Blood pressure loss along the coronary arterial length and the local magnitude of the spatial wall pressure gradient (WPG) are important factors for atherosclerosis initiation and intimal hyperplasia development. The pressure drop coefficient (CDP) isdefined as the ratio of mean trans-stenotic pressure drop to proximal dynamic pressure. It is a unique non-dimensional flow resistance parameter useful in clinical practice for evaluating hemodynamic impact of coronary stenosis. It is expected that patients with the same stenosis severity may be at different risk level due to their blood pressure situations. The aim of this study is to numerically examine the dependence of CDP and WPG on flow rate and blood viscosity using a patient-specific atherosclerotic right coronary artery model with two stenoses. Our simulation results indicate that the coronary model with a lower flow rate yields a greater CDP across a stenosis, while the model with a higher flow rate yields a greater pressure drop and a greater WPG. Increased blood viscosity results in a greater CDP. Quantitatively, CDP for each stenosis appears to be a linear function of blood viscosity and a decreasing quadratic function of flow rate. Simulations with varying size and location of the distal stenosis show that the influence of the distal stenosis on the CDP across the proximal stenosis is insignificant. In a right coronary artery segment with two moderate stenoses of the same size, the distal stenosis causes a larger drop of CPD than the proximal stenosis does. A distal stenosis located in a further downstream position causes a larger drop in the CDP.