Exit pressure

However, two other methods for obtaining normal stress data from slit rheometry have had reasonable success the exit pressure and particularly the pressure hole method. These are discussed in Sections 6.3.2 and 6.3.3. 

If we can neglect fluid inertia and any rearrangement of the velocity proflle up to the die exit, then the exit pressure can be related to the first normal stress difference 

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SheUside flow maldistribution effect is normally iacluded in the, -correction. Tubeside flow maldistribution effect is relatively small in most designs because the principal resistances are tube friction and entrance/exit pressure drop. 

These equations are consistent with the isentropic relations for a perfect gas p/po = (p/po), T/To = p/poY. Equation (6-116) is valid for adiabatic flows with or without friction it does not require isentropic flow However, Eqs. (6-115) and (6-117) do require isentropic flow The exit Mach number Mi may not exceed unity. At Mi = 1, the flow is said to be choked, sonic, or critical. When the flow is choked, the pressure at the exit is greater than the pressure of the surroundings into which the gas flow discharges. The pressure drops from the exit pressure to the pressure of the surroundings in a series of shocks which are highly nonisentropic. Sonic flow conditions are denoted by sonic exit conditions are found by substituting Mi = Mf = 1 into Eqs. (6-115) to (6-118). 

Equation (6-128) does not require fric tionless (isentropic) flow. The sonic mass flux through the throat is given by Eq. (6-122). With A set equal to the nozzle exit area, the exit Mach number, pressure, and temperature may be calculated. Only if the exit pressure equals the ambient discharge pressure is the ultimate expansion velocity reached in the nozzle. Expansion will be incomplete if the exit pressure exceeds the ambient discharge pressure shocks will occur outside the nozzle. If the calculated exit pressure is less than the ambient discharge pressure, the nozzle is overexpanded and compression shocks within the expanding portion will result. 

Choked and unchoked flow situations arise in pipes and nozzles in the same fashion for homogeneous equihbrium flashing flow as for gas flow. For nozzle flow from stagnation pressure po to exit pressure pi, the mass flux is given by... 

Beeause of temperature eonstraints, the transdueers, whieh usually do not operate above 350 °F (177 °C) are loeated outside the engine. A probe is then loeated inside to direet the air to the transdueer. Most manufaeturers provide probes to measure the eompressor inlet pressure, eompressor exit pressure, and the turbine exhaust pressure. These probes are usually loeated along the shroud of the maehine, and therefore, the pressure readings may be slightly in error due to boundary-layer effeets. 

By using dynamie pressure probes in the bleed ehamber, it is possible to deteet tip stall. A pressure rake at the eompressor exit enables aeeurate readings of exit pressure and is also helpful in the diagnosis of eompressor stall. 

Compressor analysis is done by monitoring the inlet and exit pressures and temperatures, the ambient pressure, vibration at eaeh bearing and the pressure and temperature of the lubrieation system. Table 19-5 shows the effeet various parameters have on some of the major problems eneountered in a eompressor. Monitoring these parameters allows the deteetion of ... 

I lie smallest inlet and exit pressure losses possible, the nozzle size should be increased. 

P2 = backpressure or exit pressure, psia Pi = upsu eam reliewng oresstire, psia... 

P" = maximum header exit pressure into seal, psig p = density of seal liquid, Ib/cu ft Calculate the cross section of the drum volume for vapor above the liquid level, establishing the level referenced to h), plus clearance to drum bottom, hi, normally... 

Figure 26.3 shows the relationship between port diameter and fluid velocity at 4 and 7 m/s and highlights the nominal maximum velocities for various plates. As the flow through the machine increases, the entry and exit pressure losses also increase. The nominal maximum flow rate for a plate heat exchanger limits these losses to an acceptable proportion of the total pressure losses, and is therefore a function not only of the port diameter but... 

F = (H+ cosor) (wVe/g) + (Pe-P0)Ae where oc = half of the divergence angle of the nozzle, w - weight rate of proplnt flow, g = acceleration of gravity, Ve = exit flow velocity, Pe = nozzle exit pressure, PQ = external atm pressure, and Ae = cross section at nozzle exit plane. An effective exhaust velocity is defined by... 

Case III. Back-pressure low, with pressure less than critical value at the exit. The pressure falls to the critical value at the throat and continues to fall to give an exit pressure Pei = Pb- The velocity increases to sonic at the throat and continues to increase to supersonic in the diverging cone to a value /< .. 

A nozzle is correctly designed for any outlet pressure between P[ and PE in Figure 4.5. Under these conditions the velocity will not exceed the sonic velocity at any point, and the flowrate will be independent of the exit pressure PE = Pb- It is also correctly designed for supersonic flow in the diverging cone for an exit pressure of PEj. 

Pressure drop measurements. For the majority of experiments the instrumentation was relatively similar. Due to limitations associated with the small size of the channels, pressures were not measured directly inside the micro-channels. To obtain the channel entrance and exit pressures, measurements were taken in a plenum or supply line prior to entering the channel. It is insufficient to assume that the friction factor for laminar compressible flow can be determined by means of analytical predictions for incompressible flow. 

At tube exit, pressure drop per unit lengths, using the homogeneous model homogeneous velocity = G/pm = 237/66.7 = 3.55 m/s Viscosity, taken as that of liquid, = 0.12 mN sm 2... 

The oxide is used to effect rapid decomposition of hydrazine in a high-temperature gas generator which produces exit pressures (of nitrogen, hydrogen and ammonia) of 550 bar. 

Crude oil (p = 40 cP, SG = 0.87) is to be pumped from a storage tank to a refinery through a 10 in. sch 20 commercial steel pipeline at a flow rate of 2000 gpm. The pipeline is 50 mi long and contains 35 90° elbows and 10 open gate valves. The pipeline exit is 150 ft higher than the entrance, and the exit pressure is 25 psig. What horsepower is required to drive the pumps in the system if they are 70% efficient ... 

That is, as P2 decreases, the mass velocity will increase up to a maximum value of G, at which point the velocity at the end of the pipe reaches the speed of sound. Any further reduction in the downstream pressure can have no effect on the flow in the pipe, because the speed at which pressure information can be transmitted is the speed of sound. That is, since pressure changes are transmitted at the speed of sound, they cannot propagate upstream in a gas that is already traveling at the speed of sound. Therefore, the pressure inside the downstream end of the pipe will remain at P 2, regardless of how low the pressure outside the end of the pipe (P2) may fall. This condition is called choked flow and is a very important concept, because it establishes the conditions under which maximum gas flow can occur in a conduit. When the flow becomes choked, the mass flow rate in the pipe will be insensitive to the exit pressure but will still be dependent upon the upstream conditions. 

The value of the downstream pressure (P2) at which the flow becomes sonic (P2 = P2) is given by P = Pi(l — AP /P ). If the exit pressure is equal to or less than this value, the flow will be choked and G is calculated using P. Otherwise, the flow will be subsonic, and the flow rate will be determined using the pressure P2. 

In the J-T DR (see Fig. 6.11) [32], the condensation of the 3He-4He mixture is produced by a J-T expansion (after Z,) which takes place after a precooling in a J-T heat exchanger. To achieve the correct decrease of the gas temperature and the right exit pressure, a small compressor is inserted in the circulation line at the output of the circulation pump. 

This solution applies for both subsonic and choked flow. If the flow is choked, the exit pressure ratio T 2 is replaced by the choked pressure ratio ri0h, given by... 

Pipe entrance and exit pressure losses should also be calculated and added to obtain the overall pressure drop. The loss in pressure due to sudden expansion from a diameter dtl to a larger diameter dl2 is given by the equation... 

The shock wave occurs in such a position as to allow the exit pressure to equal the imposed back pressure. The back pressure being lower for condition (d) than for condition (c), the shock wave for condition (d) is closer to the exit plane. 

Condition (g) is that condition for which the exit pressure is equal to the back pressure and no shock wave occurs. This is called the design condition for supersonic flow. 

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