The velocity of blood flow in the rabbit aorta studied with high‐speed cinematography

McDonald, D. A.

doi:10.1113/jphysiol.1952.sp004797

Cited by 37 publications

(13 citation statements)

References 6 publications

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“…The velocity of transport of bubbles in this vessel has been reported (McDonald, 1952). The velocity of the axial stream of dye is shown here (Fig.…”

Section: Resultsmentioning

confidence: 82%

“…The sequence of flow in the rabbit aorta has been described elsewhere (McDonald, 1952). The behaviour of dye during the early part of systole was that of a typical laminar parabolic profile (Fig.…”

Section: Resultsmentioning

confidence: 99%

“…The camera and lighting used for ifiming at 1500 frames/sec have been described in an accompanying paper (McDonald, 1952). Rabbits were anaesthetized with pentobarbitone sodium i.v.…”

Section: Methodsmentioning

confidence: 99%

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The occurrence of turbulent flow in the rabbit aorta

McDonald¹

1952

The Journal of Physiology

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“…The velocity of transport of bubbles in this vessel has been reported (McDonald, 1952). The velocity of the axial stream of dye is shown here (Fig.…”

Section: Resultsmentioning

confidence: 82%

Section: Resultsmentioning

confidence: 99%

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The occurrence of turbulent flow in the rabbit aorta

McDonald¹

1952

The Journal of Physiology

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“…This method has been shown to be valid for measuring arterial flow velocity (McDonald, 1952a). Injections of 0-1-0-2 ml.…”

Section: Methodsmentioning

confidence: 99%

Observations on laminar flow in veins

W.¹,

McDonald²

1954

The Journal of Physiology

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Fluid flow in pipes may be laminar or turbulent. In laminar or streamline flow the fluid particles flow in concentric laminae which vary in speed progressively from zero velocity at the wall to maximum velocity in the axial stream. A profile of these velocities forms a long parabola. With such a type of flow there is no mixing across the lumen of the tube other than that due to diffusion. Poiseuille's law only applies to laminar flow. In turbulent flow, on the other hand, the fluid particles pursue a random course so that the distribution of velocity is more nearly the same across the pipe, and there is thorough mixing of the fluid. The conditions establishing the transition from laminar to turbulent flow in pipes with steady flow were first described by Reynolds (1883), and from the use of his formula it is generally asserted that all venous flow is laminar (Burton, 1952;Green, 1944). However, the steady flow conditions of physical experiments are not found in the living body, and direct observations are needed to supplement the theoretical predictions.Laminar flow has been seen in the veins of various experimental animals. These observations have been reviewed by Franklin (1937), who first emphasized the significance of the absence of mixing across the lumen of a vein. Since the introduction of catheterization of the great veins and the right auricle to obtain samples of venous blood the problem of mixing in the veins is of considerable practical interest. In experimental work the estimation of flow velocity from the injection of dye or radiopaque materials is dependent on the clear visualization of the parabolic profile such dyes assume in laminar flow. The presence of laminar or turbulent flow may also alter the calibration of flowmeters.The present study reports the results of observations of laminar flow and disturbances of laminar flow in a wide range of veins, mainly in the rabbit, but also in the cat and the dog; estimates of the Reynolds' number have been made for each vein, so that it is possible to make some predictions of the nature of venous flow in larger species.

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Solution of the equation of motion

We consider a circular pipe of length 1, radius R, filled with a viscous liquid of density p and viscosity ,u.

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Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known

Womersley¹

1955

The Journal of Physiology

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The experiments of McDonald and his co-workers (McDonald, 1952(McDonald, , 1955Helps & McDonald, 1953) have shown that in the larger arteries of the rabbit and the dog there is a reversal of the flow. Measurements of the pressure gradient (Helps & McDonald, 1953) showed a phase-lag between pressure gradient and flow somewhat analogous with the phase-lag between voltage and current in a conductor carrying alternating current, and the simple mathematical treatment given below has strong similarities with the theory of the distribution of alternating current in a conductor of finite size. Solution of the equation of motionWe consider a circular pipe of length 1, radius R, filled with a viscous liquid of density p and viscosity ,u. We shall need also the quantity v = ,up, the kinematic viscosity. To clarify what is to follow, the solution will be compared at each stage with the corresponding well-known Poiseuille solution for steady flow.In steady flow, if Pi and P2 are the pressures at the ends of the pipe, the pressure-gradient is (P1-P2)/l.If w is the longitudinal velocity of the liquid at points at a distance r from the axis of the pipe, the equation of motion of the liquid is d2w +1dw Pr-P2=0 dr2+r dr+ /1td-'1 and its solution is W=Pl4P2 (R2 -r2) which, if we write y = r/R, may be written w =P1 _P2 R2(1 -y2).(2) 4tkd

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The velocity of blood flow in the rabbit aorta studied with high‐speed cinematography

Cited by 37 publications

References 6 publications

The occurrence of turbulent flow in the rabbit aorta

The occurrence of turbulent flow in the rabbit aorta

Observations on laminar flow in veins

Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known

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