generate equations for flow velocity and Reynolds number in the wide section (ReD) as functions of ΔP1. generate an equation for CD as a function of ΔP1 and ΔP2. based on the equations generated, calculate the values of CD and ReD corresponding to each row of ΔP1 and ΔP2 and generate an excel table with all the calculated values. create a plot of CD as a function of the Reynolds number (ReD). In the plot, use the x-axis for ReD and the y-axis for CD. Show all the derivations and theoretical work applied to arrive at the solution. Also include any excel sheet or coding utilized to generate the curve. (Hint: 1. the flow rate as measure by the pitot tube velocity is the same as the flow rate through the nozzle and 2. use ideal gas equation to find density of air)

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  1. generate equations for flow velocity and Reynolds number in the wide section (ReD) as functions of ΔP1.
  2. generate an equation for CD as a function of ΔP1 and ΔP2.
  3. based on the equations generated, calculate the values of CD and ReD corresponding to each row of ΔP1 and ΔP2 and generate an excel table with all the calculated values.
  4. create a plot of CD as a function of the Reynolds number (ReD). In the plot, use the x-axis for ReD and the y-axis for CD.

Show all the derivations and theoretical work applied to arrive at the solution. Also include any excel sheet or coding utilized to generate the curve.

(Hint: 1. the flow rate as measure by the pitot tube velocity is the same as the flow rate through the nozzle and 2. use ideal gas equation to find density of air)



Background information 

  • Utilize computer software such as excel,mathlab,ect.

 

  • The experimental set-up shown below is used to determine the discharge coefficient (CD) of the nozzle flow meter for air flow. The Pitot-Static probes (on the left part of the figure) are used as a means of accurately measuring the fluid velocity, and hence the actual volume or mass flow rate of the flow. ΔP1 represents the pressure difference between the pitot and static tubes and ΔP2 represents the pressure difference between the wide and the throat sections of the nozzle. If an experiment that has been run at T = 25 oC and P =1 atm (atmospheric conditions) results in the data shown in the table below: Create a plot of discharge coefficient (CD) as a function of the Reynolds number (ReD). In the plot, use the x-axis for ReD and the y-axis for CD. Follow the following steps to generate the plot.

 

  • Show all the derivations and theoretical work applied to arrive at the solution. Along with detailed descriptions of your derivation process. Also include any excel sheet or coding utilized to generate the curve.

 

  • Expert should not write on scratch paper and type everything out when answering 
Cross-section A - A
A
ΔΡΑ
ΔΡ2
Pressure taps
Nozzle
d D
Π
d = 4 cm
D = 8 cm
ΔΡ1 (Pa)|ΔΡ, (Pa)
10
159.978
25
395.22
50
784.684
75
1172.66
100
1559.78
125
1946.31
150
2332.4
175
2718.14
200
3103.58
225
3488.79
250
3873.78
275
4258.59
300
4643.23
Transcribed Image Text:Cross-section A - A A ΔΡΑ ΔΡ2 Pressure taps Nozzle d D Π d = 4 cm D = 8 cm ΔΡ1 (Pa)|ΔΡ, (Pa) 10 159.978 25 395.22 50 784.684 75 1172.66 100 1559.78 125 1946.31 150 2332.4 175 2718.14 200 3103.58 225 3488.79 250 3873.78 275 4258.59 300 4643.23
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