how to make graphs
TRANSCRIPT
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How to Present ExperimentalData in Graphical Form
Engineering 111
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Whats wrong with this picture?
2080
2100
2120
21402160
2180
2200
2220
2240
2260
-4 1 6 11
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Basics requirements
2080
2100
2120
2140
2160
2180
2200
2220
2240
2260
-4 -2 0 2 4 6 8 10 12 14
StaicandTotalabsolutepressure
s(lb/ft^2)
Probe position (inches)
Pressure Profile Through Ramjet
Static Pressure
Total Pressure
Title
Legend
x-axis label (abscissa)
the independent variable
y-axis label (ordinate) the dependent variable(s)
Units
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Basics requirements
2080
2100
2120
2140
2160
2180
2200
2220
2240
2260
-4 -2 0 2 4 6 8 10 12 14
StaicandTotalabsolutepressure
s(lb/ft^2)
Probe position (inches)
Pressure Profile Through Ramjet
Static Pressure
Total Pressure
Unique data symbols
Axis scaleReasonable axis minimum (origin not always at 0,0)
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Axis scales
Must use easily interpretable scales
i.e. units of 1, 2, 5, 10, 25, 50, 100, etc.
Not units of 7, 16, 67, etc.
Axis min/max must be such that the data
curve fills the entire graph
If some data isnt scaled with other data,
make it scaled
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What is wrong?
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00
0.37
0.74
1.10
1.47
1.84
2.21
2.58
2.94
3.31
3.68
4.05
0 328 656 984 1312 1640 1968 2296 2624 2952 3280 3608 3936
Efficiency
TorqueandBHP
Speed (RPN)
Impulse Turbine Performance Curves
Torque (ft-lbf)
BHP (HP)
Efficiency (%)
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What is wrong?
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00
0.37
0.74
1.10
1.47
1.84
2.21
2.58
2.94
3.31
3.68
4.05
0 328 656 984 1312 1640 1968 2296 2624 2952 3280 3608 3936
Efficiency
TorqueandBHP
Speed (RPN)
Impulse Turbine Performance Curves
Torque (ft-lbf)
BHP (HP)
Efficiency (%)
Range extends beyond dataHard to interpolate scale
Data is poorly scaled,
cant see whats going
on
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Much Better
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
0 500 1000 1500 2000 2500
Efficiency
TorqueandBHPx10
Speed (RPN)
Impulse Turbine Performance Curves
Torque (ft-lbf)
BHP (HP)
Efficiency (%)
Note the secondary y-
axis; this aids in
visualizing data with very
different ranges
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Trend lines and best fit curves
Theoretical data does not need data points as
you are plotting a curve from equation
Experimental points must be plotted and then
connected with a best fit line or trend line
You DO NOT connect experimental data points
with lines as you do not know exactly what
happened between recorded data points
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Theoretical and experimental pressure
heads in a venturi
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11
PressureHead(mm)
Position
Pressure Head and Velocity versus position
Recorded Pressure Head
Calulated Pressure Head
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Whats wrong?
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11
PressureHead(mm)
Position
Pressure Head and Velocity versus position
Recorded Pressure Head
Calulated Pressure Head
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Whats wrong?
0
50
100
150
200
250
300
1 2 3 4 5 6 7 8 9 10 11
PressureHead(mm)
Position
Pressure Head and Velocity versus position
Recorded Pressure Head
Calulated Pressure Head
Are you telling me the
slope of the data is
exactly this?
And then abruptlychanges to this?
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Consider the following equation
I want to find the average value of k
for a set of data.
Well, conveniently, the above
equation is in the form:
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The recorded Data:
Location Radius (mm)
Temperature
(Celcius) r/r1
r1 12.7 136.4 1.00
r2 19.1 110.0 1.50
r3 25.4 91.5 2.00
r4 31.8 80.5 2.50
r5 38.1 68.6 3.00
r6 44.5 59.6 3.50
r7 50.8 51.4 4.00r8 57.2 43.4 4.50
r9 63.5 36.1 5.00
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Finding the slope, B
0
20
40
60
80
100
120
140
160
0.00 1.00 2.00 3.00 4.00 5.00 6.00
Temperature(Celcius)
r/r1 Note the logarithmic data trend,
how do I find the slope of the
data to use in my equation?
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Method 1
0
20
40
60
80
100
120
140
160
1.00 10.00
Temperature(Celcius)
r/r1
Change x-axis to log scale
Slope is now calculated as:
Best fit line through the data that
we want to find the slope of
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Method 2Slope is now calculated as:
0
20
40
60
80
100
120
140
160
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800
Temperature(Celcius)
Log10(r/r1)
Axis remains normal scale but we have used
Log10(r/r1) as the independent variable this time
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Assignment
Graph the following data on one graph. The flow rate is theindependent variable.
You may need to use multiple ordinates or you can scalesome of the data.
Be sure to make it clear in the axis labeling if you scaled thedata
This is due in hardcopy format on the last day of class,Monday, Feb 7.
This assignment is to be done on a computer, NOT by hand
If you cannot get the program to give a nice best fit linethrough your data points, you can do that by hand once youhave printed it all out.
Color or black and white is fine.
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Flow Rate
(ft^3/sec)
Heat (ft) Brake Horsepower
(HP)
Efficiency (%)
0.00 116.52 0.0379 0.0
0.00 107.64 0.0360 0.0
0.42 98.76 0.0329 17.1
0.66 94.32 0.0316 26.8
0.89 85.45 0.0310 33.3
1.07 82.12 0.0278 42.8
1.22 79.90 0.0316 41.9
1.65 71.02 0.0306 51.9
1.85 63.25 0.0291 54.6
2.16 53.26 0.0272 57.4
2.34 39.95 0.0237 53.4
2.47 29.96 0.0224 44.6
2.69 21.08 0.0221 34.7
2.77 7.77 0.0215 13.6
2.77 2.22 0.0209 4.0
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