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1、Laminar and Turbulent FlowObservation shows that two entirely different types of fluid flow exist. This was demon- strated by Osborne Reynolds in 1883 through an experiment in which water was discharged from a tank through a glass tube. The rate of flow could be controlled by a valve at the outlet,
2、and a fine filament of dye injected at the entrance to the tube. At low velocities, it was found that the dye filament remained intact throughout the length of the tube, showing that the particles of water moved in parallel lines. This type of flow is known as laminar, viscous or streamline, the par
3、ticles of fluid moving in an orderly manner and retaining the same relative positions in successive cross- sections.As the velocity in the tube was increased by opening the outlet valve, a point was eventually reached at which the dye filament at first began to oscillate and then broke up so that th
4、e colour was diffused over the whole cross-section, showing that the particles of fluid no longer moved in an orderly manner but occupied different relative position in successive cross-sections. This type of flow is known as turbulent and is characterized by continuous small fluctuations in the mag
5、nitude and direction of the velocity of the fluid particles, which are accompanied by corresponding small fluctuations of pressure.When the motion of a fluid particle in a stream is disturbed, its inertia will tend to carry it on in the new direction, but the viscous forces due to the surrounding fl
6、uid will tend to make it conform to the motion of the rest of the stream. In viscous flow, the viscous shear stresses are sufficient to eliminate the effects of any deviation, but in turbulent flow they are inadequate. The criterion which determines whether flow will be viscous of turbulent is there
7、fore the ratio of the inertial force to the viscous force acting on the particle.The ratio vlconstfreViscouIntalThus, the criterion which determines whether flow is viscous or turbulent is the quantity vl/, known as the Reynolds number. It is a ratio of forces and, therefore, a pure number and may a
8、lso be written as ul/v where is the kinematic viscosity (v=/).Experiments carried out with a number of different fluids in straight pipes of different diameters have established that if the Reynolds number is calculated by making 1 equal to the pipe diameter and using the mean velocity v, then, belo
9、w a critical value of vd/ = 2000, flow will normally be laminar (viscous), any tendency to turbulence being damped out by viscous friction. This value of the Reynolds number applies only to flow in pipes, but critical values of the Reynolds number can be established for other types of flow, choosing
10、 a suitable characteristic length such as the chord of an aerofoil in place of the pipe diameter. For a given fluid flowing in a pipe of a given diameter, there will be a critical velocity of flow corresponding to the critical value of the Reynolds number, below which flow will be viscous.In pipes,
11、at values of the Reynolds number 2000, flow will not necessarily be turbulent. Laminar flow has been maintained up to Re = 50,000, but conditions are unstable and any disturbance will cause reversion to normal turbulent flow. In straight pipes of constant diameter, flow can be assumed to be turbulen
12、t if the Reynolds number exceeds 4000.Pipe NetworksAn extension of compound pipes in parallel is a case frequently encountered in municipal distribution system, in which the pipes are interconnected so that the flow to a given outlet may come by several different paths. Indeed, it is frequently impo
13、ssible to tell by inspection which way the flow travels. Nevertheless, the flow in any networks, however complicated, must satisfy the basic relations of continuity and energy as follows:1. The flow into any junction must equal the flow out of it.2. The flow in each pipe must satisfy the pipe-fricti
14、on laws for flow in a single pipe.3. The algebraic sum of the head losses around any closed circuit must be zero.Pipe networks are generally too complicated to solve analytically, as was possible in the simpler cases of parallel pipes. A practical procedure is the method of successive approximations
15、, introduced by Cross. It consists of the following elements, in order:1. By careful inspection assume the most reasonable distribution of flows that satisfies condition 1.2. Write condition 2 for each pipe in the formhL = KQn (7.5)where K is a constant for each pipe. For example, the standard pipe-
16、friction equation would yield K = 1/C2 and n = 2 for constant f. Minor losses within any circuit may be included, but minor losses at the junction points are neglected.3. To investigate condition 3, compute the algebraic sum of the head losses around each elementary circuit. hL = KQn. Consider losses from clockwise flows as positive, counterclockwise negative. Only by good luck will these add to zero on the first trial.4. Adjust th
