Fig. 2 The schematic of the water hammer test rig More

Fig. 3 The location of the instrument More

Fig. 4 Pressure taps arrangement More

Fig. 5 Amplitude of pressure signal in the test rig pressure measurement for two tubing length More

Fig. 6 The pressure oscillation and error of flowrate with different endpoints in the pressure-time method for measured data between sections B and D More

Fig. 7 Histogram of estimated flowrate based on MCM More

Fig. 8 Histogram of estimated error based on MCM-vertical lines area of probability with 95% confidence More

Fig. 9 Flowrate error between section D and E with fourassumptions: constant α and constant friction factor ( α Con − f Con ), constant α and quasi-steady friction factor ( α Con − f QS ), quasi-steady α and constant friction factor ( α QS  −  f Con ), quasi-steady α , and quasi-ste... More

Fig. 10 Flowrate error for three cases (sections C and D, sections B and C, and sections B and D) with the quasi-steady assumption and friction factor coefficient. The bars represent the random uncertainty with the 95% confidence. More

Fig. 11 The concentric reducer geometry used for derivation of equations More

Fig. 1 Illustration of geometry reconstruction workflow from 4D MRI. O1-O4 represent outlets; BCA: brachiocephalic artery, LCCA: left common carotid artery, LSA: left subclavian artery, and DA: descending aorta. More

Fig. 2 Computational mesh used for the simulations and associated element quality histogram. Inset shows a cross section of the mesh where the boundary layer elements can be observed. More

Fig. 3 Schematic of the 3-element Windkessel model. R 1 and R 2 represent the proximal and distal resistances of branching vessels, respectively. C represents the compliance of the arterial wall. More

Fig. 4 Time-averaged velocity field at the domain inlet and corresponding 4D MRI data More

Fig. 5 Flow and pressure waveforms in different branches (BCA: brachiocephalic artery, LCCA: left common carotid artery, LSA: left subclavian artery, and DA: descending aorta) More