The torque characteristics of variable fill hydraulic dynamometers are investigated, particularly the phenomenon of self-emptying of Froude F type machines under open loop control. An integrated one-dimensional model is adapted from fluid coupling and torque converter theory to cover the steady-state case, and extended to the non-linear open loop dynamic cases by incorporating varying fluid fill and the dynamic governing equations for dynamometers. Two feedback systems are included to predict the closed loop behaviour of the machines. The effect of geometric variations on the steady-state torque capacity of dynamometers is given and the cause of the self-emptying phenomenon determined. It is found that the increase in working compartment fluid pressure with shaft speed leads to the fluid outflow rate becoming greater than the supplied inflow rate. Thus the fluid fill decreases. This phenomenon is further investigated using a dynamic model, consisting of a system of first order differential equations. The Adams-Bashforth Predictor Adams-Moulton Corrector numerical method is used to solve the system of equations. In addition to the self-emptying characteristic investigation, the differences between steady state and dynamic model predictions and the system responses to changes of set point and disturbances of its inputs (driving torque, outflow valve position, fluid inflow rate) are studied. To enable closed loop performance prediction, models of two feedback system are incorporated: a back pressure water outlet valve driven by a machine-speed oil-pump, and an electrohydraulic butterfly valve governed by direct digital control. The latter model is used to investigate controller tuning around the dynamometer's operating envelope. It is also subjected to input disturbances and the responses compared to the open loop behaviour.