Sonic velocity choke flow

The exit Mach number Mo may not exceed unity Mo = 1 corresponds to choked flow sonic conditions may exist only at the pipe exit. The mass velocity G in the charts is the choked mass flux for an isentropic nozzle given by Eq. (6-118). For a pipe of finite length. 

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

A stonewall or choked flow condition occurs when sonic velocity is reached at the exit of a compressor wheel. When this point is reached, flow through the compressor cannot be increased even with further... 

The ratio of the sonic velocity in a homogeneous two-phase mixture to that in a gas alone is cm/c = Pg/ePm = Vpl/ATO — ). This ratio can be much smaller than unity, so choking can occur in a two-phase mixture at a significantly higher downstream pressure than for single phase gas flow (i.e., at a lower pressure drop and a correspondingly lower mass flux). 

Figure 4-10 Choked flow of gas through a hole. The gas velocity is sonic at the throat. The mass flow rate is independent of the downstream pressure.

The combustion gas of an internal burning of a propellant flows along the port of the propellant If the nozzle attached to a rocket motor is removed, the pressure in the port becomes equal to atmospheric pressure and no sonic velocity is attained at the rear-end of the port. Then, no thrust is generated by the combustion of the propellant However, if the mass burning rate of the propellant is high enough to choke the flow at the rear-end of the port, the pressure in the port is increased and the flow reaches sonic velocity. The increased pressure in the port is converted into thrust. The thrust F is represented by... 

In the first category, the ratio of P1 (inlet) to P2 (outlet) is approximately 2 or greater. At that ratio, the flow through the valve orifice becomes sonic that is, the flow reaches the speed of sound for that particular fluid. Once the flow becomes sonic, the velocity of the fluid remains constant (cannot go supersonic). No decrease of P2 will increase the flow in any shape or form. This is also sometimes referred to as choked flow. ... 

Volumetric flow rates of different gases are often compared to equivalent volumes of air at standard atmospheric temperature and pressure. The ideal gas law works well when used to size fans or compressors. Unfortunately, the gas law relationship, PV/T = constant, is frequently applied to choked gas streams flowing at sonic velocity. A typical misapplication could then be the conversion to standard cubic feet per minute in sizing SRVs. Whether the flow is sonic or subsonic depends mainly on the backpressure on the SRV outlet. In the API calculations, this is taken into account by the backpressure correction factor. 

With a ratio between storage pressure and ambient pressure of about 2 or greater (for air), the flow rate is limited to the sonic velocity of the fluid at the end of the flow restriction (choked flow). At this point, the fluid pressure can be greater than the ambient pressure. The remaining expansion occurs beyond the flow restriction, where the release accelerates both radially and axially. 

Choked flow occurs in the second case the outlet flow becomes sonic and the pressure at station 3 is the critical pressure of 0.271 MPa rather than the pressure of 0.101 MPa that exists just below the outlet. Air velocity increases by a factor of about 3 over the length of the pipe, and the mass flow is greater than in case (i). However, the pressure at station 2 is only a few per cent lower than in case (i), and this is significant in restricting the increase in mass flow to only about 30% above the velocity observed in case (i). 

In high-velocity subsonic flow with friction, the effect of the friction is to increase the velocity, ultimately leading to sonic flow and choking. 

In gas systems, the flow becomes choked when the exit velocity through the orifice plate reaches sonic velocity. The mass flow rate is essentially independent of downstream conditions but can be increased by increasing the upstream pressure or decreasing the temperature. For an ideal gas and isentropic flow, the pressure ratio to calculate the onset of sonic conditions depends on the ratio of the specific heats, g, and is often known as the isentropic expansion factor ... 

As the upstream pressure Pj decreases (or downstream pressure P2 decreases), a maximum is found in Eq. (2.16). This maximum occurs when the velocity of the discharging gas reaches the sonic velocity. At this point, the flow becomes independent of the downstream pressure and is dependent only on the upstream pressure. The equation representing the sonic, or choked case is... 

I have discussed in this chapter the effect of reaching sonic velocity, also called the critical flow velocity or choke flow. 

Sonic velocity is also referred to as choke flow. One characteristic of choke flow is that reducing the downstream pressure does not significantly increase the flow through the choke point. Increasing the upstream pressure increases the flow in a linear proportion to the absolute increase in pressure. 

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