At first, this paper presents a method of conformal transformation which is applicable to the latticed wing with large camber as in the case of steam turbine runner blade. The function of transformation is ; [numerical formula] where, C_z is an integral constant, u₀=r/π, W=φ+i⩛. As the next, giving a good distribution of circulation, the author corrected the form of blade which is obtained by above mentioned transformation. And further, giving the good pressure distribution which has the same distribution of circulation by above mentioned method, the author researched the blade form which satisfies the above condition.

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A method of successive approximation is shown to calculate the characteristics of the finite profiles arranged in an experimental device, and to clarify the difference between the flow in the experimental arrangement and the ideal lattice flow, on the assumption that the flow can be treated equivalently as two-dimentional and potential. The convergency of the successive approximation and the accuracy of the results are shown clearly in the numerical calculations in comparison with the experimental data. The superiority of the experimental device with movable walls is easily seen throughout these results. However, the previous study by G. Kamimoto seems, although his process of calculation is simpler, is not so numerically reliable because of the more approximate assumption in it.

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In order to obtain the profile form suitable for the blade of axial flow water turbines, a method is first stated to calculate the profile which has a given surface pressure distribution and a unmovable pressure center in a given lattice condition. The succesive approximation is applied, upon the basis of the fundamental equations of a lattice used in author's previous study, and, so far as it is concerned with the usual blade element of axial flow turbines, satisfactory results are expected to be obtained when the process of the successive approximation is repeated two or three times. For example two profiles are calculated by this method and compared respectively with Clark. Y. of the corresponding thickness ratio.

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The method used in the past to solve these problems has been to map the blade sections into a single figure, thus eliminating the periodicity of cascade, and then discover a method of further transforming that figure into a circle. However, these methods seem to become exceedingly difficult as the pitch-chord ratio of cascade decreases and as the camber and thickness of blade section increase. Method of combining the two previous operations of mapping in one is sometimes adopted but even then, it is impossible to avoid these difficulties. The author has avoided these difficulties by mapping the odd numbered blade sections into a circle, the even numbered blade sections into a concentric circle and thereby mapping the field of flow through the cascade into the region between these two circles. This method is applicable to cascade of small pitch-chord ratio and to blade section of large camber and thickness and gives rigorous solution.

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The flow in the boundary layer has been regarded by many investigators to be independent of the curvature of the wall along which it grows. This is true for high Reynolds'numbers, but the influence of curvature cannot be neglected for comparatively small Reynolds'numbers. To find the influence of curvature, the equations of motion expressed in curvilinear coordinates were solved more accurately than the usual boundary layer theory, and the tables were given to determine the pressure and velocity in the boundary layer to the order of 1/√(R_e). As examples, the flow around a circular cylinder was calculated for three cases. The influence of the curvature is small for R_e=1·85×10⁴, but cannot be neglected for R_e=2·56×10³ and 3·6×10². In this way, by taking into account the influence of curvature, we can apply the boundary layer theory to the case of the Reynolds'numbers lower than the usual.

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As far as the authors are aware, no formula, proposed up to this time concerning the frictional resistance of the turbulent flow in the annular space formed by two concentric or eccentric pipes, covers simultaneously both critical flows, i.e., the flow in a single pipe (radius ratio ε is zero), and the flow in the extremely narrow annular space (ε tends to unity) where ε=r₁/r₂, r₁ and r₂ is radius of inner and outer pipe respectively. According to Karman's One-seventh Power Law for the velocity distribution, we obtain the general formula for the frictional resistance of the turbulent flow which is applicable not only to the whole range of the radius ratio (ε=0·0∼1·0), but also to the both cases of concentric and eccentric pipes. This formula shows good agreement with experimental results.

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Hypotheses of Prandtl, Xarman and Taylor for mixing length cannot be extended to other arbitrary shapes of the cross section than a channel and a circular pipe. Even in these cases velocity distributions given by the above hypotheses show the considerable deviation from the experimental results, which must be due to the effects from all parts of the boundaries not being fully taken into account. Making a new assumption for mixing length which can be applied to any cross-sectional form, the author has been able to express the effects from all parts of the boundaries. The results have been found in good agreement with experiments in cases of channel and circular pipe flows.

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This study is intended to be a contribution to the precise measurement of the surface tension of liquids, especially of molten metals. We propose a new method for calculating the surface tension from the photograph of the pendant drop. We deal with the case in which the pendant drop has an axis of symetry. Notations : p₀=the pressure difference at the apex between in- and outside of the surface. ρ=the difference of density between the drop and its surrounding. σ=the surface tension of the liquid. g=the accelaration due to gravity. A=a constant for the case (=p₀/gp). B=the capillary constant of the liquid (=2σ/gp). Introducing two parameters X=sin θ/r and Y=z-(1/r²) ∫^z₀ r²dz, we have the relation Y=A-B X which indicates a straight line. From this we can compute the capillary constant B by the method of least square, using the values of X and Y obtained experimentally at many points on the meridian. As regards the accuracy of the method, we find that, through repeated experiments on distilled water, the range of errors is 0.5%. Such an accurate result can not be obtained by other drop shape methods.

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The most important factors for the operation of a cyclone dust separator are pressure loss and separation efficiency, and yet there are a few fundamental and exact investigations. We have measured the air flow in four small cyclone dust separators by means of a cylindrical pitot tube, and examined the effects of diameter and length of the cylindrical part and of the central exit pipe inserted, as well as the angle of cone, and the mode of inlet part of the separator. A horizontal type of the separator was also examined. The results give us a fundamental concept about design formula of pressure loss and efficiency of the separator, and some referential data of spiral flows. The error of the cylindrical Pitot tube in a cyclone was also studied. The remarkable results are following. 1. Radial velocity is not axially symmetrical. 2. The maximum velocity and zero statical pressure are at about 60% of the exit pipe radius r_e. 3. Pressure loss and the maximum velocity of a holizontal type are small. 4. Inner obstacles (including a guide vane and a Pitot tube) reduce pressure loss and the maximum velocity. 5. The effects of inserted length of an exit pipe are comparatively small. 6. Fomula of velocity distribution, r_θ×rⁿ=const. n<1, at r>0·6 r_e, where, r_θ : rotational velocity (&vBarv;, total velocity), r : radius, r_θ=r×const. at r<0·6 r_e.

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In order to find the best condition for separating powder in desirable grain size by a cyclone, we tried to investigate the air current in the cyclone and to find out mechanism of separation. We used a Pitot tube to measure the direction, the pressure and the velocity of air flow in the cyclone. The results are as follows : -(a) The direction of the flow is independent of air velocity and its inclination to the axis decreases according to the distance from the top of the cyclone and the distance from the periphery, slightly increasing near the center. (b) The tendency of the increase and decrease of the air pressure and the tangential velocity are also similar to that of (a). (c) Vertical downward velocity decreases rapidly toward the center from the wall and becomes nearly zero except in the neighbourhood of the center. (d) We observed the ascending flow of air at the center. We took photographs to observe the aspects of the powder separation in the cyclone, and we found there are three zones except the core in the cyclone. The first is the neighbourhood of cyclone wall where most of powder separated aggregate, and the second is near the core where small part of powder contained in this zone. The last one is in the middle of the two zones where there is no powder. We proved these results agree with our illustration which is based on the experiment of the air flow.

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A jet pipe has been used as an element of an automatic controller, but we know little about the performance, for example, the correlation between position of a jet and pressure at an opening on a surface on which the jet strikes. Using water jet issuing from a nozzle of 2mm diameter, the present writer investigated experimentally the influence of shape of surface on the performance. The results obtained are as follows : 1) If the diameter of an opening is nearly equal to that of a jet, and the water discharge through the opening is zero, pressure at the opening is considerably high even though the jet does not strike just on the opening. For example, when the position of the jet ξ/d is 0.5, pressure maintains nearly 0.8∼0.9 of total pressure of the jet, where ξ denotes distance of the jet from the opening ; d, diameter of the jet. But when discharge through the opening becomes large and distance of the jet ξ/d larger than 0.5, the pressure falls rapidly in proportion to quantity of the discharge. 2) Pressure at an opening on a convex surface is generally lower than that on a concave surface. It is marked specially for ξ/d=0.5. When the radious of curvature is above five times as large as the diameter of the jet, the influence of curvature becomes little. 3) If the surface is not perpendicular to a jet, the slope of fall of pressure due to displacement of the jet and that due to increase of discharge through the opening are gentle or steep according as the point on which the jet strikes is located above or below the opening on the surface. At zero discharge, when pressure at the opening is maximum, the center of the jet does not coincide with that of the opening, but is found to be below the opening on the surface. For example, when inclination of surface is 10 degree, the distance between these two centers is about one or two tenths the diameter of the jet, that is slightly less than the analytical result treated as a two dimentional jet.

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The author determined the construction of the Jet Pump which makes its effeciency maximum by experiment and theory. The best value of the diameter of nozzle is (0.5∼0.7) d (d=diameter of throat) and varies by the elevation of water to be lifted. The length from the outlet of nozzle to the inlet of throat should be less than 2d, the throat length L should be 2.5d<L<4d. The conical angle at the inlet of diffuser does not affect the efficiency in the range 30°∼50°.

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This paper suggests a method for measuring current velocity of gases on new principle which uses ion. First of all, the current of fluid under test is ionized by corona discharge made by a transformer, then it is led into two absorbers, which are put keeping some distance each other, but have some pulsating electric field. Passing through their two absorbers, the fluid arrives at an ion receiver, which catches ions escaped from them. If we change the distance between their absorbers, the quantity of ion catched by the receiver changes periodically. Measuring the change of the distance between their two absorbers for one period, we can know the fluid velocity by the following relation. w=λf where w : current velocity of gases λ : the change of the distance between their two absorbers in one period f : frequency of the pulsating electric field

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Assuming the two dimensional flow and the uniform longitudinal induced velocity on the propeller stream, the Voith·Schneider·Propeller is solved approximately. Thrust, torque, lateral force, position of thrust line, maximum attack angle of the blade element and its peripheral position are expressed by the simple functional relations. By these relations of the fundamental quantities of the Voith. Schneider. Propeller, the characteristic curves are calculated, and also the applicable region of the formula are found. Calculated example of the characteristic curves coincide closely to Hans Kreitner's experiments. Comparing with more strict solutions of the Voith. Schneider. Propeller by elliptec integrals, these approximate simple functional relations would be serviceable to explaine the complicated acting conditions of the travers or lateral circular airfoil gitter type propeller.

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A new formula for the case of Kaplan water turbines was obtained by the considerations, which are analogous to the author's former formula for the case of propeller type water turbines. Only one point of difference between the propeller and Kaplan type's case is the exponent of q=Q/Q₀. The former case is 1, the latter case is 1/2. Where, Q₀ is the water quantity at maximum efficiency. By courtesy of Factory Hitachi, comparing the full scale experimented efficiency of Kaplan turbine of the River Nippashi with the calculated efficiency by the formula for the case of Kaplan, ascertained close agreement to each other. Putting together, the author's former formulae, for the case of Francis, propeller type and this case of Kaplan water turbines, only one formula was obtained. By this formula, taking different exponent, full scale efficiency of all practical types of water turbines are calculated by their model experimented efficiency.

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There has not been presented the method of calculation of run away speed of Francis water turbine. The author showed that the run away speed ratio R_n is represented by the equation R_n=ζq_R0, from the equation of loss work at the condition of R_n, where, q_R0 is the ratio of water quantity at the speed of run away to that at the normal speed. q_R0 is calculated by the equation of energy balance at the condition of run away speed. If the efficiency of the Francis water tusbine is known, ζ is calculable, and finally R_n can be computed. Author also presents a simple formula of run away speed at the maximum effidiency. By this formula, that is obivious that the most effective terms to run away speed of Francis water turbines are the peripheral speed of runner at the normal speed and the ratio of the exit mean diameter to inlet the diameter of runner.

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The fundamental of the hydrodynamical treatment of the flow of a viscous fluid in the clearance space between the casing and the flat end of rotor of a gear pump has been studied. The main results are as follows : (1) The flow is composed of two elements, one being the rotation caused by the rotor, and the other the potential flow caused by the pressure. (2) The problem may be solved by the application of the well-known two-dimensional flow of a perfect fluid around a circle. (3) The equi-pressure lines are common to any sectional plane parallel to the rotor surface, but the configurations of stream-lines are changed. (4) The leakage through the clearance is independent of the rotation of the gear. (5) The power for driving the end surface is given by πμω² (a⁴-b⁴)/2δ, where μ=coefficient of viscosity, α=radius of gear tip, b=shaft radius and δ=amount of clearance.

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The optimum end clearance of a gear pump has been given from the standpoint that the maximum shearing stress caused on the boundary planes is minimum. The shearing stress acting at any fixed point changes periodically for the rotating boundary but is unchanged for the fixed boundary, and it is not clear whether or not the shearing stress plays a part for abrading the surface and if it does it is due to either its magnitude or its variation, but they seem to have, at least, some relation. In this paper, it was tried to determine the amount of clearance from viewpoint stated above. The result shows that (1) The diameter of shaft has little effect on the optimum value. (2) The optimum clearance becomes smaller as the inlet and outlet are nearer to the gearing part. (3) The direction of rotation does not change the result.

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Involute gear pumps are apt to suffer ill effects by the difference of closed volume of gear teeth under operaating condition. In order to avoid the appearance of the phenomena of closing, five kinds of relief grooves were considered. Several efficiency tests of such kinds of relief grcoves were performed taking into consideration of the back-rush, and a desirable relief groove were determined. The results of tests are shown on the stand point of the pressure variation and etc.

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Extending theoretical calculation of the previous paper, the author has made a theoretical formula giving the frequency of natural vibration of a penstock in the form of a cylindrical thin shell. In this formula, the following three items are taken into consideration, namely ; (1) The elasticity of wall of the shell, (2) The effect of pressure head of water contained inside the shell, which causes hoop tension in the wall material, (3) The effect of virtual mass of water contained inside the shell, due to the fact that the water makes vibratory motion at the same time with the vibration of wall.

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In this paper, natural vibration of a straight pipe of elastic material, inside which a liquid flows at a constant velocity, is considered theoretically. The calculation is based on an equation of vibration of such a pipe, which the author introduced some twenty years ago. This equation is somewhat different from that given by H. Ashley and G. Haviland in a recent paper. Moreover, the calculation is made by means of method of successive approximations, and is carried out to the second stage of approximation. According to this estimation, it is seen that natural frequency of lateral vibration is slightly lowered, when the flowing velocity V exists, as compared with the case of V=0. Also there appears a damping force, which gives rise to a damping factor δ of oscillation (y=c-<δt> sinβt) nearly proportional to the third power of V. The results are given in a form of simple algebraic expression.

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When a pressure pulsation is generated at the lower end of a penstock, due probably to the action of draft-tube, etc., the pressure wave is propagated to the penstock, and under certain condition a state of resonance may occur. In this paper the author has made theoretical estimation about the condition at which this resonance state can be established, making a simple asumption regarding the relation between pressure and velocity of flow at the lower end of the penstock. The estimation is made for both cases of uniform and non-uniform wall thickness of the penstock.

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Recently the arrangement, which makes fluid inhale through numerous small holes bored on a pipe wall, is often used in the textile industry. The authors treated the problem regarding the flow of gases inhaled through a number of small holes bored on the transverse sections existing at optional intervals along a straight pipe, and researched the discharge or pressure distribution along a pipe axis theoretically and experimentally. We used a brass pipe having the smooth inside, and bored small holes in two lines symmetrically at the opposite sides of the pipe axis, ten on each side, with equal interval. These small holes were set up to be arranged in single or double rows or zigzag, by properly opening and closing some of them, and we made the air inhale into it through the opaned holes with four gradations of the different inhaling pressures. We measured the pressures on each transverse section having small holes, and total discharges of the inhaled air through each hole, by using water manometer and orifice flowmeter respectively. In theoretical treatment of such flow, on the other hand, we used the momentum theory and energy equations. By means of these methods we calculated the inhaled discharge through each hole, and the pressures on each transverse section having them. The values gained by this calculation are, we believe, conformable to the result of the experiment to a great extent.

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In this paper the authors have calculated the loss of head of turbulent flow through rotating annular pipes and heat transfer coefficients on the both surfaces of pipes. In the calculation it has been assumed that the velocity distribution of flow from the wall followed the formula of 1/7th power. The results obtained are that the loss of head and heat transfer coefficients increase with the angular velocity of pipes and the ratio of the inner radius to the outer radius, and that heat transfer coefficient on the inner surface is larger than that on the outer surface, but the quantity of heat is transferred more from outer surface than from the inner surface. If the angular velocity contained in the equations mentioned above is put to zero, the equations for the loss of head, heat transfer coefficients and the quantity of heat in the case of flow through fixed annular pipes are obtained.

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In this paper the inlet length and the head given at the entrance of rotating annular pipes in which the fluid flows, are investigated. The moment of momentum of the fluid passes in a unit time through a section at a distance x from the entrance of pipes, is as follows : M=2πp∫r2r1vzvθr2dr, where vz : axial velocity of fluid (const.), vθ : tangential velocity (function of r), r1 : inner radius, r2 : outer radius. The increment of M for a distance dx (dM/dx) dx must be equal to the sum of moment of frictional force for the same distance onthe both surfaces of pipes, so dM/dx=2π (r22rθ-r12rθ1), where rθ1 : frictional stress on the inner surface, rθ2 : frictional stress on the outer surface. Consequently the inlet length is given by [numerical formula]. The head given at the entrance is led in the same manner as follows : [numerical formula], where ω : angular velocity of one side pipe. As the results of calculations it is shown that the inlet length is proportional to 3/4 ths power of angular velocity ω and grows shorter against the ratio r1/r2 and that the head increases in proportion to a square of angular velocity ω and to the ratio r1/r2.

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Recently the arrangement, in which the fluid is inhaled through numerous branched pipes joined to a main, is often used in the textile industry. This has been brought to our attention with questions as to variation of pressures and discharges of flowing fluid. Then we researched theoretically and experimentally the quantities of the air inhaled through each branched pipe or pressure distribution along a main pipe. In a theoretical treatment, the momentum theory and energy equations are applied. It may be said that our theory is in good agreement with the result of experiment.

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In this paper, the results of the experiment on the frictional resistance of rotating disc in a casing are described. The theoretical calculation of this problem, is already carried out by B. Hudimoto and the author. Denoting M=ρω²r₀⁵C_f/2, R=r₀ω²/ν, where M is the moment of the frictional resistance, ω is the angular velocity of the rotating disc, r₀ is the radius of the disc, ρ and ν are density and kinematic viscosity of fluid in a casing respectively, ω is the coefficient of the moment and R is Reynolds number, the results of the experiment are shown by the relation between C_f and R. The experiments are carried out for the next four cases, using the air as the fluid in a casing, and Reynolds number R is varied from 5×10⁴ to 4×10⁵. (1) smooth disc and smooth casing. (2) rough disc and smooth casing. (3) smooth disc and rough casing. (4) rough disc and rough casing. The rough surface is made up by passing the sand on the surface and the roughness is shown by the parameter r₀/k, k being the mean diameter of the sand. Moreover, in the case (1), the axial distance 8 between the disc and the casing is varied and this influence is shown by the parameter r₀/s.

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