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From the continuity equation, we have Substituting Eq. (6.17) in Eq. (6.22), the flow per unit area can be expressed in terms of stagnation pressure, stagnation temperature, Mach number, and gas properties. At the throat, M = 1, and therefore, the flow per unit area at the throat,  can be found by setting M = 1 in Eq. (6.23). The…

The relation between enthalpy h, stagnation enthalpy h0, and kinetic energy  is: For an ideal gas with constant specific heat, Eq. (6.15) can be written as: Since  = γRT, where γ = cp0/cv0 For an isentropic process, Values of  are given as a function of M in Table 6.1 for the value of γ = 1.40.   Table 6.1 One-dimensional insentropic compressible-flow functions for an ideal gas with constant specific heat and…

A nozzle with both converging and diverging section is shown in Fig. 6.11. For the control volume shown, the following relations can be written: First law: Property relation Continuity equation:   ρAc = ṁ = const. By logarithmic differentiation, we get Combining Eqs (6.11) and (6.12), we have Substituting this in Eq. (6.13), we have Since the flow is isentropic, and therefore, Figure…

The isentropic expansion of superheated steam from supply pressure p1 to back pressure pb can be represented on the Mollier diagram by line AE, as shown in Fig. 6.5. During expansion, change of phase must start at point B where the pressure line p2 meets the saturation line. However, in nozzles, under certain conditions, this phenomenon of condensation does not occur at…

Nozzle efficiency, ηn is a factor that takes into account the effect of friction during expansion of steam in the nozzle. It is defined as: The exit velocity of steam considering friction is: where K = 

The exit velocity of steam for a given pressure drop is reduced due to the following reasons: Most of these losses occur beyond the throat in the divergent section of the nozzle as the length and the velocity of steam is much higher there. The effects of these friction losses are as follows: The effect…

From Eq. (6.5), maximum mass flow rate of steam can be obtained as   As p2 is gradually reduced, the discharge gradually increases and becomes maximum as critical pressure is approached, as shown in Fig. 6.3. Figure 6.3 Discharge v’s pressure ratio in a nozzle

From Eq. (6.4), we have The mass flow rate per unit area is maximum at the throat because it has minimum area of cross-section. Therefore,  will be maximum when  is maximum Equation (6.5) gives the critical pressure ratio at which the discharge through the nozzle is maximum. Substituting for  from Eq. (6.5), we get where cs2 = velocity of sound at exit of…

The mass flow of steam per second is flowing with velocity c2 through a cross-sectional area A2, and specific volume v2 is: Now, v2 = v1  Also, from Eq. (6.3), we have  

The following assumptions are made: Consider the flow of steam through a nozzle, as shown in Fig. 6.2. Applying the energy equation to sections 1 and 2 at entrance and exit of nozzle, we have Usually c1 = 0, where (Δh)isen = h1 − h2 = isentropic enthalpy change, kJ/kg Figure 6.2 Flow through a nozzle 1 Flow of Steam Through the Nozzle Let pvn =…