The pressure drop across a stenotic vessel is an important parameter in medicine, providing a commonly used and intuitive metric for evaluating the severity of the stenosis. However, non-invasive estimation of the pressure drop under pathological conditions has remained difficult. This study demonstrates a novel method to quantify the irreversible pressure drop across a stenosis using 4D Flow MRI by calculating the total turbulence production of the flow. Simulation MRI acquisitions showed that the energy lost to turbulence production can be accurately quantified with 4D Flow MRI within a range of practical spatial resolutions (1-3 mm; regression slope = 0.91, R2 = 0.96). The quantification of the turbulence production was not substantially influenced by the signal-to-noise ratio (SNR), resulting in less than 2% mean bias at SNR > 10. Pressure drop estimation based on turbulence production robustly predicted the irreversible pressure drop, regardless of the stenosis severity and post-stenosis dilatation (regression slope = 0.956, R2 = 0.96). In vitro validation of the technique in a 75% stenosis channel confirmed that pressure drop prediction based on the turbulence production agreed with the measured pressure drop (regression slope = 1.15, R2 = 0.999, Bland-Altman agreement = 0.75 ± 3.93 mmHg).