One-dimensional flow with friction: Difference between revisions
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Figure~\ref{fig:friction:Ts} shows the Fanno flow process in a <math>Ts</math>-diagram. The dashed line represents the sonic temperature, which means that the flow states along the process line above the dashed line are subsonic flow states and the part of the line below the dashed line represents supersonic flow states. In both subsonic and supersonic flow addition of friction leads to a change in temperature in the direction towards the sonic temperature, i.e. the flow approaches sonic conditions (<math>M=1</math>). When the length of the pipe through which the fluid flows is equal to the length at which the flow is sonic, the flow is choked (friction choking) and further pipe length cannot be added without a change in the flow conditions. For an initially subsonic flow, a pipe longer than <math>L^\ast</math>, the change in flow conditions is analogous to the what happens for addition of heat to a subsonic flow that has reached sonic state discussed in the previous section. The inlet conditions will change such that the massflow is reduced without changing the inlet total conditions such as the pipe length is equal to <math>L^\ast</math> for the new inlet conditions. | Figure~\ref{fig:friction:Ts} shows the Fanno flow process in a <math>Ts</math>-diagram. The dashed line represents the sonic temperature, which means that the flow states along the process line above the dashed line are subsonic flow states and the part of the line below the dashed line represents supersonic flow states. In both subsonic and supersonic flow addition of friction leads to a change in temperature in the direction towards the sonic temperature, i.e. the flow approaches sonic conditions (<math>M=1</math>). When the length of the pipe through which the fluid flows is equal to the length at which the flow is sonic, the flow is choked (friction choking) and further pipe length cannot be added without a change in the flow conditions. For an initially subsonic flow, a pipe longer than <math>L^\ast</math>, the change in flow conditions is analogous to the what happens for addition of heat to a subsonic flow that has reached sonic state discussed in the previous section. The inlet conditions will change such that the massflow is reduced without changing the inlet total conditions such as the pipe length is equal to <math>L^\ast</math> for the new inlet conditions. | ||
{{ | {{InfoBox|<math> | ||
M_{1^\prime} = f(L^\ast) | M_{1^\prime} = f(L^\ast) | ||
</math><br><br><math> | </math><br><br><math> | ||
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</math><br><br><math> | </math><br><br><math> | ||
u_{1^\prime} = M_{1^\prime}a_{1^\prime} | u_{1^\prime} = M_{1^\prime}a_{1^\prime} | ||
</math> | </math>}} | ||
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