Pressure converging/diverging nozzles

With a converging-diverging nozzle, the velocity increases beyond the sonic velocity only if the velocity at the throat is sonic and the pressure at the outlet is lower than the throat pressure. For a converging nozzle the rate of flow is independent of the downstream pressure, provided the critical pressure ratio is reached and the throat velocity is sonic. 

Air passes from a large reservoir at 70°F through an isentropic converging-diverging nozzle into the atmosphere. The area of the throat is 1 cm2, and that of the exit is 2 cm2. What is the reservoir pressure at which the flow in the nozzle just reaches sonic velocity, and what are the mass flow rate and exit Mach number under these conditions ... 

The case of flow through a convergent-divergent nozzle is shown in Figure 6.2. On reducing the back pressure PB, while keeping the supply... 

Pressure profiles for compressible flow through a convergent-divergent nozzle... 

Air flows from a large reservoir where the temperature and pressure are 25°C and 10 atm, through a convergent-divergent nozzle and discharges to the atmosphere. The area of the nozzle s exit is twice that of its throat. Show that under these conditions a shock wave must occur, (y = 1.4.)... 

Nozzleless rockets are very simplified and low-cost rockets because no nozzles are used. Their specific impulse is lower than that of conventional rockets even when the same mass of propellant is used. Normally, a convergent-divergent nozzle is used to expand the chamber pressure to the atmospheric pressure through an isentropic change, which is the most effective process for converting pressure into propulsive thrust The flow process without a nozzle increases entropy and there is stagnahon pressure loss. 

The supersonic air induced into the air-intake is converted into a pressurized subsonic airflow through the shock wave in the air-intake. The fuel-rich gas produced in the gas generator pressurizes the combustion chamber and flows into the ramburner through a gas flow control system. The pressurized air and the fuel-rich gas produce a premixed and/or a diffusional flame in the ramburner. The combustion gas flows out through the convergent-divergent nozzle and is accelerated to supersonic flow. 

Figure 8.16 Cross-sectional diagram of a single-use disposable powder injection system highlighting the major components. When the actuator button is depressed, the driver gas (He) is released into the surrounding rupture chamber. At a specific pressure, the plastic membranes of the drug cassette burst and the drug particles are entrained in the gas flow, which is accelerated through the convergent-divergent nozzle. [From Hickey (2001). Reproduced with permission from Euromed Communications.]...

However, never confuse the lift of the valve with its capacity, as even a perfect convergent/divergent nozzle s flow rate is reduced beyond the medium s critical pressure ratio, as shown in the graph in Figure 5.40. In principle, a perfect nozzle has a KD (flow factor) = 1. 

Figure 6-23 shows a converging/diverging nozzle. When p2/p0 is less than the critical pressure ratio (p a/p ), the flow will be subsonic in the converging portion of the nozzle, sonic at the throat, and supersonic in the diverging portion. At the throat, where the flow is critical and the velocity is sonic, the area is denoted A. The cross-sectional... 

Venturi tubes and converging/diverging nozzles. For these devices,p2 in the equations in the preceding subsection is the pressure at the throat where the velocity is V2. In the following discussion it is assumed that the initial values of p1 and T1 remain constant while P2 varies. 

It must be remembered that Eqs. (10.94) to (10.97) are to be used only when the velocity of approach is negligible and when p2 at the throat of a venturi tube or converging/diverging nozzle is reduced to a value pc as obtained from Eq. (10.92). For an orifice p2 is the pressure in the space into which the jet issues, no matter how low this pressure may become. 

Example 10.8 Air enters a converging/diverging nozzle (venturi) at a pressure of 120 psia and a temperature of 90°F. Neglecting the entrance velocity, and assuming a frictionless process, find the Mach number at the cross section where the pressure is 35 psia. 

For a converging/diverging nozzle with negligible entrance velocity in which expansion isentropic, sketch graphs of mass flow rate m, velocity u, and area ratio A/A, vs. the pressure i P/ P,. Here, A is the cross-sectional area of the nozzle at the point in the nozzle where the press" is P, and subscript 1 denotes the nozzle entrance. 

Steam expands isentropically in a converging/diverging nozzle from inlet conditions of200(p 600(, F), and negligible velocity to a discharge pressure of 50(psia). At the throat, the cross-seeds area is I (in)2. Determine the mass flow rate of the steam and the state of the steam at the exit of nozzle. 

It is also true that in the converging section of a converging/diverging nozzle the maximum obtainable fluid velocity is the speed of sound, reached at the throat. This is because a further decrease in pressure requires an increase in cross-sectional area, i.e., a diverging section. The explanation for this is as follows. At the relatively high pressures in the converging section, a given pressure drop... 

The speed of sound is attained at the throat of a converging/diverging nozzle only when the pressure at the throat is low enough that the critical value of P-JP is reached. If insufficient pressure drop is available in the nozzle for the velocity to become sonic, the diverging section of the nozzle acts as a diffuser. That is, after the throat is reached the pressure rises and the velocity decreases this is the conventional behavior for subsonic flow in diverging sections. The relationships between velocity, area, and pressure in a nozzle are illustrated numerically in Example 7.3. 

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