Steam is expanded in a set of nozzles from 10 bar and 200ºC to 5 bar. What type of nozzle is it ? Neglecting the initial velocity find minimum area of the nozzle required to allow a flow of 3 kg/s under the given conditions. Assume that expansion of steam to be isentropic.(AMIE Summer, 1999)

Question

Steam is expanded in a set of nozzles from 10 bar and 200ºC to 5 bar. What type of nozzle is it ? Neglecting the initial velocity find minimum area of the nozzle required to allow a flow of 3 kg/s under the given conditions. Assume that expansion of steam to be isentropic. (AMIE Summer, 1999)

Accepted Answer

Steam pressure at the entry to the steam nozzles,

[latex] p_{1} = [/latex] 10 bar, 200ºC

Steam exit pressure, [latex] p_{1} [/latex] = 5 bar

We know that, [latex] \frac{ p_{2} }{ p_{1} } = (\frac{2}{n + 1})^{\frac{n}{n - 1}} = [\frac{2}{(13 + 1)}] ^{\frac{1.3}{0.3}} [/latex]

= [latex] (\frac{2}{2.3})^{4.333} [/latex] = 0.5457

∴ [latex] p_{2} = p_{1} × 0.5457 = 10 × 0.5457 \simeq 5.5 bar [/latex]

Since throat pressure ([latex] p_{2} [/latex]) is greater than the exit pressure, the nozzle used is convergent-divergent nozzle. The minimum area will be at throat, where the pressure is 5.5 bar.

From Mollier chart, [latex] h_{1} - h_{2} \simeq 120 kJ / kg [/latex]

Specific volume, v [latex] \simeq [/latex] 0.345 m³/kg

Velocity at the throat, [latex] C_{2} = 44.72 \sqrt{120} = 489.88 m/s [/latex]

Throat area, [latex] A_{2} = \frac{\dot{m}v}{C_{2}} = \frac{3 × 0.345}{489.88}[/latex] = 0.0021 m².

Question 5.3: Steam is expanded in a set of nozzles from 10 bar and 200ºC ...

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