Discussion: “Graphical Solution of Fluid-Friction Problems” (Dennison, E. S., 1942, ASME J. Appl. Mech., 9, pp. A82–A84)

C. A. Meyer

doi:10.1115/1.4009254

Discussion: “Graphical Solution of Fluid-Friction Problems” (Dennison, E. S., 1942, ASME J. Appl. Mech., 9, pp. A82–A84)

Journal of Applied Mechanics ◽

10.1115/1.4009254 ◽

1943 ◽

Vol 10 (1) ◽

pp. A51-A52

Author(s):

C. A. Meyer

Keyword(s):

Graphical Solution ◽

Fluid Friction

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Graphical Solution of Fluid-Friction Problems

Journal of Applied Mechanics ◽

10.1115/1.4009188 ◽

1942 ◽

Vol 9 (2) ◽

pp. A82-A84

Author(s):

E. S. Dennison

Keyword(s):

Experimental Data ◽

Reynolds Number ◽

Friction Coefficient ◽

Analytical Methods ◽

Trial And Error ◽

Graphical Solution ◽

Fluid Friction

Abstract It is customary to present fluid-friction data in the form of a diagram to log scale in which friction coefficient appears as a function of Reynolds number. Such data are widely applicable to physical circumstances other than those which pertained to the original experiments. The present paper describes a graphical procedure for utilizing data of this character, where analytical methods are not practicable, and resort is made to trial-and-error methods. Similar methods to that described may be found useful in other fields than that of fluid friction, provided the experimental data are capable of being represented in nondimensional form.

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Closure to “Discussion of ‘Graphical Solution of Fluid-Friction Problems’” (1943, ASME J. Appl. Mech., 10, p. A51–A52)

Journal of Applied Mechanics ◽

10.1115/1.4009255 ◽

1943 ◽

Vol 10 (1) ◽

pp. A52

Author(s):

E. S. Dennison

Keyword(s):

Graphical Solution ◽

Fluid Friction

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HEAT TRANSFER AND FLUID FRICTION ACROSS COMPACT EXCHANGERS FORMED FROM THE SOLID BY ELECTRO-EROSION

10.1615/ihtc3.860 ◽

2019 ◽

Author(s):

R. Doussain

Keyword(s):

Heat Transfer ◽

Fluid Friction

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Role of Dissipation Characteristics in Predicting Flow from Dissimilar Centrifugal Pumps

Proceedings of the Institution of Mechanical Engineers Part A Journal of Power and Energy ◽

10.1243/pime_proc_1994_208_049_02 ◽

1994 ◽

Vol 208 (4) ◽

pp. 285-294 ◽

Cited By ~ 1

Author(s):

E A Bunt ◽

B Parsons ◽

F Holtzhausen

Keyword(s):

Flow Characteristics ◽

Maximum Flow ◽

Centrifugal Pumps ◽

Graphical Solution ◽

Dissipative Flow ◽

In Series ◽

Lower Maximum ◽

Output Field ◽

High Series

Examination of flows in a particular case of dissimilar pumps coupled in series or in parallel (without check valves) showed that the ‘classical’ graphical solution of combined characteristics in the [+H, +Q] quadrant did not accord with the output field in certain regions. To predict the full flow fields, it was necessary to take into account dissipative flow characteristics in two other quadrants: for low-output parallel flow (when there is still flow available from the pump of higher head when the ‘weaker’ pump's flow has been reduced to zero), that in the [+H, –Q] quadrant; and for high series flow (after the output head of the pump of lower maximum flow has been reduced to zero), that in the [–H, +Q] quadrant. This problem does not arise when the pumps have identical characteristics.

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A graphical solution of a differential equation with application to hill’s treatment of nerve excitation

Proceedings of the Royal Society of London Series B Biological Sciences ◽

10.1098/rspb.1937.0058 ◽

1937 ◽

Vol 123 (832) ◽

pp. 382-395 ◽

Cited By ~ 4

Keyword(s):

Viscous Medium ◽

Graphical Solution ◽

Initial Value ◽

First Order ◽

Rate Dependent ◽

Monomolecular Reaction ◽

Constant Coefficients ◽

Linear Differential ◽

Physical And Chemical ◽

Nerve Excitation

Linear differential equations with constant coefficients are very common in physical and chemical science, and of these, the simplest and most frequently met is the first-order equation a dy / dt + y = f(t) , (1) where a is a constant, and f(t) a single-valued function of t . The equation signifies that the quantity y is removed at a rate proportional to the amount present at each instant, and is simultaneously restored at a rate dependent only upon the instant in question. Familiar examples of this equation are the charging of a condenser, the course of a monomolecular reaction, the movement of a light body in a viscous medium, etc. The solution of this equation is easily shown to be y = e - t / a { y 0 = 1 / a ∫ t 0 e t /a f(t) dt , (2) where y 0 is the initial value of y . In the case where f(t) = 0, this reduces to the well-known exponential decay of y .

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