Steady-flow energy equation

Solution The steady flow energy equation may be written as... 

In defining the thermal efficiency of the closed gas turbine cycle, such as the one shown in Fig. 1.2, we employed the first law of thermodynamics (in the form of the steady-flow energy equation round the cycle), which states that the heat supplied is equal to the work output plus the heat rejected, i.e. 

For the open circuit gas turbine of Fig. 1. .3, if the reactants (air and fuel My) enter at temperature T,), and the exhaust products (M. - - My) leave at temperature T4. then the steady-flow energy equation yields... 

If the same quantities of fuel and air were supplied to a calorific value experiment at Tq (Fig. 1.7) then the steady-flow energy equation for that process would yield... 

From the steady-flow energy equation, the work output in an actual (irreversible) flow through a control volume CV, between states X and Y in the presence of an environment at To (Fig. 2.2), is... 

For a real (irreversible) flow process through the control volume CV between fluid states X and Y (Fig. 2.4), with the same heat rejected at temperature T [Q x = [0rev]x)> the work output is [WcvJx. Heat [Qq x Iso be transferred from CV directly to the environment at Tq. From the steady-flow energy equation,... 

We assume low velocity (constant pressure) mixing of the extra cooling gas mass flow (ifi) at absolute temperature T2 with the gas stream (of unit mass flow), which has been heated to the maximum temperature = Tg. From the steady flow energy equation, if both streams have the same specific heat (Cp), it follows that... 

In the simplified a/s analysis of Section 4.2 we assumed identical and constant specific heats for the two streams. Now we assume semi-perfect gases with specific heats as functions of temperature but we must also allow for the difference in gas properties between the cooling air and the mainstream gas (combustion products). Between entry states (mainstream gas 3g, and cooling air, 2c) and exit state 5m (mixed out), the steady flow energy equation, for the flow through control surfaces (A + B) and C, yields, for a stationary blade row,... 

In an experiment to determine the calorific value of the fuel at temperature 1, . and for the same fuel flow the steady flow energy equation would yield... 

But of course these two equations may be combined with Eq. (6.12) to give the steady flow energy equation for the whole plant as... 

But if combustion is adiabatic, then the steady flow energy equation for the open-circuit gas turbine (with exhaust of enthalpy (//p)s leaving the HRSG and entering the exhaust stack with a temperature Ts greater than that of the atmosphere. To) is... 

The quantity >p requires discussion. The steady flow energy equation for the WHB is... 

This can be solved using the steady-flow energy equation ... 

The Steady Flow Energy Equation relates the changes in potential and kinetic energy, and enthalpy of streams flowing in and out of a control volume, to the rate of heat transfer to, and the rate of shaft work from, the control volume. Here the generation term is zero. If a chemical reaction were occurring within the control volume, the heat of reaction would need to be accounted for in a generation term. Note that if we are... 

Mechanical Energy Balance Equation. Assuming no heat transfer to or from the surroundings (q = 0) and that frictional losses end up being dissipated as heat, the Steady Flow Energy Equation for a constant density fluid becomes ... 

When the fluid is compressible, an energy equation must be written which will take into account changes in internal thermal energy of the system and the corresponding changes in temperature. For a one-dimensional flow system this equation is the steady-flow energy equation for a control volume,... 

The steady flow energy equation states that the upstream stagnation enthalpy, Hi = (h + + gz)i, differs from the downstream value H2 only... 

A very common application of the steady flow energy equation is for low speed flow with no shaft work and negligible viscous work, such as liquid flow in pipes. For this case we may write the energy balance relation as ... 

Comparing equation (1) to the steady-flow energy equation (equation (2)) illustrates the significant difference between the two properties energy and availability ... 

For a single inlet and outlet, the mass flow rate may be divided out of Equation 23.42 using Equations 23.13 and 23.14, producing the steady flow energy equation for single inlet... 

There is no shaft work then, the steady-flow energy equation can be written... 

The qualities, and x, are computed from the steady flow energy equation. Since enthalpy data are available and since the experiments are adiabatic, the computational form is ... 

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