Lect 17 Open Systems 2

7/29/2019 Lect 17 Open Systems 2

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ME 209Basic Thermodynamics

Analysis of Open Systems-2

Kannan Iyer

[email protected]

Department of Mechanical Engineering

Indian Institute of Technology, Bombay

Review of Lecture 16

Identified that Open Systems are of engineeringimportance

Derived the Conservation of Mass

Derived the Conservation of Energy

Understood the concept of flow work

Most engineering devices have one inlet and one exitand operate in steady mode and the relevantequations are

mmm ei &&& ==

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

Today, we shall look at the various engineering

devices, make relevant assumptions and apply the First

law of thermodynamics (Energy Equation)

Velocity and temperature are uniform at the inlet and

exit.

Approximations in Open Systems

At each location equilibrium property relations apply

Heat transfer is assumed zero for cases, when

Control surface is insulated

Exposed area is small

T between system and surroundings small

Common Approximations

No work transfer, if

No rotating shafts

No movement of system boundaries

Kinetic Energy Transfer Devices-I

In applications like rocket motors, steam ejectors,

there is a need to accelerate a fluid to very high

velocity

A device that accelerates fluid velocity is called a

nozzle and that which reduces velocity is called a

diffuser

Everyday experience of watering the garden

suggests that the area has to be decreased to

increase velocity. However, in Fluid Mechanics,

you will learn that at supersonic conditions it is

just the opposite

At times, a high velocity fluid has to be decelerated

to lower velocity


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Kinetic Energy Transfer Devices-II

Subsonic Nozzle Superonic Nozzle

Subsonic Diffuser Superonic Diffuser

Kinetic Energy Transfer Devices-III

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

Device area small

No moving shaft

Change in elevation

negligible

2

VV

)hh(

2

i

2

e

ei

=

Many occasions

this is negligible

)hh(2V eie =

Work Transfer Devices In many application, work is supplied to increase

the fluid pressure

The most common ones are

Compressor (Gas, High p, but low flow)

Blower (Gas, High Flow, but low p)

Pump (Liquid, all p)

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

Negligible Change in elevation

negligible

Change in KE negligible

)hh(m

Wei

CV=

&

&

Heat Transfer Devices-I

There are many heat transfer devices

The most common ones are

Boiler (To produce steam)

Condenser (To condense steam)

Heat Exchanger (To heat/cool fluids)

The construction varies from device to device,

but they can be idealized as two concentric

tubes


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Heat Transfer Devices-II

First Law can be simplified for any one tube as

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

No shaft Change in elevation

negligible


)TT(cm)hh(mQ iepieCV == &&&

Heat Transfer Devices-III

If we combine both the tubes together in our

control volume, it becomes multiple inlet

)hh(m)hh(m 2e2i21i1e1 == &&

++

+++=

e

2

eee

i

2

iiiCVCV

gz2

Vhm

gz2

VhmWQ0

&

&&&

Pressure Reduction Device

In many application the pressure of a flowing fluid

is to be reduced to control the flow. These are

called Valves

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

Negligible Change in elevation

negligible


ei hh =

No shaft

This isenthalpic process is also called throttling

Flow Measuring Device-I

A convergent divergent device operating at low

velocities is called a venturimeter and is used to

measure flow

Prior to showing the basis, let us get back the so

called Bernoullis equation from First law

+

++= )zz(g

2

VV)hh(mWQ0 ei

2

e

2

ieiCVCV

&&&

e

2

eei

2

ii gz

2

Vhgz

2

Vh ++=++

e

2

e

e

eei

2

i

i

ii gz

2

Vpugz

2

Vpu ++

+=++

+


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Flow Measuring Device-II

If the velocities are low, then in such cases flow

can be approximated to be isothermal

Further, when velocities are low, even a gas flow

can be considered incompressible

e

2ee

i

2ii gz

2

Vpgz

2

Vp++

=++

The above is incompressible Bernoullis Equation

e

2

e

e

eei

2

i

i

ii gz

2

Vpugz

2

Vpu ++

+=++

+ e

2

e

e

eei

2

i

i

ii gz

2

Vpugz

2

Vpu ++

+=++

+

Flow Measuring Device-III

Now we can deduce the expression for flow in

terms of measured pressures at 1 and 2

1

2

2

2

221

2

11 gz2

Vpgz

2

Vp++

=++

=

=

2

A

A1

V2

VVpp2

1

2

2

2

2

2

1

2

221

Thus, the final expression for Velocity at 2 is

Flow Measuring Device-IV

( )

=

21

2

2

212

A

A1

pp2V

The volumetric flow rate or mass flow rate can

now be obtained easily by multiplying by area or

the product of area and density

Lect 17 Open Systems 2

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