chapter 5 nozzle

7/27/2019 Chapter 5 Nozzle

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CHAPTER 5NOZZLE


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NOZZLE INTRODUCTION.

A nozzle is a device that increases the velocity of a fluid at

the expense of pressure.

Example: a nozzle used at the end of a garden hose


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DIFFUSER INTRODUCTION.

A diffuser is a device that increases the pressure of a fluid

by slowing it down.

Several types of pumps operate by using shaft work toturn an impeller which will increase the kinetic energy of

the fluid, followed by a diffuser that converts some of the

kinetic energy to an increased pressure.


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SKETCH


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TYPES & SHAPES OF NOZZLE

The convergent nozzle

The cross-section converges from the entry area to a

minimum area which is the exit.


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TYPES & SHAPES OF NOZZLE

Convergent divergent nozzle

It can be seen from the inlet area the nozzle converges to a

minimum area called the throat and then to the outlet area.


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Universal Gases Law

Usually, the universal gases used at two point of one streamline.

But, in practice, there was nearly none of gases rigidly follow this

rule. So, an imaginary situation ideal situation that obey this rule

was found and it called as,


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Perfect Gases Law

Where R - gas constant. (kJ/KgK)

The equation can be modified as

Where m mass (kg)To use this equation make sure V is volume (m3) NOT specific volume (m3/kg).

For kilogram-mole derivation, for m,

m = nM

Where M - molecular weight

n number of moles

And the equation become

An another perfect gas law derivation as follow,


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Specific Heat

Cp = specific heat capacity at constant pressure (kJ/kgK)

Cv = specific heat capacity at constant volume (kJ/kgK)

The sum of heat energy must be supplied to raise 1 K

temperature at constant pressure/volume.

Perfect Gas Constant

R = Cp - CvWhere R0 = 8314 kJ/kmolK standard


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Specific Heat Ratio

Note that since Cp - Cv=R, from equation, it is clear that Cp

must be greater than Cv for any perfect gas.

v

p

C

C


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Adiabatic Process (Q=0)

There was no heat transfer from nozzle to outside, so the

nozzle facing adiabatic process. Thus, the universal gas

law becomes

The above equation is applied to states 1 & 2

=


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Sub-Sonic, Sonic and Supersonic

The velocity at the throat of a correctly designed nozzle is

the velocity of sound. The flow-up to the throat is sub-

sonic while the flow after the throat is supersonic. It

should be noted that a sonic or supersonic flow requires a

diverging duct to accelerate it.


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In the same way, for a nozzle that is convergent, the fluid

will attain sonic velocity at the exit if the pressure drop

across the nozzle is large enough.

To find sonic velocity at the throat,

Where Tc Throat temperature.


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EnthalpyThe heat content of a chemical system is called the enthalpy(symbol: H)

Steady Flow EquationNozzle is a one of various steady flow processes.

Where Q heat received or rejectedW external work done

gZ potential energy

u internal energy

PV - flow or displacement energy

C2/2 kinetic energy


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Enthalpy continue.

Apply u = h +PV, the equation become,

For most nozzle problem,

Q = 0 there was no heat produce by the nozzle

W = 0 there was no moving part inside a nozzle

gZ = 0 if there was no high different between inlet and outlet.

So, the equation become


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Nozzle Velocity

Assuming point 1 is inlet and point 2 is outlet. Velocity at

point 1 is negligible because it to small rather than

velocity at point 2, and the previous steady flow equation

become


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Mach Number

In case of venturi meter (convergent-divergent nozzle),

Mach number is a ratio between local velocity and sonic

velocity (at throat)


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Critical Point

The throat of venturi meter is critical point. Besides thevelocity; pressure and temperature at this point alsodecent as critical.

The critical temperature ratio given as

And critical pressure ratio given as

Where subscript 1 - inlet of meter venturi.


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Maximum Mass Flow Rate and Cross-sectional Area

This equation can use at any point of venturi meter. It alsocan use at two point at one streamline.


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EXAMPLE 1

A fluid at 6.9 barand 93Centers a convergent nozzle

with negligible velocity, and expands isentropically into a

space at 3.6 bar. Calculate the outlet temperature and

mass flow per m2of exit area.

(a) when the fluids is helium (Cp=5.23 kJ/kgK)

(b) when the fluid is ethane (Cp=1.66 kJ/kgK)

Assume that both helium and ethane are perfect gases,

and the respective molecular weights as 4 and 30.

chapter 5 nozzle

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