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`R.J. Reynolds Vapor
`IPR2016-01268
`R.J. Reynolds Vapor v. Fontem
`Exhibit 1032-00001
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`FLUID FLOW
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`in Fluid Mechanics .
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`ROLF H. SABEIRSKY
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`ALLAN J. ACOSTA
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`R.J. Reynolds Vapor Exhibit 1032-00002
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`R.J. Reynolds Vapor Exhibit 1032-00002
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`© Copyright, The Macmillan Company, 1964
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`All rights reserved. No part of this book
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`may be reproduced or utilized in any form
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`or by any means, electronic or mechanical,
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`including photocopying, recording or by
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`any information storage and retrieval
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`system, without permission in writing from
`the Publisher.
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`Second Printing 1966
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`a Library of Congress catalog card number: 64—12865
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`THE MACMILLAN COMPANY NEW YORK
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`COLLIER-MACMILLAN COMPANY, LTD.,
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`TORONTO, ONTARIO
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`Printed in the United States of America
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`R.J. Reynolds Vapor Exhibit 1032-00003
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`R.J. Reynolds Vapor Exhibit 1032-00003
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`(Sec. 6.1)
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`I
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`Introduction
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`171
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`through a rapidly expanding duct—“the reverse of the flow in Fig. 6-la. Here,
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`because of the large and rapid increase of pressure required of the low energy
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`boundary layer (it has a lower kinetic energy than the main stream), it cannot
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`regain pressure together with the main stream to fill completely the down-
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`stream duct. Instead the main flow, while remaining more or less unaffected
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`by viscosity, does not follow the wall but continues into the channel as a jet.
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`The region between the jet and the wall is filled with fluid of lower velocity
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`that churns and eddies in an irregular way. In this way the boundary layer
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`Separation point
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`Separation behind a cylinder. In this particular instance the wake
`Fig. 6-ld
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`formed is nonsteady.
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`has brought about a rather severe alteration of the flow picture. When the
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`‘inain stream (that portion unaffected by Viscosity) does not follow the walls of
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`3hr: surrounding duct or adjacent solid surface,
`it is said to separate or
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`yank-away. A similar situation is observed for the flow around a cylinder
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`Fig. 6-ld). The main flow separates at a position near the maximum height;
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`hind the cylinder there is an eddying wake which extends for many diam-
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`bters downstream. On the forward portion of the cylinder a relatively thin
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`:fioundary layer develops (at fairly large Reynolds numbers), and the flow
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`interior to this and to the wake may be considered to be inviscid.
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`These examples illustrate two features of recurring importance in fluid
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`mechanics: the development of viscous regions and the occurrence of the
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`hparation phenomenon. Because of the possibility of separation one cannot
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`Ways assume that the inviscid portion of the flow will conform to the shape
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`flsolid boundaries in the flow. In the absence of separation and at sufficiently
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`high Reynolds numbers, however, the. actual boundaries may be taken as the
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`bonndaries for the inviscid flow, because of the thinness of the boundary
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`yer. In general these conditions are fulfilled in the forward portions of
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`"ant bodies or along airfoil-like shapes, particularly in regions where the
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`name decreases in the direction of flow.
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`R.J. Reynolds Vapor Exhibit 1032-00004
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`R.J. Reynolds Vapor Exhibit 1032-00004
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