Nozzle efficiency

Obviously nozzles are not perfectly efficient and there are several ways to define the nozzleefficiency. One of the effective way is to define the efficiency as the ratio of the energy converted to kinetic energy and the total potential energy could be converted to kinetic energy. The total energy that can be converted is during isentropic process is

$$E = h_0 - {h_{exit}}_s$$ (6.1)

where ${h_{exit}}_s$ is the enthalpy if the flow was isentropic. The actual energy that was used is

$$E = h_0 - h_{exit}$$ (6.2)

The efficiency can be defined as

$$\eta = { h_0 - h_{exit} \over h_0 - {h_{exit}}_s} = {\left(U_{actual}\right)^2 \over \left(U_{ideal}\right)^2}$$ (6.3)

The typical efficiency of nozzle is ranged between 0.9 to 0.99. In the literature some define also velocity coefficient as the ratio of the actual velocity to the ideal velocity, $V_c$

$$V_c = \sqrt{\eta} = \sqrt{{\left(U_{actual}\right)^2 \over \left(U_{ideal}\right)^2}}$$ (6.4)

There is another less used definition which referred as the coefficient of discharge as the ratio of the actual mass rate to the ideal mass flow rate.

$$C_d = {\dot{m}_{actual} \over \dot{m}_{ideal}}$$ (6.5)