... the all of the tube the formula 4 and 5 are equivalent. Figure 5. Continuous turbulent profile according to formula 5.Transient effectsAt transitions in the diameter of the tube the flo profile ill generally be disturbed over some distance the flo needs a certain distance to stabilise again.This effect can also occur due to disturbances such as by a non-smooth all of the tube or a bend in the tube. The distance over hich the disturbances can be observed depends on the velocity of the flo, the diameter of the tube and the initial profile. Empirically the folloing formula has been established for the distance over hich the flo profile can be disturbed. EMBED Equation.3 6For a laminar flo ith EMBED Equation.3 in a tube ith the radius R 1 cm one may thus expect a disturbance over a distance of 2 meter. Notice that the formula does not give hard criteria but rather represents an crude estimate i2s.Transition beteen laminar and turbulentith increasing Reynolds number it takes more time for small disturbances to die off. Above a certain flo velocity, characterised by the critical Reynolds number EMBED Equation.3 , a transition to turbulence ill take place disturbances are longer damped but rather do reinforced one another. Usually one finds 2300 EMBED Equation.3 2600. hoever, in the case very precisely controlled initial profiles critical Reynolds numbers amounting to more then 10000 have been obtained i2,7s.2.1.b Laser Doppler velocity measurementDoppler shiftIn laser Doppler velocity measurements use is made of the frequency shift that is inflicted on light that is scattered on moving particles. This very small frequency shift remains undetectable under normal circumstances. Hoever, detection can be accomplished by splitting the laser beam and having the to beams cross one another under an angle EMBED Equation.3 figure 6 and 7. INCLUDEPICTURE http.dipmec.unian.itmisurestrumentiLDAimglens.jpg t MERGEFORMATINET Figure6. A laser is splitted into to equal-intensity, parallel beams. A lens causes these beams to cross and focus at common point F i1s.A particle that passes the focal point ill scatter light both ith a somehat higher as ell as ith a somehat loer frequency. The beam that is directed mainly opposite to the velocity of the particle ill give a positive frequency shift blue shift and the beam that is directed mainly in conjunctions ith the velocity of the particle ill give a negative shift red shift. If a particle passes the focal point of the to beams than both signals ill be emitted simultaneously. In fact one has a point source emitting ith to different avelengths. This situation can be described ith a sum-and a difference frequency. The sum frequency can not be detected easily, but the difference frequency can. For the difference frequency, knon as the Doppler frequency EMBED Equation.3 the folloing relations holds EMBED Equation.3 7The observed frequency is thus a measure for the flo velocity. A larger frequency corresponds to a larger flo velocity.i2sFringe modelIf to coherent laser beams cross one an other an interference pattern fringes ill exist in the crossing volume. INCLUDEPICTURE http.dipmec.unian.itmisurestrumentiLDAimgfringe.jp
g t MERGEFORMATINET Figure7. LDA description according to the fringe model i1sThe distance EMBED Equation.3 beteen the maxima of the fringes depends on EMBED Equation.3 , the crossing angle EMBED Equation.3 8The number of maxima is depending on the diameter of the laser beam and the geometry of the set-up. In a properly lined up experimental set-up in the student-lab this number ill be approximately be eight. In figure 7 only 4 maxima are depicted f ... Download