Because easy oil is gone is gets ever more difficult to find new oil and gas reserves. New discoveries are usually smaller, deeper and much more difficult to get access to. Therefore new technologies, such as managed pressure drilling, real time data analysis and early kick/loss detection become more and more necessary to reach these reservoirs safely and economically. In order to be able to drill in very narrow pressure windows and to minimize non-productive time induced by kicks or lost circulation modern drilling systems incorporate a closed loop mud system to precisely control bottom hole pres-sure and to measure inflow and outflow of the well to identify kicks and losses early on. For measuring these mud flows in such closed loop systems it is common today to use Coriolis flow meters, which have proven to be very accurate even under difficult mud properties. This thesis purpose is it to review all currently available measurement methods and sensor systems and evaluate their possible use on conventional drilling rigs. Due to the high complexity and cost of Coriolis type flow meters a widespread use or upgrade of old rigs, especially onshore is not viable. Therefore the thesis tries to show alternative methods that are cost effective and equally capable of measuring flow or identify kicks and losses and distinguish them from ballooning effects. A computational fluid dynamics study is conducted to examine the outflow behavior of drilling mud on conventional drilling rigs and how it may affect the accuracy and reliability of flow measurements in terms of early kick and loss detection. Based on an initial case simulations have been conducted with varying flow rates, channel drop angle, mud density and mud viscosity to determine the influencing factors for open channel flow rate measurement. It could be observed that mud properties in the range of conventional drilling muds have little effect and that the ratio of the geometric factors such as pipe diameter and drop angle are the main factors for accurate flow rate measurement.