Aims: Echocardiography and tomographic imaging have documented dynamic changes in aortic stenosis (AS) geometry and severity during both the cardiac cycle and stress-induced increases in cardiac output. However, corresponding pressure gradient vs. flow relationships have not been described. Methods and results: We recruited 16 routine transcatheter aortic valve implantations (TAVI's) for graded dobutamine infusions both before and after implantation; 0.014″ pressure wires in the aorta and left ventricle (LV) continuously measured the transvalvular pressure gradient (ΔP) while a pulmonary artery catheter regularly assessed cardiac output by thermodilution. Before TAVI, ΔP did not display a consistent relationship with transvalvular flow (Q). Neither linear resistor (median R2 0.16) nor quadratic orifice (median R2 < 0.01) models at rest predicted stress observations; the severely stenotic valve behaved like a combination. The unitless ratio of aortic to left ventricular pressures during systolic ejection under stress conditions correlated best with post-TAVI flow improvement. After TAVI, a highly linear relationship (median R2 0.96) indicated a valid valve resistance. Conclusion: Pressure loss vs. flow curves offer a fundamental fluid dynamic synthesis for describing aortic valve pathophysiology. Severe AS does not consistently behave like an orifice (as suggested by Gorlin) or a resistor, whereas TAVI devices behave like a pure resistor. During peak dobutamine, the ratio of aortic to left ventricular pressures during systolic ejection provides a 'fractional flow reserve' of the aortic valve that closely approximates the complex, changing fluid dynamics. Because resting assessment cannot reliably predict stress haemodynamics, 'valvular fractional flow' warrants study to explain exertional symptoms in patients with only moderate AS at rest.