The simplified Bernoulli equation relates fluid convective energy derived from flow velocities to a pressure gradient and is commonly used in clinical echocardiography to determine pressure differences across stenotic orifices. Its application to pulmonary venous flow has not been described in humans. Twelve patients undergoing cardiac surgery had simultaneous high-fidelity pulmonary venous and left atrial pressure measurements and pulmonary venous pulsed Doppler echocardiography performed. Convective gradients for the systolic (S), diastolic (D), and atrial reversal (AR) phases of pulmonary venous flow were determined using the simplified Bernoulli equation and correlated with measured actual pressure differences. A linear relationship was observed between the convective ( y) and actual ( x) pressure differences for the S ( y = 0.23 x + 0.0074, r = 0.82) and D ( y = 0.22 x + 0.092, r = 0.81) waves, but not for the AR wave ( y = 0.030 x + 0.13, r = 0.10). Numerical modeling resulted in similar slopes for the S ( y = 0.200 x − 0.127, r = 0.97), D ( y = 0.247 x − 0.354, r= 0.99), and AR ( y = 0.087 x − 0.083, r = 0.96) waves. Consistent with numerical modeling, the convective term strongly correlates with but significantly underestimates actual gradient because of large inertial forces.
Investigation of the Flow Structure in the Tundish with the Use of Rans and Les Methods
