The forms of the square outer rotor and the triangular inner rotor of the Feuerheerd type rotary pump are investigated mathematically. And we obtained the result that the corner radius of the inner rotor must be about a half of that determined by Feuerheerd.

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From the hydrodynamical standpoint, the characteristics of a gear pump have been theoretically and experimentally dealt with : (1) The equations of characteristics of a gear pump have been constructed as a development of the writers'previous treatments. (2) The equations were proved by experimental test to be applicable to the case in where the cavitation does not occur in the pump. (3) The coefficient of resistance, due to the eddies induced in the space between the gear teeth, was determined by experiments and its variations with the change of the head, the number of revolutions and the oil temperature were examined. (4) The equation giving the optimum value of clearance between the casing and the flat end of rotor was derived to give a maximum power efficiency, together with the numerical treatment. (5) The procedure of determining the optimum flat end clearance and gear tip clearance has been discussed.

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The author has made experiment on the gear pump by using precise exprimental apparatus. The volumetric efficiency of the gear pump was proved to be the function of μ N/P (μ=viscosity of the oil, N=number of revolution, P=pressure given to the oil by the gear pump) and coincided with the theoretical value which had been obtained by the author in his 1st Report. The total efficiency was roved also to be the function of μ N/P, excepting the loss due to the packing friction having the maximum value when the best value of side clearances was adopted, which had been obtained by the author in his 3rd Report.

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The author calulated the leakage of oil through the clearances between the casing and the tips of the gear-teeth of sine-curved gear pump devised by Dr.S. ITAYA. And considering the resistance to the motion of gear-teeth also, the author gave the best value of clearances which makes the energy loss at the clearances minimum expressed by the next equation : [numerical formula], where μ=viscosity of oil kg. sec/cm², N=r.p.m., P_d And P_s=delivery and suction pressure kg/cm², R=radius of curvature at the tips of gear-teeth cm, T=no. of teeth contacting the casing, and 2 R₂=external diameter of gears.

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It is very important to examine whether the performance characteristics of a centrifugal compressor should fall rapidly as soon as the absolute velocity of the air at the impeller exit exceeds the local sonic velocity. The experiments were performed by the present author with a centrifugal supercharger coupled with an electric dynamometer of 300 HP. The conclusions of these experimental study were that (1) the performance characteristics showed no rapid breakdown when the absolute velocity of the air at the impeller exit exceeds the local sonic velocity, this velocity being 400 m/s or so on account of the temperature rise of the air in the impeller channel, and (2) the maximum obtainable value of the pressure ratio of single stage centrifugal compressor was found to be 2.79 at the tip speed of the impeller of 435.3 m/s in this case.

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With respect to the flow of viscous fluid through parallel plane walls without a sink or source at their center, Schulz-Grunow discussed in the paper on disk friction. The present paper deals with the flow with a sink or source. The principal conclusion is as follows. When a plate is rotating, while another is fixed, the flow is characterized by two Reynold's numbers pertaining to the radial and tangential flows, respectively, The pressure shows a minimum value at a certain radius due to the centrifugal force in the case of outward flow, while it decreases with the decreasing radius in the case of inward flow. When both plates are fixed, the pressure shows a maximum value at a certain radius due to the inertia force in the case of outward flow, while it decreases with the decreasing radius, as the above case, in the case of inward flow. The velocity distribution across the plates is flat in the case of inward flow, while it has a peak in the case of outward flow. When two plates are rotating with different speeds without sink or source, the pressure increase along radius is minimum at a certain rotating speed ratio when the character of radial flow changes.

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Boussinesq's theory on the suppressed weir is derived from the assumption of the velocity distribution at the vena contracta i. e. rv=const. however, in this paper the velocity distribution is assumed r^mv=const. And better results about the coefficient of discharge and the dimensions of vena contracta are obtained.

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The fluid friction on the rotating disc in the fluid enclosed within the cylindrical vessel, which has flat ends and the cylindrical shell, was analytically treated and compared with the experimental results obtained by others. For laminar flow, the approximate solution was derived, on the basis of Navier-Stokes'equations, especially taking into consideration the existence of the cylindrical shell, which has been ignored in all treatments hitherto shown. For turbulent flow, the momentum equation has been adopted, in the assumption that (1) the flow in the boundary layer along the disc is forced radially outwards and circulates along the cylindrical surface and afterwards along the flat end surface, (2) the flow outside the boundary layer rotates in a fixed angular velocity, and (3) the parabolic and the seventh-root law holds for the velocity distribution in the laminar and the turbulent boundary layer.

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In the first report one of the authors mentioned that a selfinduced vibration of a fluid column can be generated in a pipeline to the end of which a fluttering valve supported by a spring is installed, and that the period of the vibration can be either longer or shorter than the natural period of the pipe according to the charasteristics of the system. In the present paper, vibrations based on the natural one of the water column are studied, and those vibrations can be step-wise waves having periods T=2n/c (n=2, 3, 4…………), which show, as a special case, a rectangular wave having a period T=4/c for n=2. For n=2 the maximum pressure is twice as high as the mean pressure, while for n>3 it increases with n. Further, step-wise waves can be generated even when the mean pressure is higher than the valve-closing pressure, if only the initial disturbance is sufficiently strong.

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Among the six types of simple pipe nets which we have previously treated, Type A₃ (Fig. 1) has a peculiar characteristics ; the flow in pipe line II may take a normal or reverse direction, according to the value of Reynolds number in the inflow pipe line and the length ratio l_I/d of pipe line I. We discovered these phenomena at first by experiments on a pipe net made of 10 mm glass tube (Fig. 6). Then we carried out another series of experiments on a wooden air-duct with a cross section of 8 cm square (Fig. 8), and could thereby determine the velocities of contra-flow in pipe line II. These have been compared with the results obtained by computations using the equations established by ourselves.

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Although vibrations of the draft tube of water turbines have been frequently observed under part load operation, character and mechanism of the vibration are not known exactly. Some experiments on the vibration were carried out with a model of the draft tube of a water turbine, and the obtained results may be sumarized as follows : (1) The draft tube makes very complicated vibration with many frequencies. (2) There is one kind of dominant vibration, of which frequency varies as the rate of discharge, and its intensity becomes violent as the whirling angle of water increases. (3) Some kinds of longitudinal (axial) vibrations are likely to occur.

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It is shown, by a simple calculation, that the so-called phenomenon of power swing in hydro-electric power plant can occurr only when the length of the penstock is so chosen as to make possible the resonant oscillation of water column of the penstock with the oscillation of water column of draft-tube.

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This paper presents the experimental results on a small multiclone-type unit cyclone with a dia. of 30 mm, which is connected to the suction side of high speed motor fan, in order to investigate the characteristics of small cyclone separator using to measure the dust content of flow-gas. From the test results, we assumed that, the entering stream in the annular space above the bottom of the exit pipe flows down forming a forced voltex flow, and below the bottom of the exit pipe, its flow changes to a double eddy type flow consisting of an outer downward free voltex and an inner upward combined voltex such as Rankine's flow. The tangential velocity distribution of gas flow above and below the bottom of the exit pipe may be given by the following expression. v_i=c/rⁿ The value of n determined in the present experiment is 0.5∼-1. The test cyclone has shown that the separating eff. exceeds 99% for nealy all kinds of industrial dust particles with a dia. of between 0.7∼1.0 micron, and slightly more increases than with no an enlarged dust hopper. We compared the partial separating capacity at various points in cyclone with the total separating eff. by injecting known quantities of dust at these points and determined the equal partial eff. distribution curve.

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