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Lecture 12 FIRST LAW ANALYSIS FORLecture 12 – FIRST- LAW ANALYSIS FOR A CONTROL VOLUME

Throttling valve

Throttling valves are any kind of flow-restricting devicesg y g

that cause a significant pressure drop in the fluid.

f fThe pressure drop in the fluid is often accompanied by a large

drop in temperature, and for that reason throttling devices

are commonly used in refrigeration and air-conditioning

applications.

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Throttling valve

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Throttling valve

Helium is adiabatically throttled from 1.2 MPa,y20°C, to a pressure of 100 kPa. The diameter ofthe exit pipe is so much larger than the inlet pipeth t th i l t d it l iti l Fi dthat the inlet and exit velocities are equal. Findthe exit temperature of the helium and the ratioof the pipe diametersof the pipe diameters.

BITS Pilani, Pilani Campus

BITS Pilani, Pilani Campus

Helium is adiabatically throttled from 1.2 MPa, 20°C, to a pressure of 100 kPa. The diameter of the exit pipe is so much larger than the inlet pipe that the inlet and exit velocities are equal. Find the exit temperature of the helium and the ratio of the pipe diameters.

wgZV1hgZV1hq 2i

2ii +++=+++ wgZV

2hgZV

2hq eeeiii ++++++

ei hh =⇒

Assuming for Helium as an ideal gasAlso please note here that for Helium specific heat remains

C20TT oei ==⇒

constant (Fig. 5.17)

eee

iii

VAmVAmNow === &&e

ei

i vvo

288683.0PPdAie

ii ===∴

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288683.0PPdA ieee

∴

Turbine

A rotary steady-state machine whose purpose is to produce shaft work ( powerpurpose is to produce shaft work ( power on rate basis) at the expense of energy of flowing fluid. Eg. Steam turbine, Gas turbine, Hydraulic turbine.

Normally turbine process is adiabatic.

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Turbine

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Turbine

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Turbine

A small adiabatic turbine, shown in Fig., is operatedt t l d b th ttli 0 25 k / t l tat part load by throttling a 0.25 kg/s steam supply at

1.4 MPa, 250°C down to 1.1 MPa before it entersthe turbine and the exhaust is at 10 kPa If thethe turbine and the exhaust is at 10 kPa. If theturbine produces 110 kW, find the exhausttemperature (and quality if saturated).p ( q y )

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A small adiabatic turbine, shown in Fig., is operated at part load by throttling a 0.25 kg/s steam supply at 1.4 MPa, 250°C down to 1.1 MPabefore it enters the turbine and the exhaust is at 10 kPa. If the turbine

d 110kW fi dth h tt t ( d lit if t t d)

Control volume: throttle valve

produces 110 kW, find the exhaust temperature (and quality if saturated).

Steady state process, q = 0 and w = 0. single stream entry and exitAssume no change in kinetic or potential energy. g p gyThe energy equation then reduces to

ZV1hZV1h 22 wgZV21hgZV

21hq e

2eei

2ii +++=+++

h1 = h2 = 2927.22 kJ/kg

BITS Pilani, Pilani Campus

A small adiabatic turbine, shown in Fig., is operated at part load by throttling a 0.25 kg/s steam supply at 1.4 MPa, 250°C down to 1.1 MPabefore it enters the turbine and the exhaust is at 10 kPa. If the turbine

d 110kW fi dth h tt t ( d lit if t t d)

Control Volume: Turbine,

produces 110 kW, find the exhaust temperature (and quality if saturated).

Steady state process, adiabatic turbine q=0, Assume no change in kinetic or potential energy. The energy equation then reduces to gy q

wgZV21hgZV

21hq e

2eei

2ii +++=+++

specific work: w = 110/0.25 = 440 kJ/kg h1 = h2 = h3 + w = 2927.2 kJ/kg

22

h3 = 2927.22 - 440 = 2487.22 kJ/kg h < hg 2487.22 = 191.81 + x3 × 2392.82

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3x3 = 0.9593, T = 45.81°C

Turbine

A steam turbine (adiabatic) receives water at 15 MPa, 600°C at a rate of 100 kg/s shown in Fig In the middle section 20 kg/sa rate of 100 kg/s, shown in Fig. In the middle section 20 kg/s is withdrawn at 2 MPa, 350°C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine power output.

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A steam turbine (adiabatic) receives water at 15 MPa, 600°C at a rate of 100 kg/s, shown in Fig. In the middle section 20 kg/s is withdrawn at 2 MPa, 350°C, and the rest exits the turbine at 75 kPa, and 95% quality. Assuming no heat transfer and no changes in kinetic energy, find the total turbine power g gy, poutput.

321 mmm &&& +=

332211 hmhmWhm T &&&& ++=

t blf kg/kJ963136hkg/kJ33582htablefrom kg/kJ96.3136h,kg/kJ3.3582h 21 ==

59.227895.036.384hxhh f3f3 ×+=+=kg/kJ02.2549

59.227895.036.384hxhh fg3f3=

×++

kW2.569,91hmhmhmW 332211T =−−= &&&&

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Compressor

Compressors, as well as pumps are devices used to p , p p

increase the pressure of a fluid. Work is supplied to these

devices from an external source through a rotating shaftdevices from an external source through a rotating shaft.

A compressor is capable of compressing the gas to very

high pressures.

Pumps work very much like compressors except that theyPumps work very much like compressors except that they

handle liquids instead of gases.

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Compressor

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Compressor

BITS Pilani, Pilani Campus

Compressor

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