Nozzle efficiency

The velocity of water flowing from the tub through the drain is 20 ft/s. The pressure drop, in psi, of the water as it escapes from the tub, is 

The pressure at P1 is now the 1-psi static head, minus the 5-psi nozzle exit loss, or negative 4 psig (or positive 10.7 psia). That is, the pressure at the drain is a substantial partial vacuum, or a negative pressure, meaning that it is below atmospheric pressure (atmospheric pressure at sea level is 14.7 psia). 

This suggests that the pressure in a water drain can get so low, that air could be sucked out of the bathroom and down the drain. Of course, we all see this happen several times a day—typically when we flush a toilet. So much air is drawn into the water drainage piping, that we install vents on our roofs, to release this air. The only requirement, then, for vapors to be drawn into a flowing nozzle is for the nozzle exit loss to be larger than the static head of liquid above the nozzle. 

Incidentally, if a bird builds its nest on top of one our roof toilet vents, we find the toilet will no longer flush properly. The experienced plumber states that the toilet won t flush because it is suffering from vapor lock and this is true. A working knowledge of process equipment fundamentals often comes in quite handy around the home. 

But how about the liquid at point B Is this liquid also at its boiling or bubble point It is the same liquid, having the same temperature and composition as the liquid at point A. But the pressure at point 6 is slightly higher than the pressure at point A.  

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The feed enters the evaporator at 295 K and the concentrated liquor is withdrawn at the rate of 0.025 kg/s. The concentrated liquor exhibits a boiling-point rise of 10 degK. Heat losses to the surroundings are negligible. The nozzle efficiency is 0.95, the efficiency of momentum transfer is 0.80 and the efficiency of compression is 0.90. 

As the jet from a nozzle is frequently employed for power purposes in a steam turbine or a Pelton wheel, we are interested in its energy efficiency. The efficiency of a nozzle is defined as the ratio of the power in the jet to the power passing a section in the pipe at the base of the nozzle. As the discharge is the same for the two points, the efficiency is merely the ratio of the heads at these two sections. Thus, referring again to the conical nozzle, e = HJH. But H2 = V2/2g, and Hr = pjw + V t2g, and so from Eq. (10.59) it follows that H2 = C2,H1. Hence the nozzle efficiency is... 

Because of the normally small length of the nozzle, it is reasonable to omit the effect of friction in this preliminary analysis of nozzles. (Frictional effects are customarily catered for in nozzle analysis by using the concept of nozzle efficiency.) Setting dF = 0 in equation (4.15) gives the differential for fluid speed as ... 

Velocity and enthalpy relationships in a turbine nozzle nozzle efficiency... 

Hence the nozzle efficiency equation may be reexpressed in terms of outlet temperatures ... 

It will be seen that the recalculated value of nozzle efficiency deviates increasingly from the true value at the lower pressure ratios, with the deviation being greater when the original efficiency value is lower. However, the errors introduced will normally be small even in off-design conditions because of the combinations of pressure ratio and nozzle efficiency that are likely to be encountered in practice. 

We shall discuss in Section 14.7 the nozzle efficiency for the convergent-only nozzle and hence calculate the outlet velocity and mass flow. We shall then develop similar methods for the convergent-divergent nozzle in Section 14.8. 

Estimating nozzle efficiency for a convergent-only nozzle... 

Using equation (14.66) and also the definition of m in terms of nozzle efficiency, equation (14.50), allows us to re-express equation (14.65) as... 

Imagine the situation where the manifold pressure. Pi, is gradually decreased below the inlet pressure, po, causing the mass flow, W, to increase. Row will be subsonic initially at all parts of the nozzle, so that the pressure at the exit from the nozzle will be identical with the discharge pressure p = pi. Let the nozzle efficiency to the nozzle throat be and the overall nozzle efficiency be rjN, with corresponding expansion... 

Given the isentropic index, y, the nozzle efficiency to the throat, riso, the overall nozzle efficiency, and the nozzle geometry to define A /A it is possible to solve the implicit equation (14.73) for the throat pressure ratio, Ptlp j, in terms of the exit pressure ratio, P /pqt- Figure 14.5 below shows the solution... 

We can expect the flowsheet to provide values of the pressure and temperature or enAalpy at the inlet and outlet of the nozzle at the design point. We may note also that the conditions just inside the nozzle outlet, station Nl , will be the same as the conditions in the discharge manifold, station at the design point. We may use these flowsheet values to deduce the overall nozzle efficiency at the design conditions using equation (14.5) ... 

This expression may be used in equation (14.76) to find the overall nozzle efficiency at the design point. 

Given an estimate of overall nozzle efficiency, we may apply equation (14.75) once more and solve iteratively to find the upper critical pressure ratio for the design inlet conditions, (picm i/porlo) ... 

Nozzle efficiency in off-design, choked conditions for a convergent-divergent nozzle... 

Having determined the temperature, nozzle efficiency may be determined firom equation (14.7), which compares the actual outlet temperature ratio given by... 

The first step is to calculate the efficiency at the design point. Since air is a mixture of essentially two diatomic gases, we may take y = 1.4. The design pressure ratio is 3.69/20.0 = 0.1845, and the overall nozzle efficiency follows from equations (14.76) and... 

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