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The reverse problem of computing the shape of a weir profile for achieving an assumed discharge-head relation is solved. In a logarithmic weir, the discharge is proportional to the logarithm of the head measured from a certain datum. This weir needs a compensating bottom since its discharge-head relation involves a term of head which has less than 3/2 power. Different shapes of compensating bottoms as provided earlier in a linear proportional weir are also fitted for the logarithmic weir. The ranges of logarithmic weir profiles have been increased for the purpose of passing a design discharge under weir flow condition. This has been achieved with the help of an arbitrary number introduced into the discharge-head relation. Experiments were conducted on two typical logarithmic weirs that yielded a value of 0.60 for the coefficient of discharge.

Leakage tests have been run over a wide range of pressure ratios and clearances for several types of seals. The results of tests of labyrinth seals show some important differences compared to previous theory. The discharge coefficient of a single seal has been found to jump from 0.62 to 0.78 when a second seal is added downstream. This effect depends on the clearance, pitch, and the pressure ratio across the seal. This phenomena has not been considered in past theories which assumed fixed seal discharge coefficients independent of the seal position and its pressure ratio in the Labyrinth. The test results are presented in a form which is easier to use than those based on the more complicated previous theory.

This study is concerned with predicting the performance of an air-augmented waterjet with a converging-diverging nozzle. The device under study is one in which compressed air is injected into the high-pressure water stream leaving the water pump. A mixture of water and finely dispersed air bubbles is generated in a constant-area mixing chamber, which joins the water-pump outlet. The two-phase bubbly mixture enters the coverging-diverging thrust nozzle and expands under the action of a negative pressure gradient. The two-phase nozzle flow is analyzed through application of the conservation laws for a single air bubble and an incremental control volume over a nozzle section. Three different models which describe the heat transfer between the air bubbles and the water are considered. Results indicate that thrust augmentation is most effective for low pump-outlet pressures and for high mass flow ratios in the range permitting bubbly fow. The solution of the nozzle flow was accomplished by specifying the velocity distribution in the nozzle and calculating the nozzle geometry. Several expressions were used to calculate sonic velocity and it is shown that discrepancies exist between the computed results of the different expressions. Also none of the expressions place the sonic velocity at the throat. Thus, it is shown that further work is needed in determining sonic speed in two-phase compressible mixtures.

The effects of initial velocity and temperature lags between the solid particles and the gas in the high speed flow of a gas-solid mixture through a convergent-divergent nozzle are investigated. The results are interpreted physically in terms of the relative importance of heat, momentum, and kinetic energy transfer between the solid particles and the gas, and nozzle area variation. The influences of solids loading, solids specific heat, solids density and particle diameter on the flow process are also examined.

Intake towers and weirs in reservoirs with samll water depth and for small floods can be designed with polygon in plan in several cases. The polygon is easier to construct compared to the circle in plan, but the hydraulic computation is more complicated. The article shows the influence of an individual corner of the polygonal weir on the discharge coefficient and therefore on the discharge capacity. The independent variable hydraulic and geometric parameters, e.g., corner angle, weir height, and overall head influence the flow at the weir and over the weir crest in different ways. All the results of this basic investigation show that a simple mathematical relation between disturbing effect of the corner and the overall head can be assumed. A simplified two-dimensional flow theory is developed to make the hydraulic computation of the discharge capacity of polygonal weirs possible.

Values of the discharge coefficient for air flow through single holes in a pipe wall, and for the angle of efflux are reported. The variation of static pressure along tubular polyethylene air ducts with a maximum length-to-diameter ratio of 250 containing pairs of diametrically opposed holes has been measured. This information was used with data on friction loss to determine values for the coefficient of static pressure regain. It was possible to predict variations in static pressure and air discharge along uniformly perforated ducts which were in good agreement with those observed experimentally.

Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures (100 atm (100 × 105N/m2)) where real-gas corrections are significant. Throat Reynolds number range extended up to 8 × 106. Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 percent. Experimental coefficients for a long-radius ASME nozzle agreed to within 1/4 percent to an empirical equation representing the most probable subsonic discharge coefficient.

The situation chosen for study is a gaseous jet that is injected through a transverse slot nozzle in a wall and into a supersonic external flow which is uniform outside of a turbulent boundary layer. Experiments were conducted with normal, sonic jets and forward-facing steps at external flow Mach numbers of 2.5 to 13, and Reynolds numbers based on running length of 7.5 X 10 to 5.5 x 10. The amplification factor (the upstream interaction force plus the jet thrust normalized by the vacuum thrust of a sonic jet) is relatively insensitive to variations in external flow Mach number and Reynolds number. The effect of pressure ratio on amplification factor is very small when the external flow properties and jet mass flow rate are held constant. Plateau pressures associated with separation upstream of the jet or step, and wall static pressure distributions near the separation line are in good agreement with existing correlations.

The exit condition at the trailing edge of a nozzle for slightly unsteady flow has been investigated experimentally. This problem plays a crucial role in sound transmission through nozzles with flow. The measuring technique used is new and is based on the synchronization of a laser beam to the wave motion of a small smoke filament in the boundary layer leaving the nozzle. The resolution of the jet flow deflexion measurements is of the order of 1–3μm. The authors found the jet deflexion envelope to have a nearly parabolic shape near the nozzle edge. The size of this ‘parabolic’ region decreases with decreasing Strouhal number. This statement applies to the motion of the exterior border of the boundary layer at the dividing streamline between flow originating from the interior of the nozzle and flow coming from outside. It was found that the unsteady flow problem near the edge remains linear for fluctuating velocities of small magnitude.

The effect of inlet edge roundness on the discharge coefficient of an orifice plate is studied experimentally. Several methods for measuring edge roundness are discussed and applied. An optical method in particular is shown to provide reliable measurements of edge roundness. Flow results are summarized in terms of radius of curvature by the empirical equation ΔCD/CD = 0.85 ln (rk/d × 103) + 1.74.

The UVT provides Classical Venturi tube type metering performance with less than half the laying length, no annular chambers, and about half the permanent head loss. Data presented reveal the flow mechanism inside the tube and substantiate its performance over a wide range of Reynolds numbers, line sizes, beta ratios, tube materials, upstream and downstream piping configurations for incompressible and compressible flow. The experience of the past five years indicates ± 0.5 percent two times standard deviation uncalibrated accuracy for C.I. UVT’s. Due to its depth and method, the substantiation work was unique; consequently, it is recommended as a standard procedure for the performance substantiation of any kind of flow meter presently in use or to be introduced in the future.

A generalized rational equation is derived for the discharge coefficient of differential pressure-type fluid meters. Its factors are particularized for throat tap meters, pipe wall tap nozzles, and for orifice-type flow meters. Comparisons are made with available theories and with current Fluid Meter practices, and these support the new formulation. Because of its rational basis, the generalized equation may be useful for extrapolations to Reynolds numbers which lie beyond the capabilities of calibration laboratories.

Using Walz’s approximation method for boundary layer calculation, along with a one-dimensional treatment of the compressible inviscid core flow, discharge coefficients for small nozzle to pipe diameter ratios have been calculated. Discharge co-efficients calculated for the ASME long radius nozzle agree with those recommended by the ASME Power Test Code. In addition, experimental confirmation of an indicated Mach number effect has been achieved in a nozzle modified to minimize two-dimensional effects.

The history of pipe wall tap nozzles and throat tap nozzles, as to performance characteristics, is briefly reviewed. A series of tests was conducted on pipe wall tap and throat tap nozzle installations at three independent calibration laboratories. These results are presented, analyzed, and compared with existing rational, empirical, and nominal performance characteristics in the form of discharge coefficient versus the throat Reynolds number. On the basis of these results, a recommendation is made that both pipe wall tap and throat tap nozzle installations be considered as equally accurate for use in precision fluid metering work.

A formulation is presented to describe the rate at which a solidified crust is formed (and possibly remelted) on the inside walls of a nozzle through which molten metal is being poured. The molten metal stream is considered to be turbulent and in the formulation allowance is made for transient heat conduction in the skull and in the refractory walls, together with the time dependent mass flow rate due to the presence of the skull. The resultant differential equations are solved numerically and computed results are presented for conditions that are thought representative of some tundish pouring practices. It was found that the growth and possible remelting of the solidified crust would take place very rapidly, in a matter of seconds. The effect of several parameters was examined, including the role played by the nozzle diameter, the superheat of the steel and the preheating of the nozzle walls. It was found that the nozzle diameter was the most critical variable; nozzles less than about 1/2 in. in diam were likely to freeze rather readily. The superheat of the steel was found important in affecting closure, but the preheat of the nozzle appeared to be less significant a variable, provided the nozzle was brought within about 500‡F of the freezing temperature of the steel.

An electric discharge in a flow of ionized gas is widely used in many physics and engineering problems. Among them are problems associated with current flow in various magnetohydrodynamic devices (generators, accelerators), arc shunting in a plasmatron, physical experiments in shock tubes, etc. It is known that with cold electrodes providing the contact between the plasma and the external circuit and relatively high pressures, two modes of current flow occur: at low current, the discharge is of a distributed nature; as the applied voltage increases, the discharge abruptly shifts into a discharge with a clearly developed cathode spot at some critical current density (we call this form of discharge an arc discharge). Existing experimental data [1–20] refers to varying experimental conditions. Furthermore, the critical voltage (or current) at which the transition of the discharge from a distributed discharge to an arc discharge occurs varies within very broad limits. From an analysis of the experimental data, a condition is formulated which the discharge parameters satisfy at the time of transition from a distributed discharge to an arc discharge.

An experimental investigation was made of electrical discharges in supersonic unsteady streams of molecular gases generated by exploding acetylene-oxigen-nitrogen mixtures. High-speed photography was used in an investigation of the discharge configuration in the case of flow around cylindrical electrodes placed along a wedge-shaped nozzle. No contraction of the discharge was observed when the power input was up to 0.5 kW/cm3.

A digital computer program is described for aircraft ejector performance analyses. The effects on performance of temperature ratios, pressure ratios, specific-heat ratios, pressure losses, and aircraft forward speed are included. Momentum correction factors are computed within the program, and the method by which these are determined for rectangular ejectors with multiple nozzles is described. Theoretical and experimental results are compared for rectangular ejectors employing hypermixing nozzles and microjet nozzles. It is demonstrated that the predictions of thrust augmentation ratio are within 3% of the test data. The effects on performance of pressure ratio, temperature ratio, nozzle spacing, mixing section length, inlet and diffuser performances, and the degree of mixing achieved are presented. The analysis clearly demonstrates the importance of rapid mixing, and the role that the ARL hypermixing nozzle has played in advancing the state-of-the-art of aircraft ejectors.

A theoretical discussion is presented of the noise generated when a jet exhausts from a constant pressure plenum chamber into an unsteady atmosphere. That unsteadiness provokes fluctuations at the nozzle exit and these are evaluated by taking into account a model of the axisymmetric jet instability modes. It is found that the radiated noise is virtually omnidirectional and that it depends strongly on both the jet Mach number and nozzle contraction ratio. This sound mechanism vanishes completely when the jet becomes sonic. Then, despite the unsteady external field, the nozzle flow is unperturbed. The sound power radiated scales on the sixth power of jet speed so that it is likely to dominate over the jet mixing noise at low Mach number. The mechanism can be driven by any aerodynamic perturbation around the nozzle, but it is found that if the perturbation is acoustic, the scattered energy is an altogether negligible fraction of that incident on the nozzle area.

Recently published work concerning the dynamic flow-rate through servo-valves is discussed. It is shown that there is some disagreement amongst workers concerning the effects that fluid inertia and valve discharge coefficients have on the dynamic performance of these devices. The problem of measuring pulsating flow is discussed and the various commercially available transducers are shown to have shortcomings when used in conjunction with servo-valves. An alternative indirect dynamic flow measurement technique is described. The technique is evaluated using an analogue model. It is concluded that the method is capable of determining the dynamic volumetric flow-rate. The difficulties involved in identifying the valve dynamics from these measurements are discussed. The method is applied to determine the volumetric flow-rate in an experimental rig consisting of a servo-valve controlling a rectilinear motor used to position an inertial load.

A method is proposed which has been experimentally verified for analyzing porosity‡ data in terms of two dimensionless parameters—the discharge coefficient and Reynolds number—char— acterizing the flow through interyarn pores of a metallic fabric. It is experimentally shown that porosity data for wire screens ranging in texture from 8 to 120 wires per in. and in porosities from 30 to 680 ft.3/ft.2, min. can be plotted within rather narrow limits as a single line relating the two dimensionless flow coefficients.

Hydraulically speaking, two extreme cases can be distinguished, depending on the degree of envelopment of the flow by solid walls, i.e. a) the flow is completely surrounded by the walls, e.g. as in a bottom outlet (Fig. 1) ; b) the liquid is in free fall through the air (Figs. 4 and 6). The aeration coefficient α (ratio of air flow rate to liquid flow rate) is given by equation (3) for case (a) and by graphs 5 a and 5 b for case (b) * *. Symbols H and he are explained in Figures 1 and 2 and the coefficient K is given by table No. 1, in terms of the geometric and hydraulic characteristics of the bottom outlet. The symbols used in graphs 5 a and 5 b are explained in Figures 4 and 6. The vent cross-sectional area for a bottom outlet (case a) is found from equation (11), in which the number 28 is found from √(Ywater/Yair), ma is given by (7), Bc and hc are the width and depth respectively of the contracted section of the jet of water immediately downstream of the gate and Ha the permissible depression in metres of water. Equation (13) gives the area of the aeration ducting for case (b). α. is taken as 0.5 α to allow for the fact that aeration need only affect the lower part of the sheet of water. mdev. = the weir discharge coefficient. The other symbols are indicated on Figures 4 and 6. The critical negative pressures and corresponding air velocities for cases (a) and (b) are shown in tables Nos. 2 and 3 respectively, the former with ma = 0.7 and the latter with ma= 0.95. Paragraph V consists of two complete numerical examples, i.e. Case (a) : a 3.5 m diameter bottom outlet with a flat 3 by 2.8 m gate. The critical opening is about 80 %. Case (b) : rectangular weir of width B = 4 m, head of water hdev = 0.85 m. Vertical distance between weir crest and downstream channel Z = 1.80 m. The dimensions of the shafts on each size of the weir can be calculated from Figure 6. A very short bibliography is appended.

In this paper, various rational, semirational, and, empirical approximations for the ASME long-radius, flow-nozzle discharge coefficients are first reviewed. These approximations are then compared to obtain the most probable representation of ASME flow-nozzle data according to a mathematical method developed in the paper. A table of most probable discharge coefficients versus the throat Reynolds number is given, based on the results of this study.

The results of a number of previous investigations of the discharge characteristics of parallel-bore orifices with length/diameter ratios up to 10 and Reynolds numbers up to about 105are collected and discussed, together with new data which extend to Reynolds number as low as unity. Simple empirical expressions, which fit the data well, are suggested for design purposes.

SummaryA choked nozzle with an appropriate wall contour has adischarge coefficient, CD, so close to unity that a theoretical calculation of (I—CD) would allow the nozzle to be used as an absolute meter for air flow. The high discharge coefficient results basically from the fact that ∂(ρv)∂p=0 at M=1.Simplified calculations yield formulae for the boundary layer displacement thickness and for the flow reduction resulting from the variation in static pressure across the throat. The optimum profile for the wall at the throat of an absolute meter is suggested to be a circular arc of radius of curvature equal to about twice the throat diameter. For such a meter the theoretical discharge coefficient is found to be within ¼ per cent of 0·995 over a wide range of Reynolds numbers.The uncertainty in the discharge coefficient for a steady flow at Reynolds numbers of 106 and over appears to be less than ±0·15 per cent, both when the boundary layer is known to be entirely turbulent and when it is known to be entirely laminar. When the state of the boundary layer is not known the corresponding figure appears to be ±0·25 per cent. Experimental information might therefore be helpful on transition—under the appropriate conditions of flow unsteadiness and rig vibration. Available experimental results with known boundary layers tend to confirm the theoretical discharge coefficients down to a Reynolds number of 0·4x106.A pressure ratio of about 1·1/1 or less would probably be sufficient to establish fully supersonic flow if the nozzle were followed by a suitable diffuser.

In this report the author has made an experimental analysis on the lateral forces, the discharge coefficient, the stability and frequency of a poppet valve. The results are compared with the theoretical analysis reported already in the first report. It is made clear that (1) in order to increase the lateral stability of a poppet valve, it is necessary to make a valve seat ratio larger, to lower a valve lift and to use a working fluid of high viscocity, (2) the theoretical computations show good qualitative agreement with the experiments, and if we adopt the concept of "the effective valve seat ratio", the theoretical computations show good quantitative agreement with the experiments.

The numerical solution of the problem of the motion of a swirling flow of an ideal gas in a Laval nozzle in axisymmetric formulation is obtained by the method of stabilization. As a result, a number of effects appear that are essentially not one-dimensional, in particular, the drawing-in of the sonic line into the nozzle, an effect that leads to a decrease in the nozzle's expansion coefficient. The dependence of this coefficient on the intensity of the swirling is obtained. A number of problems connected with the control of the expansion of a gas through a Laval nozzle and with variation of the thrust of a nozzle can be solved successfully in cases where a rotary motion is imparted to the flow of gas exhausted from the nozzle. Investigation of such a swirling flow in [1, 2] and a number of other papers are based on a one-dimensional model of gas flow, which makes it possible in principle to obtain integrated characteristics of the flow.

This paper discusses two important forms of loading experienced by sounding rockets: the running loads due to distributed aerodynamics, and loads due to aerodynamically induced pressure differentials across the skin and across internal bulkheads. An empirical method, based upon experimental data, for the rapid and accurate determination of distributed aerodynamic loads on arbitrary bodies of revolution is outlined, and comparisons of typical results with wind-tunnel data are presented. In addition, the equations describing the venting of an "ra" volume system have been derived and a comparison of experimental with analytical results for a four-volume system subjected to a typical launch pressure profile are included.

The choking of nozzles at pressure ratios below the critical has long been understood. Knife edge orifices however do not appear to choke. This can be explained and the variation of discharge coefficient with pressure ratio may be calculated. The present paper is an experimental investigation into the discharge through thick plate orifices when the pressure ratio is in the vicinity of its critical value. A comparison is made with the results of other workers and an attempt is made to explain the discharge characteristics of thick plate orifices.

This paper presents the results of experimental work carried out recently to determine the effects on the discharge coefficient of various degrees of pipe roughness adjacent to and at different distances from an orifice plate. Experiments were carried out for air flow in 12-, 6-, and 3-inch pipes and water flow in 3-inch pipes. Downstream, severe incrustation has no significant effect. Upstream, the effects vary with degree of roughness, pipe diameter, m value, and Reynolds number. For an m value of 0·5 and severe conditions of roughness, the combined effects of roughness and pipe diminution produce disturbance factors of the order of 1·40, 1·17, and 1·08 respectively for 3-, 6-, and 12-inch pipes. A length of two diameters of rough pipe immediately upstream from an orifice plate gives an effect close to that which would be obtained for a very long rough pipe. It has been found possible to extrapolate the results to very large pipes. One of the most important findings is that cleaning a rough upstream pipe adjacent to an orifice plate for a relatively short distance reduces errors which may be otherwise very considerable to within known small limits. A table detailing the extent of such cleaning for various pipe sizes, mvalues, and degrees of roughness is given. It is recommended that, where reasonable accuracy is required in the flow measurement of dirty fluids, installations should be designed for easy periodic inspection and cleaning of the upstream pipe adjacent to the orifice plate.

Results of laboratory experiments conducted to provide data on accuracy of Palmer-Bowlus flume; coefficient of discharge for flumes and hydraulic aspects of Venturi flow, such as energy criteria, channel slope, submergence, and velocity of approach, are discussed; results show influence of various flume dimensions such as throat length, side slope, base height, transitions, and point of depth measurement on accuracy of flume.

A standard-shaped spillway, when operating at greater than design head, experiences a subatmospheric crest pressure. Quantitative data obtained from laboratory measurements of minimum pressure and discharge occurring during flow over spillways are presented in dimensionless form. Minimum crest pressures as well as discharge coefficients are shown to be functions of the spillway design-head-to-height and head-to-design-head ratios. A dimensionless parameter involving discharge and minimum pressure, but not head, is formulated and evaluated. The results are used in a numerical design example to proportion a standard-shaped spillway to pass a particular discharge with a predetermined pressure occurring on the crest. The resulting design is compared with an actual design for the same spillway.

A theoretical equation for estimating the mixing loss coefficient is given for mixing of two concentric jets. The equation has been experimentally verified with water as the working fluid. In the experiments, two outer nozzles of semicone angles of 12○ and 24○ were used for different velocity ratios varying from 0.00824 to 0.792. For an area ratio of 0.228 and main nozzle semicone angle of 12○ four nozzle distances of 2.4 cm, 3.4 cm, 4.4 cm, and 7.9 cm were tested. The mixing loss constant reduces with increase in velocity ratio to unity, beyond which it increases with increase in velocity ratio for a given area ratio and angle. The mixing loss constant increases with nozzle angle when all other parameters are constant. For a particular mixing configuration the mixing efficiency increases with nozzle distance and reaches an optimum value; with further increase of nozzle distance it decreases. An optimum efficiency for mixing of the order of 98% was obtained at a velocity ratio of 0.642 for a nozzle semicone angle of 24○ at a nozzle distance of 7.9 cm.

Results are presented of an experimental investigation of the dependence of the apparent mass on the number Ma at the nozzle exit, on the off-design factor n, and the distance ¯x from the nozzle exit.

The discharge characteristics of nozzle or orifice for high-pressure type air-micrometer were investigated for pressure difference from 0.2 kg/cm2 to 3.0 kg/cm2 over a range of pressure ratio from 0.25 to 0.95. The experiment has revealed the following : 1. By plotting (c : discharge coefficient of incompressible fluid, e : expansion factor) against the pressure ratio, using parameter l/d, a nearly linear relation is obtained. For rounded nozzle, cylindrical nozzle and knife-edged orifice, a change of flow regime occurs respectively at the pressure ratio of 0.53, 0.55, and 0.63. 2. The values of ce at a position where the pressure ratio is equal to 1 agree with discharge coefficients of incompressible fluid over the so-called "limit of constancy"of Reynolds number. 3. Discharge coefficients of each type of nozzle and orifice were collected and one experimental formula is worked out for each. 4. Downstream pressure and temperature are recovered at a position respectively 5 times and 4 times the pipe diameter. 5. Recovery rate of pressure was nearly same as in 1 st Report.

Simple theory indicates that when critical flow of a gaseous fluid is established in a given passage, the rate of mass flow becomes dependent only on the absolute pressure and temperature upstream, and changes in downstream conditions no longer have any influence. In practice, some modifications of the theoretical conclusions may sometimes be necessary. The discharge coefficient of a simple plate orifice, for instance, is greatly dependent on the amount of jet contraction, and this may be influenced by changes in downstream pressure even under critical-flow conditions. However, a properly shaped flow nozzle is not affected in this way, and is well suited for flow measurement under critical conditions. In the experiments described, a large number of small-diameter nozzles with quadrant entrances was tested, and the effects of nozzle length/throat diameter ratio and entry radius/throat diameter ratio were carefully examined. A range of simple cylindrical nozzles was also tested. Such nozzles are easily reproduced and are to be recommended in cases where a rather low discharge coefficient is not a disadvantage. The above experiments were made with smoothed steady flows but in addition a number of trials with pulsating flows was carried out and it was found that the observed coefficients of discharge for pulsating flow differed very little from those applying to steady-flow conditions. In view of the acknowledged difficulty in metering unsteady flows, this is a most valuable property, and it is thought that critical flow meters are very suitable for measuring the output of reciprocating compressors, free piston gasifiers and other plant delivering gas at high pressure.

The viscous core of an incompressible, swirling flow through the nozzle is treated by momentum-integral equations. These equations, together with the statement of the conservation of mass in the whole nozzle and the conservation of momentum along the nozzle axis, form a system of four ordinary, nonlinear differential equations. This system of equations is solved for the circumferential and axial velocities both inside and outside the core. This system has a singularity which occurs when the square of the ratio of the circumferential to axial velocities, at core boundary, reaches a certain value depending upon the axial velocity profile. This singularity divides the possible solutions into those in which the core is massflow dominated and those in which the core is swirl dominated. The massflow-dominated core occurs at low swirl and is characterized by high discharge coefficient, which is essentially unaffected by the swirl and by a certain maximum total pressure loss which is inversely dependent on nozzle contraction. The flows with the swirl-dominated core have their discharge strongly throttled by the swirl, have the capability to sustain very large total pressure loss, and usually have regions of reversed axial velocity. The increase of Reynolds number tends to decrease the discharge coefficient, whereas the change from laminar to turbulent flow tends to increase the discharge coefficient. Both of these effects are particularly pronounced in swirl-dominated flows.

1. The values of the initial coefficients of discharge for double-bevel diaphragms were determined for moduli of 0.0905, 0.1624, 0.2504 and 0.3694 in the Re range of 240 to 1900. 2. The root-mean-square error of the initial discharge coefficient did not exceed 0.18%. 3. The relation ofαu=f(m; Re) derived in the article makes the calculation of double-bevel diaphragms possible for Re values between 240 and 1900.

The discharge coefficient of orifice meter in a commercial 1/2" gas pipe for plastic fluid was calculated and C vs. Re diagrams were drawn.The concentrations of sludge tested were 4.1, 10.8, 15.0, 17.5, 23.1, 26.6, 31.2, in wt. % and the ratios of the orifice areas to the sectional area of the pipe were 0.096, 0.247, 0.348, 0.467, 0.652.The results of the experiments were as follows:(1) The limits of the concentration for measurable flow rates are, m=0.247, up to 31wt.% or more. m=0.467, up to 26wt.%m=0.348, up to 31wt.% m=0.652, up to 17wt.%(2) The drag coefficient C increases rapidly when Reynolds number Re is less than 104, and after having reached maximum value, it decreases as Re decreases.The more the value of m becomes the greater is the value of Cmax., and tbe steeper is the slope of the curve.(3) The more the concentration of sludge becomes the smaller is the value of Re at the point where C reaches maximum.(4) When m is constant, C approaches a constant regardless of concentrations of sludge within the range for Re>2×104.

The duration of uniform flow and wall boundary-layer growth have been measured in the conical nozzle of a reflected-shock tunnel operating at high-enthalpy conditions. Experiments were performed in air for shock-tube Mach numbers of 16.5 and 11.5, with corresponding initial driven-tube pressures of 0.5 and 10.0 torr, respectively. Several different diagnostic techniques were used to measure the uniform-flow period and the results are compared. Radiation-intensity and electron-density measurements were found to be the most sensitive flow indicators. The boundary-layer displacement-thickness growth on the nozzle wall was determined for both of the aforementioned experimental conditions using velocity and density profiles deduced from Pitot-pressure and stagnation-point heat-transfer measurements. Good agreement was found between experimental and theoretical Pi tot pressures at comparable inviscid area ratios. The measured boundary-layer and displacement thicknesses are compared with the results of two typical prediction techniques. ART I of this paper describes the studies of the shock-tube flow and nozzle starting time. The purpose of Part II is to describe the subsequent nozzle-flow experiments in which the test time and the boundary-layer growth were experimentally determined for high-enthalpy reflected-shock conditions. The results are presented here because boundary-layer measurements obtained for such flow conditions are relatively scarce in the literature. The nozzle boundary layer was investigated with the aid of radial surveys of Pitot pressure and stagnation-point heattransfer rate at several axial locations. These measurements were used to deduce the local velocity and density relative to the corresponding values on the nozzle centerline, and the experimentally determined profiles were used to calculate the appropriate boundary-layer displacement thickness. Many authors1"11 have proposed techniques that may be used to predict the boundary-layer growth on the wall of a conical nozzle, and the present results can be used to test these techniques. However, the major emphasis of Pt. II has been placed on the experimental measurements, with only a limited comparison with prediction. Two particular prediction techniques2-5 have been selected as typical and the experimentally determined boundary-layer and displacement thicknesses are compared with these. The experimental apparatus used in this work was described in detail in Pt. I. The first part of Sec. 2 of Pt. II presents the experimentally determined test time at different locations in the nozzle and compares the results of the various diagnostic techniques. Section 2 concludes with a discussion of the boundary-layer data obtained at each of the experimental conditions and compares the results with existing prediction techniques.

The rate at which evaporation can occur from a surface is limited by the rate of heat flow into the surface. Because of this limitation when a liquid at its boiling point commences to flow, the proportion of vapour which forms as a result of the Bernoulli fall in pressure is less than is calculated from adiabatic expansion. A theory for the actual amount of vapour which will form is given, together with an analysis of its effect upon the velocity of flow and the quantity of fluid passed by a nozzle. It is found that although the system consists of a central core of liquid and an envelope of vapour, the calculated limiting velocity of flow, which is the velocity of pressure propagation in the system, is low. The order of magnitude is 20 m./sec. as compared with 400 and 1500 m./sec. for vapour alone and liquid alone respectively. There is a corresponding critical pressure, analogous to that in a gas nozzle, but in contrast to the gas case, both the critical pressure and the limiting velocity itself are functions of the diameter and length of nozzle. Experiments are described which confirm these theoretical deductions in all respects, and which also show good quantitative agreement with calculated velocities, critical pressures, and amount of discharge and of evaporation. On the basis of this experimental verification general phenomena to be expected in pressure propagation through liquids near saturation temperature are discussed.