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State and derive Steady flow energy equation and apply it to a boiler, condenser, nozzle and turbine.
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Steady Flow System - Defined as the system in which the mass flow rate into the system is equal to mass flow rate out of the system.

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Mass flow rate in m1 = Mass flow rate out, m2 = constant = m

Consider the flow of fluid through a pipe of cross sectional area A,

specific volume V, at Velocity C.

volume flow rate = A (m2) × C (m/s)

Mass flow rate m (kg/s) = Volume flow rate / Specific volume

m =AC/V = ρAC= Continuity Equation

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Heat transfer rate to the system = Q [ J/s ]

Work transfer rate from the system = W [ J/s ]

Assumptions-

  1. There is no accumulation or decrease of mass in the control volume at anytime

  2. The rate of mass transfers at inlet and exit are equal.

  3. The state and energy of the fluid at inlet, exit and in the control volume do not vary with time.

4.The rate of heat and work transfers across the control volume are constant.

S.F.E.E. on unit time basis -

Total energy flow rate into the control = total energy flow rate out of control volume.

Q+ m [Internal energy + Flow work + KE + PE ]1 = W +m [ Internal energy + Flow work + KE + PE ]2

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Boiler - A boiler is a device used for steam generation at constant pressure.

Heat is supplied to boiler drum externally by combustion of fuel in presence of air. Products of combustion are called Flue gases.

For a boiler - W =0, ΔK.E.=0 and Δ P.E.=0

On using these conditions S.E.E.Equation,

Q = m (h2 - h1)

Condenser -

A condenser is a device used for steam condensation at constant pressure.

For a condenser - W =0, ΔK.E.=0 and Δ P.E.=0

On using these conditions S.E.E.Equation,

Q = m (h1 – h2)

Nozzle: In case of a nozzle as the enthalpy of the fluid decreases and pressure drops simultaneously the flow of fluid is accelerated. This is generally used to convert the part of the energy of steam into kinetic energy of steam supplied to the turbine.

For this system, ∆PE=0,W=0,Q=0

Applying the energy equation to the system,

$h1+(C1^2/2) =h2+(C2^2/2)$

Turbine: In a steam or gas turbine steam or gas is passed through the turbine and part of its energy is converted into work in the turbine. This output of the turbine runs a generator to produce electricity. The steam or gas leaves the turbine at lower pressure or temperature.

Applying energy equation to the system,

Here, Z1=Z2

$h1+(C1^2/2)−Q=h2+(C2^2/2)+W$

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