velocity of flow at point A, v_{1}, to the velocity offlow at point B, v_{2}.Since Q_{1 }= Q_{2}, A_{1}v_{1 }= A_{2}v_{2}From figure 2-13; A_{1 }= 16sq. in., A_{2 }= 4sq. in.Substituting: 16v_{1 }= 4V_{2 }or v_{2 }= 4v_{I}Therefore, the velocity of flow at point B is fourtimes the velocity of flow at point A.VOLUME OF FLOW AND SPEEDIf you consider the cylinder volume you mustfill and the distance the piston must travel, youcan relate the volume of flow to the speed of thepiston. The volume of the cylinder is found bymultiplying the piston area by the length the pistonmust travel (stroke).Suppose you have determined that twocylinders have the same volume and that onecylinder is twice as long as the other. In this case,the cross-sectional area of the longer tube will behalf of the cross-sectional area of the other tube.If fluid is pumped into each cylinder at the samerate, both pistons will reach their full travel at thesame time. However, the piston in the smallercylinder must travel twice as fast because it hastwice as far to go.There are two ways of controlling the speedof the piston, (1) by varying the size of the cylinderand (2) by varying the volume of flow (gpm) tothe cylinders. (Hydraulic cylinders are discussedin detail in chapter 10. )STREAMLINE ANDTURBULENT FLOWAt low velocities or in tubes of small diameter,flow is streamlined. This means that a givenparticle of fluid moves straight forward withoutbumping into other particles and without crossingtheir paths. Streamline flow is often referred toas laminar flow, which is defined as a flowsituation in which fluid moves in parallel laminaor layers. As an example of streamline flow,consider figure 2-14, which illustrates an openstream flowing at a slow, uniform rate with logsfloating on its surface. The logs represent particlesof fluid. As long as the stream flows at a slow,uniform rate, each log floats downstream in itsFigure 2-14.—Streamline flow.own path, without crossing or bumping into theother.If the stream narrows, however, and thevolume of flow remains the same, the velocityof flow increases. If the velocity increasessufficiently, the water becomes turbulent. (Seefig. 2-15.) Swirls, eddies, and cross-motions areset up in the water. As this happens, the logs arethrown against each other and against the banksof the stream, and the paths followed by differentlogs will cross and recross.Particles of fluid flowing in pipes act in thesame manner. The flow is streamlined if the fluidflows slowly enough, and remains streamlined atgreater velocities if the diameter of the pipe issmall. If the velocity of flow or size of pipe isincreased sufficiently, the flow becomes turbulent.While a high velocity of flow will produceturbulence in any pipe, other factors contributeto turbulence. Among these are the roughness ofthe inside of the pipe, obstructions, the degree ofcurvature of bends, and the number of bends inthe pipe. In setting up or maintaining fluid powersystems, care should be taken to eliminate orFigure 2-15.—Turbulent flow.2-10

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