Abstract
A viscous one-dimensional compressible pipe flow under gravity effect is studied analytically. The compressible one-dimensional pipe flow with friction is called Fanno flow and the solution is given by analytical formula. In gas dynamics, the gravity effect is minimal and it is not included in the equations. However, it was shown by the present author that the elevation of a pipe could change the flow conditions in a one-dimensional compressible potential flow under gravity. The sonic condition is reached at the maximum height for an inviscid pipe flow. In this paper, the gravity effect is extended to the viscous one- dimensional pipe flow. Subsonic–supersonic transition is also possible by up and down of the pipe as in the inviscid flow, and it is found that the sonic condition deviates from the peak position of the pipe.
Highlights
In gas dynamics, the gravity effect is negligible and not included in the governing equations
The gravity effect is not evident in an ordinary air flow, it can be noticeable near the sonic condition and in the low acoustic velocity like cryogenics
The viscous pipe flow is known as Fanno flow and choke occurs at the exit of the pipe
Summary
The gravity effect is negligible and not included in the governing equations. The effect is evident in astrophysics, i.e. Bondi flow [1], [2]. The gravity effect is not evident in an ordinary air flow, it can be noticeable near the sonic condition and in the low acoustic velocity like cryogenics. This sonic condition occurs at the peak location of a pipe and the gravity has a similar effect to that of the throat of a Laval nozzle [3]. The gravity term is added to the Fanno flow equations
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