Many engineering devices operate essentially under the same conditions for long periods of time. These devices can be treated as steady-flow devices.

Recall, the energy balance for a control volume is:


    Nozzles and Diffusers




Nozzles and diffusers are commonly utilized in jet engines, rockets, and spacecrafts. Any fluid-mechanical device designed to accelerate a flow is called a nozzle and any fluid-mechanical device designed to decelerate a flow is called a diffuser. For subsonic flow (velocity under the speed of sound), a converging duct is a nozzle and a diverging duct is a diffuser.

Nozzle and diffuser are single-stream (one-inlet-one-exit) systems. If the inlet is denoted by subscript 1 and exit is denoted by subscript 2, the mass balance and energy balance for single-stream steady-flow systems become


There are several common assumptions that are made in the energy analysis of nozzles and diffusers:

  • The fluid has high velocity and thus not spending enough time in the device for any significant heat transfer to take place.

  • Nozzles and diffusers are properly shaped ducts and no shaft or electric work can be transferred in or out.

  • As a fluid passes through a nozzle or diffuser, it experiences a large change in its velocity. Hence, the kinetic energy change must be accounted for.

  • The fluid experiences small or no change in its elevation as it flows through the nozzle or diffuser.

Summarizing the above analysis, the energy balance for nozzles and diffusers is:

      (h2 - h1) + ( v22 - v12)/2 = 0

    Throttling Devices

Throttling Valves


A significant reduction in pressure can be achieved by introducing a restriction into a line through which a gas or liquid flows. This is commonly done by means of an adjustable valve, a porous plug, or a capillary tube. They are called throttling devices.

There are several common assumptions that are made in the energy analysis of throttling devices:

  • Throttling devices are usually small devices. There is neither sufficient time nor large enough area for significant heat transfer to take place.

  • No work is done to or from the devices.

  • The increase in kinetic energy is insignificant.

  • The change in potential energy is very small.

Hence, the energy balance for throttling devices is:

      h2 = h1

When the flow through a valve or other restrictions is idealized in this way, the process is called a throttling process.