Uncertainties are present in most engineering applications such as turbomachines. The performance of turbomachinery can be highly affected by the presence of uncertainties and these effects should be considered in the design procedure. The present study is the first work to quantify the impact of various uncertainties in a hydraulic machine. The paper is concerned with the combined effects of geometrical and operational uncertainties on the flow field and performance of a low specific-speed centrifugal pump. The uncertainty analysis is performed for three different flow rates, i.e., Q/Q_d=0.825,1.0 and 1.1175. The volumetric flow rate, rotational speed and blade geometry of the pump are assumed to be stochastic with uniform Probability Distribution Functions (PDFs). The randomness in the blade geometry, due to the manufacturing tolerances, is imposed through two Karhunen-Loève (KL) expansions. The eigenvalues of covariance kernel of KL expansions rapidly decay due to the large correlation lengths and thus a few terms are used in the truncated KL expansion to describe the blade geometrical uncertainties. The uncertainties are propagated in the flow field and performance of the pump using the Non-Intrusive Polynomial Chaos (NIPC) method. The respective effects of assumed uncertain variables on the quantities of interest are assessed using Sobol’ indices. The uncertain operational and geometrical conditions have significant influences on the flow field and performance of the pump. It is observed that while variation of the pump head coefficient under operational and geometrical uncertainties is significant, the pump efficiency shows a robust behavior under assumed uncertain conditions.