of compressible fluid flow.

Propagation of sound wave

Stagnation properties :- Stagnation Point – it is a point in fluid stream where the velocity of flow is become zero and kinetic energy converted into pressure energy. Stagnation properties – the value of pressure, density and temperature at stagnation point is called the stagnation properties.

Thus this is the stagnation property of compressible fluid

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