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at location 1. To get around this limitation on measurement locations, we must improvise.Firstly, the total pressure at location 1 is the same as the total pressure at locationmwhenthe immersed object is removed from the test section. This is expressed atPt,1=P*t,wherethe asterisk denotes that the measurement is made without the immersed object present.Secondly, we can assume that viscous losses between locationsmand 2 are negligibly smallto thatPt,2=Pt,m. Noting thatP2=P1, it then follows thatV1=r2ρ(P*t,m-P1)(6)V2=r2ρ(Pt,m-P1).(7)Substituting Eq. (6) and (7) into Eq. (4) and approximating the integral numerically by asummation of the dynamic pressure over discrete points on the pitot rake givesCD=2LnXi=1" sPt,m,i-P1P*t,m,i-P1-Pt,m,i-P1P*t,m,i-P1!Δyi#(8)where Δyiis the distance between theith and (i+ 1)th pitot tubes.In the present setupPt-P=ρwgΔhiis measured by the hydrostatic pressure difference inwater-filled manometer columns. The manometer contains 16 columns, of which the first15 are connected by plastic tubes to the 15 pitot tubes on the rake positioned in the wakeof the immersed object. The 16th manometer column is connected by another plastic tubeto the upstream static pressure wall tap. The height difference is Δhi=h16-hi. The dragcoefficient is therefore given byCD=2L15Xi=1" sΔhiΔh*i-ΔhiΔh*i!Δyi#(9)Pre-workAll pre-work should be recorded in your individual laboratory log book priorto attending your assigned laboratory session.The log book entry should beclearly labelled and dated and all entries should be legible.The pre-work isworth 20% of the grade for this piece of assessment!Answer the following questions. The laboratory demonstrator will orally test you on yourunderstanding at the start of the lab, and will also check off your log book entries. Somewider reading may be necessary to answer the questions.1. Write down the mathematical definitions of the Reynolds number and the drag coef-ficient.2. Print out the figure in Appendix A showing the drag coefficient of a sphere versusthe Reynolds number. Clearly mark the points on the graph corresponding to flowsof air at 250C and 101.3 kPa over an 80 mm diameter sphere with velocities ofV= 5,10,15,20,25 and 28 m/s.
3. A pitot tube and a static pressure tap are placed in a flow of air and connected toadjacent columns of a manometer containing fresh water as shown in the figure below.The columns at connected to a common reservoir such that the water pressure at thebase of the columns is the same. Calculate the air velocity,V, when the manometerheight difference is 53 mm. You may use the same air density as used in Question 1.Figure 3: Pitot and static pressure measurements using a multitube manometer.Experimental ProcedureSafety: Never open the wind tunnel test section while the fan is spinning. Whensafe to do so, open and close the test section carefully avoiding damage to thetunnel and components.The procedure has three parts. Set-up deals with making careful observations of the wind-tunnel and components. Part A deals with using the force transducer to measure the drag