On Drag of Circular Cylinder Suspended in uniform viscous Flow -Application to Tension Thread Flow Meter-


  • Ai Nakagawa and Takeo Academy of Hakusan, 2-14, Meiko, Hakusan 920-2152 Japan
  • R. M. Nakagawa Academy of Hakusan, 2-14, Meiko, Hakusan 920-2152 Japan


Turbulence, Oscillatory Flow, Flowmeter, Viscous Flow, Cylinder, Drag


This paper is concerned with an exact solution of a circular cylinder in uniform viscous flow and its application to a flowmeter named Tension Thread Flow Meter. An analytical procedure to lead the exact solution for a drag of a circular cylinder suspended in a uniform viscous flow has been demonstrated, and it is found that the drag is proportional to the square of velocity weakly rather than the linear dependency on the velocity, as Stokes law for a sphere. When the Reynolds number Re < 0.4, the relation between the drag coefficient Cf and Re, as well as the drag of a circular cylinder in uniform flow and Re, have been derived and presented as simple analytical expressions. The theoretical results on the drag of a circular cylinder in a uniform flow have been applied directly to the prototype flowmeter, and to the velocity calibration for the selected scales of the thread, and their arrangements together with the velocity range, to be used. A prototype flowmeter has been manufactured and then deployed successfully to measure three velocity components in oscillatory waves. It is suggested that the potential of the flowmeter is almost limitless so that it is strongly recommended to develop the commercial version for general users, who are interested in measuring boundary layer flow, oscillatory wave, and turbulence


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Lamb, H.(1932) Hydrodynamics. 6th Edition, Cambridge University Press, Cambridge. pp.738.

Nakagawa, T. (1983) On characteristics of the water-particle velocity in a plunging breaker. J. Fluid Mech. 126, 251-268. https://doi.org/10.1017/S0022112083000142

Nakagawa, T. (2006) Philosophy of Flow. vol.10, Scientific Papers on Turbulence by Shunichi Tsugé. Columbus University Press, Hakusan, pp.304.

Navier, M. (1827) Mémoire sur les Lois du Mouvment des Fluides. Mém. de l'Acad. d. Sci. 6, 389-416.

Richards, G.J.(1934) On the motion of an elliptic cylinder through a viscous fluid. Philosophical Transactions of the Royal Society of London, A233, 279-301. https://doi.org/10.1098/rsta.1934.0019

Stokes, G.G. (1845) On the theories of internal friction of fluids in motion. Trans. Cambr. Phil. Soc. B, 287-305.

Stokes, G.G. (1851) On the effect of the internal friction of fluids on the motion of pendulums. Transaction of Cambridge Philosophical Society, 9, 8-106.

Tsugé, S. (1969) A theory of fluctuation based on the hierarchy equation. Physics Letters 24A, 235-236. https://doi.org/10.1016/0375-9601(68)90621-X

Tsugé, S.(1974) Approach to the origin of turbulence on the basis of two-point kinetic theory. Phys. Fluids 17, 22-33. https://doi.org/10.1063/1.1694592

Wieselsberger, C. (1920) Der Luftwiderstand von Kugeln. AFM, 5, 140-144.




How to Cite

Ai Nakagawa and Takeo, & R. M. Nakagawa. (2020). On Drag of Circular Cylinder Suspended in uniform viscous Flow -Application to Tension Thread Flow Meter-. To Physics Journal, 6, 44-57. Retrieved from https://purkh.com/index.php/tophy/article/view/873



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