Unsteady Water Flow Research Articles

International symposium on unsteady water flow at high velocities

International symposium on unsteady water flow at high velocities

Self-similar flows with increasing energy—IV: Piston driven flows of water

Self-similar solutions for one dimensional unsteady adiabatic flow of water, considered to be a compressible fluid, driven by an expanding spherical or cylindrical or plane piston are investigated. The shock ahead of the piston is assumed to be strong. The energy of the flow between the shock and piston is assumed to be dependent on shock radius obeying a power law. Approximate solutions are obtained. In the case of a uniformly moving plane piston, a particular analytical solution has been derived. Exact numerical solutions are also given. A comparative study between these solutions shows a good agreement. The general behaviour of the solutions for the flow of water behind a piston driven shock is similar to that of the classical solutions for the flow of a perfect gas.

MECHANISM OF GROUND WATER RESERVOIRS

The article deals with unsteady ground water flow in an aquifer of limited horizontal extent. The changes in storage are taken to be dependent on a storage coefficient S, and flow rates are taken to be dependent on the coefficient of transmissibility T. Here the relation to Darcy's constant k is that T ≿ kD, where D is the aquifer thickness. The equilibrium ground water surface is found and further calculations are based on the departure of the ground water level from this equilibrium value. An expression of the impulse response function (the instantaneous unit hydrograph or IUH) is found, and its use demonstrated. Finally, it is shown how such calculations have been used to analyse the inflow into a water reservoir in Iceland, serving as guidelines in the planning of field investigations of a major ground water reservoir in a nearby lava field.

Transients in Pipelines Carrying Liquids or Gases

Unifying equations are developed for unsteady flow of natural gas, water or petroleum products through long pipelines. Second order accuracy terms for fluid friction are used with the exponential equations in common use. The equations are solved by either the method of characteristics or the centered implicit method. Results of computer studies indicate stability and accuracy of the implicit method, although it requires more computer time than the characteristic method.

Development and evaluation of a hot-film velocity probe for cardiovascular studies.

The application of constant temperature hot-film anemometry to measurement of point blood velocity in arteries is discussed and the importance of certain aspects of design, and of provision of means for detecting flow reversal, is demonstrated. Hot film probes suitable for intra-arterial use have been constructed and tested in regimes of steady and unsteady water flow. At overheat ratios compatible with use in blood three different commercially available anemometers had unsatisfactory frequency responses. Oscillatory calibrations performed in the absence of mean flow were further subject to error due to generation of secondary flows. The likely significance of these various effects in distorting intra-arterial measurements is discussed.

Paper 12: Generation of Hydraulic Noise in Centrifugal Pumps

The production of hydraulic noise by two types of centrifugal pumps—volute pumps and diffuser pumps—was examined to determine the effect of design and operating conditions on the level of noise generated in the pumped liquid. Experimental work with hydrophones in the exit and entrance to the pumps showed that for both pumps, the dominant frequencies in the noise spectrum were at rotational speed and blade number times rotational speed. It was also found that the distance between cutwater and impeller tip is critical in a volute pump as far as blade frequency noise is concerned. Analysis of the relation between the noise measured by the hydrophones and the fluctuating pressure produced by the pump and the water flow in the inlet and outlet ducts showed that the noise can be interpreted as being directly related to the unsteady flow of water issuing from the impeller. Test results of blade frequency noise levels were correlated with a theoretical analysis for static pressure fluctuations in the pump exit and were shown to be in good agreement. A correlation of general hydraulic noise level with pump specific speed and power consumption was also developed and shown to be reliable to within +2 dB.

Hysteretic Moisture Characteristics and Hydraulic Conductivities for Glass‐Bead Media

AbstractThe hysteretic effects in the moisture characteristics and the hydraulic conductivity characteristics of two different glass‐bead media were measured while unsteady water flow was occurring. A gamma‐ray moisture sensor, a combination of pressure transducers and tensiometers, and a capillary‐tube flux meter were combined with a simple box‐like flow chamber for simultaneous measurement of (i) the degree of saturation, (ii) the water‐phase pressure, and (iii) the hydraulic conductivity. These quantities were recorded through out water‐pressure changes which traversed the main‐branch wetting and drying curves as well as the families of “rewet” and “redry” scanning loops.Large hysteresis was recorded in the relation of pressure to saturation or to conductivity. The relation of conductivity to saturation showed hysteresis which, though significantly larger than the experimental error, would for most practical purposes be negligible.The independent domain theory of hysteresis was used to check the relation between the “rewet” and “redry” families of moisture characteristics. By this test the theory was found to be very poorly suited to a description of these media. Two basic approximations of the theory were assumed to be responsible for this lack of applicability.

Unsteady Flow of Water Over a Porous Bed Having Constant Infiltration

Unsteady Flow of Water Over a Porous Bed Having Constant Infiltration

Unsteady Flow of Ground Water into Drain Tile

Solution to nonlinear differential equation describing unsteady flow toward equally spaced drains above horizontal impermeable boundary is presented; solution was compared with field data and published numerical results and suitable agreement was found when drain spacing was large relative to depth of drains.

Unsteady Flow of Ground Water into a Surface Reservoir

Existing methods are not exact for prediction of water table position and amount of water discharged in cases when ground water is flowing from aquifer to surface reservoir; nonlinear partial differential equation that describes shape of water table is difficult to solve; new approximate solutions, obtained by two different methods for nonlinear equation, are presented; both solutions agree well with experimental results.

Unsteady Flow of Ground Water into Drain Tile

Solution to nonlinear differential equation describing unsteady flow toward equally spaced drains above horizontal impermeable boundary is presented; solution was compared with field data and published numerical results and suitable agreement was found when drain spacing was large relative to depth of drains.

Unsteady Flow of Ground Water into a Surface Reservoir

Existing methods are not exact for prediction of water table position and amount of water discharged in cases when ground water is flowing from aquifer to surface reservoir; nonlinear partial differential equation that describes shape of water table is difficult to solve; new approximate solutions, obtained by two different methods for nonlinear equation, are presented; both solutions agree well with experimental results.

Sounds Produced by the Unsteady Flow of Water

The production of sound by the unsteady flow of a homogeneous fluid is discussed, with special attention given to those phenomena of practical concern as sources of underwater noise. Brief reviews are given of recent experimental and theoretical investigations of the sound associated with the following flow phenomena: (1) unsteady flow within an unbounded fluid, related to the noise from turbulent jets and wakes; (2) fluctuating hydrodynamic forces due to unsteady flow about a rigid body, related to “aeolian tones” and the rotation sound from a propeller; and (3) excitation of the vibration of an elastic body by the flow. A short motion picture produced by L. Prandtl will be shown to illustrate several kinds of unsteady flow.

Engineering Research in the U.S.S.R

VOL. 1, No. 2 of the Engineering Review (Russian) (dated 1941) contains a collection of papers dealing with the mathematics of stress calculations for rotating disks, springs and conical shells. Other papers in the applied mechanics section describe very large mechanical testing machines and an electrical analogy for the investigation of torsion in bars. The hydrodynamics section has papers on filtration in non-homogeneous soils and the unsteady flow of water in canals. A short summary of each paper is given in English or German.