An approximate solution for the velocity profiles for the oscillatory flow in the inlet region of a circular tube was obtained on the basis of the author's previous work, and it was compared with the experimental results and numerical results.
To estimate the pressure drop, the frequency-dependent unsteady viscous friction coefficient in the inlet region of a circular tube was defined and derived.
The results show that the magnitude of the friction coefficient is nearly proportional to the square root of the frequency in the high frequency region and to the square root of the reciprocal of the distance from the entrance of the pipe in the inlet region, and it is verified that in a sufficiently high frequency region the same friction coefficient as for the oscillatory flow in the developed region can be applied for the oscillatory flow in the inlet-region.

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Generally, the noise emitted by a bent-axis type of hydraulic pump in normal steady-state operating conditions occurs from internal stress fluctuation of the pump casing, caused by changing of the number of cylinder bores connecting with the delivery port in this paper, the vibrative force of the fluctuations is calculated by development of the method on Fourier's series for trapezoidal waves, which are assumed by the progress of the pressure of the cylinder bores, and it is clarified that the theoretical value of the vibrative force can be calculated using the values of the surge pressure progress in the cylinder bore and the pressure pulsations in the delivery port, which are calculated by known theories (for example gedmann's and Iclulawa's formula), and some experiments were performed to investigate the characteristics o f those calculation vahies. As the result, it is clarified that the calculation method by trapezoid assumption is useful for prediction of the vibrative force in an oil-hydraulic pump.

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