With the transition towards renewable energy, offshore wind power farms are being constructed or planned in many places involving placing wind turbines in the sea. The monopiles for these wind turbines are vertical cylinders which are situated in a flow with high Reynolds numbers and low to intermediate Keulegan- Carpenter numbers. The Reynolds and Keulegan-Carpenter number are dimensionless numbers for the quantification of respectively currents and waves. Previous research has not covered the Reynolds and Keulegan-Carpenter numbers in which energy generating devices are situated. The current research is focused on filling the gap and investigating the drag forces on these cylinders via means of experiments. Additional simulations focussing on the free surface and end effects were also conducted. The forces at play and the Morison equation to model these forces have been evaluated. It was discovered that in the investigated range, the drag and inertia coefficients depend on both Reynolds and Keulegan-Carpenter numbers. By analyzing the results of the experiments in the time and frequency domain, indications of vortex shedding and second-order harmonic wave forces, as well as forces from wave-wave interaction were found. The Morison equation itself is analyzed to find that it either underestimates or neglects these forces. By means of simulations, the effects of the free surface and the aspect ratio of the cylinder on the drag and inertia coefficients are found. Lastly, it is proposed to use a rewritten Morison equation to find the drag on a cylinder in a flow with irregular waves. This equation is found to describe the drag forces more accurately.