We examine flow in a cylindrical electrorheological clutch and discuss the fluid dynamic and inertial effects which limit the speed of operation. Time-dependent solutions of the equation of motion are developed in which the fluid is treated as a homogeneous continuum obeying the Bingham plastic constitutive equation. Some approximations have to be made but the results give a realistic description of the acceleration in clutches of practical dimensions. The problem is also approached in an entirely different way by direct numerical integration using an alternative time-dependent model. There is agreement between the two methods and the results show that the fluid density and viscosity place an upper limit on the acceleration of the output rotor. This is only reached if very low moment of inertia rotors are used, otherwise the output hardware inertia is the limiting factor. Design formulae are developed to give a rough estimate for the fluid limited acceleration and to define the minimum output moment of inertia that can usefully be employed to give maximum available acceleration.