2019_VL3_LU_480386777.docx - INTRODUCTION The aim of this...

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INTRODUCTIONThe aim of this virtual laboratory experiment is to determine the dependence of thesuspension height of a ball by an upward jet of fluid on the properties of the ball, the type offluid and the flow rate of the jet. The experiment also aims to enhance an understanding ofthe applications of dimensional analysis modelling and similitude. The specific variablesrelevant to this experiment include: h: the suspension height of the ball (m), W: the weight ofthe ball (N), D: the diameter of the ball (m), d: the diameter of the jet (m), Q: the jet flow rate(m3/s), ρ: the density of the fluid (kg/m3) and μ: the viscosity of the fluid (Ns/m2). However,due to the limited scope of this experiment, only the weight of the ball, the diameter of theball, the flow rate and the type of fluid (water and air) may be varied freely.METHODOLOGY1.Carry out dimensional analysis to determine π groups In order to reduce the number of experiments and simulations necessary to investigate theaim of this report, dimensional analysis may be used. Dimensional variables are to beselected together to form dimensionless groups. Determine the (k–r) π groups needed forthe experiment, where k is the number of variables and r is the number of basicdimensions of the variables. Common dimensionless groups, such as geometry and forcedbased groups should be adopted wherever possible. The remaining groups should beselected following the Buckingham π Theorem or Trial and Error approach. In thisexperiment, the dependence of the suspension height of the ball hon six other variables ish= f (W, D, d, Q, ρ, μ), where there are (7–3) = 4π groups. When designing experiments,only one π group may be varied at a time while others π groups remain constant, hencevariations of other π groups should be minimised. Since only the variables W, Dand Qcould be varied freely in this experiment, d, ρand μwere chosen as the repeatingvariables for each π group. The results of the dimensional analysis are 1= hd, 2=μ2, 3= Ddand 4= , where hmay be described in terms of its π groups ash= df (μ2,Dd,).See the details of the dimensional analysis in the Appendix.2.Choose π group to vary and maintain other π groups constantConduct the experiment on the Virtual Laboratory platform. According to the outcome ofthe dimensional analysis, choose one π group i.e. 2= μ2, to vary by selectingdifferent ball size and mass, different fluids (air or water) and different jet flow rates.Maintain the other π groups constant. The π group containing the variable being sought isto be excluded as its dependence on the other variables is to be investigated. 3.Make sure that the ball suspension height is above zero Ensure that as the chosen π group is varied the suspension height of the ball is above zeroby trying out the values that are to be tested. If the ball is unable to be suspended abovethe jet for consecutive runs regardless of how the parameters are varied, the dependence

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