# 11.7.6.1: Variations of The Tube Length ($$ld$$) Effects

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In the analysis of this effect, it should be assumed that back pressure is constant and/or low as possible as needed to maintain a choked flow. First, the treatment of the two branches are separated.

## Fanno Flow Subsonic branch

Fig. 11.24 The effects of increase of $$\dfrac{4\,f\,L}{D}$$ on the Fanno line.

For converging nozzle feeding, increasing the tube length results in increasing the exit Mach number (normally denoted herein as $$M_2$$). Once the Mach number reaches maximum ($$M=1$$), no further increase of the exit Mach number can be achieved with same pressure ratio mass flow rate. For increase in the pipe length results in mass flow rate decreases. It is worth noting that entrance Mach number is reduced (as some might explain it to reduce the flow rate). The entrance temperature increases as can be seen from Figure 11.24. The velocity therefore must decrease because the loss of the enthalpy (stagnation temperature) is "used.'' The density decrease because $$\rho = \dfrac{P }{ R\, T}$$ and when pressure is remains almost constant the density decreases. Thus, the mass flow rate must decrease. These results are applicable to the converging nozzle. In the case of the converging–diverging feeding nozzle, increase of the dimensionless friction, $$ld$$, results in a similar flow pattern as in the converging nozzle. Once the flow becomes choked a different flow pattern emerges.

This page titled 11.7.6.1: Variations of The Tube Length ($$ld$$) Effects is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.
This page titled 11.7.6.1: Variations of The Tube Length ($$ld$$) Effects is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Genick Bar-Meir via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.