Problem 2 Fluid Mechanics
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Problem 2 – Fluid Mechanics Ethanol flows from Tank 1 through the following pipe system and enters Tank 2. The fluid is being transported in 250 mm ID stainless steel piping. open gate valve 42 m of pipe 45 ° elbow 16 m of pipe 45 ° elbow 20 m of pipe 90 ° elbow 1 m of pipe ε SS = 2.00∙10 ‐7 m EtOH = 789 kg/m 3 μ EtOH = 1.20∙10 ‐3 Pa∙s g=9.81 m/s 2 1. Write a MATLAB script to plot the system curve (total head Loss (m) vs (m 3 /s) at flow rates between 0 and 200 L/s, in 10 L/s increments. In your code, you will need to produce the output vectors for the variables specified below: Output vectors required (in units of) Variable name Flow rate (m 3 /s) Q Velocity of fluid (m/s) v Reynolds number Re Darcy friction factor f Total head loss for pipes (m) h_pipe Total head loss for fittings (m) h_fittings Total head loss of system (m), including the elevation h Plot the head loss data as red square points and a connecting red solid line to make the system curve [hint: only use a single line plot command e.g. plot(x,y,'c+‐‐')]. Include a title and axes labels for the plot. Caution when performing calculations: All calculations should be done purely using vector arrays (e.g. .* and ./), you are not allowed to use loops. Do not use if/else selection statement to check flow regime. Directly apply the appropriate formula for the friction factor calculation. All calculations to be performed in MATLAB. Manually calculated values that are entered into MATLAB are not accepted. For constants, use applied MATLAB functions e.g. pi instead of 3.142. 1 2 pipe system h 2 =20m h 1 =2m
Transcript of Problem 2 Fluid Mechanics
Problem 2 – Fluid Mechanics
Ethanol flows from Tank 1 through the following pipe system and enters Tank 2. The fluid is being
transported in 250 mm ID stainless steel piping.
open gate valve
42 m of pipe
45 ° elbow
16 m of pipe
45 ° elbow
20 m of pipe
90 ° elbow
1 m of pipe
εSS = 2.00∙10‐7 m EtOH = 789 kg/m3 μEtOH = 1.20∙10‐3 Pa∙s g=9.81 m/s2
1. Write a MATLAB script to plot the system curve (total head Loss (m) vs 𝑄 (m3/s) at flow rates between
0 and 200 L/s, in 10 L/s increments.
In your code, you will need to produce the output vectors for the variables specified below:
Output vectors required (in units of) Variable name
Flow rate (m3/s) Q Velocity of fluid (m/s) v Reynolds number Re Darcy friction factor f Total head loss for pipes (m) h_pipe Total head loss for fittings (m) h_fittings Total head loss of system (m), including the elevation h
Plot the head loss data as red square points and a connecting red solid line to make the system
curve [hint: only use a single line plot command e.g. plot(x,y,'c+‐‐')]. Include a title and axes labels
for the plot.
Caution when performing calculations:
All calculations should be done purely using vector arrays (e.g. .* and ./), you are not allowed to
use loops.
Do not use if/else selection statement to check flow regime. Directly apply the appropriate
formula for the friction factor calculation.
All calculations to be performed in MATLAB. Manually calculated values that are entered into
MATLAB are not accepted.
For constants, use applied MATLAB functions e.g. pi instead of 3.142.
100 m
h1 = 7 m 1
2h2 = 20 m
20 m
Pump
D = 500 mm
pipe
system
h2=20m
h1=2m
2. A pump with the following pump curve is going to be used to overcome the losses of the system
above.
Flow [L/s]
0 25 50 75 100 125 150 175 200
Head [m]
21.0 20.2 18.8 16.9 14.6 11.7 8.3 4.4 0
Plot the pump curve onto the same axis as the system curve from Q2 using blue circles and a
connecting solid blue line. Use a legend to differentiate the curves.
Define your pump variables as:
Pump curve parameters (in units of) Variable name
Pump flow rate (m3/s) Q_pump Pump head (m) h_pump
Based on the two plots, determine the operating point of the system by reading the flow rate of
the intersection point of the two plots. Store your answer as variables Q_op and H_op.
Reference solution for Problem 2:
Assessment Tests for Problem 2:
