Pressure flow relationship

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

Both axial and centrifugal compressors are subject to an unstable region of low flow operation called surge. This region is defined by the pressure-flow relationship which has a peak determined by the operating speed. For various compressor speeds, these peaks may be connected to determine a surge line, which defines a region of unstable operation at lower flows. 

FIGURE 20.1 Pressure-flow relationships of a U.S. Army M40 field mask. (From Musa, S.R., Banderet, L.E., Cadarette, B. Textbook of Military Medicine Medical Aspects of Harsh Environments, Volume 2, K.B. Pandolf and R.E. Burr, eds. Office of the Surgeon General, Department of the Army, United States of America, Falls Church, VA, 2002.)... 

In most of the venous circulation, the pressure inside the vessels is greater than the external pressure, so that the pressure-flow relationship is like that in the arteries. However, in the vena cava, in certain organs such as the lungs and during certain procedures such as resuscitation or measurement of blood pressure using a cuff, venous collapse may occur [Fung, 1984]. Thus, in contrast to an artery in which only one condition normally exists, two additional conditions must be considered for a vein. 

Braakman, R., Sipkema, R, and Westerhof, N. 1983. Steady state and instantaneous pressure-flow relationships characterisation of the canine abdominal periphery. Card. Res. 17 577-588. Burattini, R., Borgdorff, R, Gross, D.R., Baiocco, B., and Westerhof, N. 1991. Systemic autoregulation counteracts the carotid baroreflex. IEEE Trans. Biomed. Eng. 38 48-56. 

Shoukas, A.A., Brunner, M.J., Frankie, A.E., Greene, A.S., and Kallman, C.H. 1984. Carotid sinus baroreceptor reflex control and the role of autoregulation in the systemic and pulmonary arterial pressure-flow relationships of the dog. Circ. Res. 54 674-682. 

FIGURE 56.2 Input impedance derived from the pressure and velocity data in the ascending aorta of Figure 56.3. The top panei contains the modulus and the bottom panel the phase, both plotted as functions of frequency. The peripheral resistance (DC impedance) for this plot was 16,470 dyne sec/cm. (From Mills C.J., Gabe I.T., Gault J.N. et al. 1970. Pressure-flow relationships and vascular impedance in man. Cardiovasc. Res. 4 405. With permission.)... 

Conrad, W. A., Pressure-flow relationships in collapsible tubes, IEEE Trans. Biomed. Eng., 16 284-295,1969. 

Isabey, D., and H. K. Chang, Steady and unsteady pressure-flow relationships in central airways, /. Appl. F/jysio/., 51 1338-1348, 1981. 

This Ohm s law representation of the pressure-flow relationship forms the basis for measurements of airway resistance and is the principle on which several flow-measuring devices are based. The pressure required to move gas u r conditions of turbulence is always greater than that required to achieve the same flow under laminar conditions, as additional pressure (or energy) is required to accelerate molecules in directions other than the direction of bulk flow. This will be manifested as an upward curve and deviation from linearity on a plot of flow (jc axis) versus pressure drop (y axis). 

Archie JP (1978) Transmural distribution of intrinsic and transmitted left ventricular diastolic intra-myocardial pressures in dogs. Cardiovasc Res 12 255-262 Bellamy RF (1978) Diastolic coronary artery pressure flow relationship in the dogs. Circ Res 43 92— 101... 

It is assumed that a Poiseuille type pressure-flow relationship is valid for the individual vessels, whereby the apparent blood viscosity can be diameter dependent (Fahraeus-Lindqvist effect). The symmetric conductance tensor is depen-... 

ANS We have not studied these agents except to see whether prostaglandin synthesis affected coronary blood flow. The administration of indomethacin did not alter the pressure-flow relationship of the coronary cirulation. 

Braakman, R., Sipkema, R, and Westerhof, N. 1983. Steady state and instantaneous pressure flow relationships characterisation of the canine abdominal periphery. Card. Res. 17 577 588. 

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