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Mechanics of Engineering Fluids a Treatise On Hydraulics And Pneumatics for

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Mechanics of Engineering Fluids a Treatise On Hydraulics And Pneumatics for
Irving P Irving Porter Church
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Compons. Of the acting forces) -f- mass of lamina, i. E. , tang. Ace. = * -=- g (2) Now, Fig. 535, at a definite instant of time, conceive the volume of water in the pipe to be subdivided into a great number of laminae of equal mass (which implies equal volumes FIG. 535.
in the case of a liquid, but not with gaseous fluids), and let the ds just mentioned for any one lamina be the distance from its centre to that of the one next ahead ; this mode of subdivision 6, )4 MECHANICS OF ENGINEERING.
ma
...kes the ds of any one lamina identical in value with its thickness ds', i. E. , have also ds cos > = dz] or ds' cos = da ; . . (4) z being the height of the centre of a lamina above any con- venient horizontal datum plane. Substituting from (2), (3), and (4) in (1), we derive finally vdv + ^dp + dz = 0. . (5V 7 9 > The flow being steady, and the subdivision into laminae being of the nature just stated, each lamina in some small time dt moves into the position which at the beginning of dt was filled by the lamina next ahead, and acquires the same velocity, the same pressures on its faces, and the same value of z, that the front lamina had at the beginning of dt.

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