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From the above analysis, the pressure drop along the HADT, which is also the pressure
difference between the chamber and the mask, can be expressed as:
du
P P P f u L
(2.22)
Ta 2
T
C M (2 T T Ta
) T
DTi dt
The HADT inner wall is corrugated. However, since the relative roughness is small, the
pitch is long and the Reynolds number is no more than 10 5 . This inner surface friction
may not be too much different from a smooth tube. Darcy-Weisbach friction factor may
be applicable [42]:
0.3164
fT (2.23)
Re
After substituting Eq. (2.23) in, Eq. (2.22) can be rearranged as follow to calculate
pressure in the mask:
25
0.25
Ti
P 0.6328
du
P L [ u u ]
2.3.6 Mask air mass balance
0.75
C T
M Ta
T T T
Ta
L D
T
TiTa 0.25
DTi
( )
dt
Ta
(2.24)
The mask is the interface for patient to use the CPAP machine. The mask is strapped
tightly onto patient’s face to prevent leakage. When a patient inhales, air flows into the
mask through an elbow with bias vent holes and gets mixed with air already in the mask
before being inspired into the patient’s upper airway. When the patient exhales, exhaled
air from patient gets mixed before leaving the mask. One of the objectives for this
project is to investigate the influence of mask capacity on the CPAP machine’s
performance.