Exam Question

### (a) Ducted Propellers (Kort Nozzles)
**Principle of Operation:**
A ducted propeller system, commonly known as a Kort Nozzle, consists of a propeller rotating within a non-rotating, hydrodynamically shaped duct or nozzle. The nozzle's cross-section is an airfoil. As water flows through the converging section of the nozzle, its velocity increases, and pressure decreases. This acceleration of flow into the propeller disc increases the mass flow rate ($$\dot{m}$$). According to momentum theory, Thrust ($$T$$) is the product of mass flow rate and the change in fluid velocity ($$T = \dot{m} \Delta v$$). By increasing the mass flow rate, the propeller can generate more thrust for the same power input, especially under heavily loaded conditions (high thrust, low speed).
Additionally, the pressure difference between the inner (low pressure) and outer (high pressure) surfaces of the nozzle generates hydrodynamic lift, which has a significant forward component that adds to the total thrust. A key efficiency benefit is the prevention of tip vortex formation. In an open propeller, pressure differences at the blade tips create powerful vortices, which represent a significant energy loss. The duct acts as an end-plate, suppressing these vortices and conserving energy.