Figure 1.
Sketch of the liquid jet flow exiting an elliptical orifice.
Figure 2.
Experimental and computational models describe the shape of the urine flow pattern.
(a) Computational fluid dynamics (CFD) indicates the pressure distribution and shape of a liquid stream exiting from an elliptical orifice such as the urethral meatus. (b) Experimental models with a rigid walled elliptical orifice produced the characteristic flow pattern of the urine stream (,
).
Figure 3.
Computational modelling solves the 3-dimensional jet flow from a wide range of orifice shapes.
Two examples are shown here for aspect ratios () of 3 and 6, and
,
.
Figure 4.
Experimental and computational models show the influence of flow rate and orifice size and geometry on the shape of the jet flow.
(a) For any given orifice, there was a perfect linear correlation between flow rate, and wavelength,
, with excellent agreement between the experimental and CFD analysis as shown for an orifice with cross sectional area and
of
and
respectively. The relationship between flow rate and wavelength was also estimated using the method of Rayleigh which assumes small amplitude perturbations from a cylindrical jet in contrast to the current CFD analysis. For large amplitude oscillations which occur when aspect ratios
, the Rayleigh method significantly under estimated the wavelength. (b) The dilation parameter,
, is dependent on the cross sectional area and the aspect ratio (
) and therefore may be used to describe urethral/meatal opening. Comparisons between the CFD and experimental data for a range of orifice shapes show an excellent agreement in the values of
.
Figure 5.
The human urine flow stream shows a characteristic pattern that is dependent on flow rate and orifice dilation as predicted by the experimental and computational modelling.
(a) Selected video images from which the wavelength was measured by calibrating against a rule held alongside the flow stream. (b) Representative plot for an individual void showing the temporal change in instantaneous flow rate, , and wavelength,
. The wavelength is a function of both the flow rate and the shape and size of the meatus. (c) The opening of the urethral orifice during voiding was quantified by the minimum diameter of the meatal ellipse (
) measured from the video images. The size and shape of the orifice is also characterised by the dilation parameter
, such that a reduction in
corresponds to an increase in opening. (d) The resulting plot of wavelength,
, versus flow rate,
, shows a clear correlation. Note that the relationship is non-linear due to the changes in the meatal opening.
Figure 6.
Self measurement of the maximum wavelength provides an estimate of the peak urine flow rate for healthy males, but requires individual calibration for patients undergoing treatment for urethral obstruction.
(a) Plot of versus
showing a statistically significant positive correlation for healthy men (
, solid line) but not for the patient cohort (dashed line). A peak flow rate
was considered as abnormally low (red region). The green region represents the
confidence envelope for
values based on data from the normal group. Individuals with
and
values within the yellow region have a normal flow rate but reduced urethral dilation. (b) Frequency distributions for the dilation parameter,
, for the healthy and patient groups showing a statistically significant difference suggesting that the latter have reduced urethral opening.
Figure 7.
Flow rate measurement accuracy can be improved if an individual's dilation parameter is calibrated for.
The open symbols show the predicted based on
multiplied by the sample mean value of
/
. The closed symbols show the predicted
based on an individual's
measured at the first recorded voiding event. The open symbols show the increased scatter if the sample mean
value is used rather than the individual's
.