#### 2.1.2. Swallowing capacity

Whilst the effect of pressure drop is useful in throttle valves for reducing load it is a restriction on the turbine itself. The pressure drop produced at the nozzles of the turbine inlet and all subsequent fixed blades restricts the mass flow through the turbine and hence the power output. A relationship between mass flow and the fall in pressure across the turbine was first produced by Stodola in 1927 [4].

where qm is the mass flow rate, p, and p2 are the inlet and exhaust pressures and К is a constant. The relationship is known as the 'Ellipse Law'.

The relationship was later modified to include the effect of inlet temperature:

where T, is the inlet absolute temperature.

A more comprehensive analysis is given by Traupel [5] who showed that:

where V represents the specific volume and n is the polytropic exponent, related to the efficiency *rj *and isentropic exponent k by:

The Ellipse Law is a useful tool when modelling the effects of partial load on a turbine. Generally, sufficient accuracy is obtained by using the version given in Equation (1.2) where steam is the working fluid. The Ellipse Law constant К can be obtained from either design or test data for the turbine, and knowing the required flow, the pressures at each stage of the unit can be evaluated successively from the exhaust end where the conditions remain at constant condenser levels.