A conduit with a variable cross-sectional area in which a fluid accelerates into a high-velocity stream. The effect of the changing cross-sectional area on the fluid velocity can be explained by the principle of mass conservation applied to successive cross-sectional planes of the nozzle. Equation (1)
must be satisfied, where ρ is the mass density of the fluid [in kilograms per cubic meter (kg/m3)], V is the average velocity in the cross section [in meters per second (m/s)], A is the cross-sectional area [in square meters (m2)], and is the rate of mass flow through the nozzle [in kilograms per second (kg/s)]. Decreasing A along the length of the nozzle must result in an increase in ρV since is the same at every cross section. See also: Fluid mechanics
Design and operation
An important parameter of nozzle operation is the difference in pressure [in pascals (Pa)] between the inlet and outlet. Higher pressure differences push the fluid to higher velocities and achieve higher mass flow rates for a given nozzle size.
For liquid nozzles it can be assumed that ρ is constant and therefore V increases as A decreases and vice versa. Liquid nozzles, such as those on fire hoses, are called converging because the area decreases along the length of the nozzle to increase the speed. Typical liquid nozzles have a simple conical shape and are designed to a specific ratio of inlet to outlet areas. To produce good uniformity of the velocity profiles in the issuing jet, the total cone angle should be less than 30°. In cases where the pressure difference across the nozzle is fixed, the mass flow rate from the nozzle can be regulated by pushing a conical spear into the exit plane of the nozzle from the inside. This has the effect of reducing the outlet flow area and hence the mass flow rate.
The difference between the reservoir pressure (Po) and the nozzle exit pressure (Pb) required for a given exit velocity Ve can be determined approximately, using Bernoulli's theorem, as given by Eq. (2).
In cases where the pressure difference is less than 10 kPa, air may be treated as if its density were constant. See also: Bernoulli's theorem
High-speed gas nozzles
In the case of gas nozzles the gas density can change dramatically as a result of the pressure reduction between the inlet and outlet of the nozzle. At very high gas speeds this effect is so significant that the basic shape of the nozzle must change to a converging-diverging form (Fig. 1). The diverging portion is necessary to accommodate the expansion of the gas as it accelerates to lower pressure.
An understanding of the operation of the converging-diverging nozzle requires knowledge of the Mach number, which is the ratio of the gas speed to the speed of sound in the gas c; Ma=V/c. A subsonic flow has Ma≤1, a sonic flow has Ma=1, and a supersonic flow has Ma > 1. Figure 2 shows how the pressure, temperature, and speed of air flowing in a nozzle are related to Mach number and profile of nozzle cross-sectional area. From this figure, it can be seen that the flow in the converging portion of the nozzle must be subsonic, the flow at the throat can at most be sonic, and supersonic flow can occur only in the diverging portion. To achieve supersonic flow in the diverging section, the reservoir pressure must be sufficient to achieve sonic flow at the throat. The fall of air temperature with increasing Ma indicated in Fig. 2 is a direct result of the gas expansion. See also: Compressible flow; Mach number; Sound
To achieve a particular Mach number at the nozzle exit (Mae), the ratio of the pressures at the outlet (Pb) and inlet (Po) of the nozzle must follow Eq. (3).
If Pb/P0 is somewhat higher than this value and the same supersonic flow condition prevails inside the divergent part of the nozzle, then an oblique shock wave will originate at the edge of the nozzle. For even higher back-pressure ratios, supersonic flow cannot be realized at the exit, although the throat can still be sonic. Under this condition, a normal shock wave occurs in the divergent part of the nozzle. This operating condition is not desirable, because the flow is subsonic at the exit of the nozzle and the useful mechanical energy is degraded into thermal energy whenever a shock wave occurs. When the back-pressure ratio is lower than the value given by Eq. (3), the jet stream from the nozzle will expand to form a plume (Fig. 1). See also: Jet flow; Shock wave
There is a very interesting phenomenon observed in the operation of gas nozzles known as choking. Once the velocity at the throat reaches sonic speed, the back pressure has no further effect on throat conditions and the mass flow is entirely determined by the reservoir conditions and throat area. For air flow, this relationship is Eq. (4),
where To is the absolute reservoir temperature [in kelvins (K)] at the nozzle inlet. This equation specifies the maximum mass flow for a given throat area, or alternatively, it specifies the minimum throat area for a given mass flow. See also: Choked flow
The above discussion is based upon the assumption that the fluid is frictionless (inviscid). Although all real fluids are viscous, the influence due to viscosity is generally very minor. Only when using a very viscous liquid, such as heavy oil, or when a gas accelerates to a very high Mach number inside the nozzle (Ma > 5) do viscous effects become important. See also: Gas dynamics; Viscosity
A nozzle can be used for a variety of purposes. It is an indispensable piece of equipment in many devices employing fluid as a working medium. The reaction force that results from the fluid acceleration may be employed to propel a jet aircraft or a rocket. In fact, most military jet aircraft employ the simple convergent conical nozzle, with adjustable conical angle, as their propulsive device. If the high-velocity fluid stream is directed to turn a turbine blade, it may drive an electric generator or an automotive vehicle. High-velocity streams may also be produced inside a wind tunnel so that the conditions of flight of a missile or an aircraft may be simulated for research purposes. The nozzle must be carefully designed in this case to provide uniformly flowing fluid with the desired velocity, pressure, and temperature at the test section of the wind tunnel. Nozzles may also be used to disperse fuel into an atomized mist, such as that in diesel engines, for combustion purposes. See also: Atomization; Impulse turbine; Internal combustion engine; Rocket propulsion; Turbine propulsion; Wind tunnel
Nozzles may also be used as metering devices for gas or liquid. A convergent nozzle inserted into a pipe produces a pressure difference between its inlet and outlet that can be measured and related directly to the mass flow. For this purpose, the shape of the nozzle must be designed according to standard specifications or carefully calibrated against a mass flow rate standard. A unique feature of gas metering nozzles is that the mass flow rate through the nozzle depends only on the inlet pressure if the pressure ratio across it is sufficient to produce sonic velocity at the throat. See also: Flow measurement