Abstract
The behaviour of the flow regime downstream of the choke point in a flow-limited water filled penrose tube was examined. The transmural pressure along the length of the tube was measured with a moveable side-tap catheter and tube area and stiffness were derived from the tube's static pressure/area curve. Stable supercritical flow, in which the local fluid velocity is greater than the local speed of wave propagation, was demonstrated to extend downstream from the choke point. Speed ratios (fluid velocity divided by tube wavespeed) as large as ten were measured in tube segments in which the area changed so gradually with length as to rule out significant longitudinal tension effects on the tube pressure/area curve. The predicted transition from supercritical to subcritical velocity, or elastic jump, was also studied. Sidewall friction along the jump and longitudinal tension effects due to longitudinal wall curvature were found to be significant factors governing the variation of pressure within the jump. Taking friction into account, the flow momentum equation was found to describe the overall size of the elastic jump adequately if its upstream and downstream limits were taken at points where wall curvature effects were negligible.
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Abbreviations
- A :
-
tube cross-sectional area
- a :
-
disturbance component of tube area
- B :
-
static recoil component of transmural pressure
- b :
-
tube width
- C :
-
wave propagation speed relative to fluid
- f :
-
friction factor=wall shear stress/1/2ρU 2
- k :
-
wave number=2π/wavelength
- P :
-
transmural pressure
- P f, Pc :
-
fluid pressure and elastic tube pressure, respectively
- dP/dA :
-
tube stiffness
- Q :
-
flow rate
- Q max :
-
maximum flow rate
- q :
-
disturbance component of tube flow rate
- S :
-
speed ratio=U/C
- T :
-
longitudinal tension
- t :
-
time
- U :
-
mean fluid velocity
- V :
-
wave-propagation speed relative to tube
- W :
-
tube cross-sectional perimeter
- x :
-
tube axial displacement
- Z :
-
amplitude of area disturbance
- ρ:
-
fluid density
- μ:
-
fluid viscosity
- ω:
-
wave frequency
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Elliott, E.A., Dawson, S.V. Fluid velocity greater than wavespeed and the transition from supercritical to subcritical flow in elastic tubes. Med. Biol. Eng. Comput. 17, 192–198 (1979). https://doi.org/10.1007/BF02440928
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DOI: https://doi.org/10.1007/BF02440928