Combine Asynchronous Measurements
A liquid flows from two tanks and is combined into a single flow. The individual flows from each tank are calculated via the measurement of liquid levels in each tank and given as times series. Compute the combined flow from both tanks.
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In[1]:=
✖
h1 = TemporalData[TimeSeries, {{
StructuredArray[QuantityArray, {101},
StructuredArray`StructuredData[QuantityArray, CompressedData["
1:eJwBNQPK/CFib1JlAQAAAGUAAADe5APaz4oAQCSFr48qYgBAQzBMKDxTAEDX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"], "Meters", {{1}}]]}, {
TemporalData`DateSpecification[{2016, 2, 3, 17, 0, 0.}, {2016, 2, 7,
21, 0, 0}, {1, "Hour"}]}, 1, {"Continuous", 1}, {"Discrete", 1},
1, {ResamplingMethod -> {
"Interpolation", InterpolationOrder -> 1}}}, True, 314.1];
h2 = TemporalData[TimeSeries, {{
StructuredArray[QuantityArray, {101},
StructuredArray`StructuredData[QuantityArray, CompressedData["
1:eJwBNQPK/CFib1JlAQAAAGUAAADe5APaz4oAQCOFr48qYgBAWwPf4N9MAEBS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"], "Meters", {{1}}]]}, {
TemporalData`DateSpecification[{2016, 2, 3, 17, 30, 0.}, {2016, 2, 7,
21, 30, 0}, {1, "Hour"}]}, 1, {"Continuous", 1}, {
"Discrete", 1}, 1, {
ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}},
True, 314.1];Plot the liquid levels.
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In[2]:=
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DateListPlot[{h1, h2}, FrameLabel -> Automatic, Joined -> False,
Filling -> Axis]Out[2]=
The measurements are not simultaneous—the time series have different time stamps.
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In[3]:=
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SameQ[h1["Dates"], h2["Dates"]]Out[3]=
The net flow from each tank depends on the common discharge coefficient 
, the area of the cross sections of an outlet, and the liquid level, and is given as the following function.
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In[4]:=
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flowFun[c_, a_, height_] :=
Evaluate[c*a*
Sqrt[2*UnitConvert[Entity["Planet", "Earth"]["Gravity"]]]*
Sqrt[height ]]Compute the flow from each tank by applying the formula to each time series.
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In[5]:=
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flow1 = flowFun[.7, Quantity[\[Pi] 0.25^2, "Meters Squared"], h1];Copy to clipboard.
In[6]:=
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flow2 = flowFun[.7, Quantity[\[Pi] 0.26^2, "Meters squared"], h2];Calculate the total flow.
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In[7]:=
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TotalFlow = flow1 + flow2;The time stamps of the sum are the union of the time stamps from both time series over a common time range.
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In[8]:=
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newtimes =
Union[Complement[flow1["Dates"], {flow1["FirstDate"]}],
Complement[flow2["Dates"], {flow2["LastDate"]}]];Copy to clipboard.
In[9]:=
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SameQ[newtimes, TotalFlow["Dates"]]Out[9]=
Plot the flows.
show complete Wolfram Language input
Out[10]=
