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Linear Interpolation Explained | What is a linear interpolation?
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Welcome to Engineering Hack! In today's video we are going over the theory of linear interpolation. What is it? How does it come to be?
Often students know how to do the interpolation in their calculators (or computers), but don't know understand what they are actually doing. This can lead to silly mistakes and poor judgement when deciding whether to use it or not. Explaining liner interpolation requires understanding functions and the general equation of a line. But other than that the concept is straight forward. If we have two discrete values (that is, values that are not continuous like one given by common equation), we can infer a value between the two by assuming the function is a straight line. Other functions can also be used, but the linear interpolation assumes it is a line (hence, linear). This can be done with little error in several situations, and is often used in property tables. Property tables are created by people who actually measure the properties of substances under given conditions. Since we haven't found a function that fits the experimental data perfectly, we use the tables as a reference. But since the data was obtained experimentally, it comes in discrete values (e.g. 10 then 15 then 20, etc.). So we take the values in between these discrete values using a linear interpolation, which is a method that (generally) incurs in little error.
To learn more please watch the video till end and if you have a question just ask in the comments section.
If you like the video, please SUBSCRIBE and don't forget to press the bell 🔔, 👍like, comment and share. ---------------------------
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#interpolation #linearinterpolation #thermodynamics #Engineeringuniversity #problemsolving #EngineeringHack #steamtables #saturatedmixture #engineeringsolutions #engineeringaustralia #engineering #saturatedliquid #propertytables #steamtables #university #saturatedvapor #qualitygas #puresubstance
Often students know how to do the interpolation in their calculators (or computers), but don't know understand what they are actually doing. This can lead to silly mistakes and poor judgement when deciding whether to use it or not. Explaining liner interpolation requires understanding functions and the general equation of a line. But other than that the concept is straight forward. If we have two discrete values (that is, values that are not continuous like one given by common equation), we can infer a value between the two by assuming the function is a straight line. Other functions can also be used, but the linear interpolation assumes it is a line (hence, linear). This can be done with little error in several situations, and is often used in property tables. Property tables are created by people who actually measure the properties of substances under given conditions. Since we haven't found a function that fits the experimental data perfectly, we use the tables as a reference. But since the data was obtained experimentally, it comes in discrete values (e.g. 10 then 15 then 20, etc.). So we take the values in between these discrete values using a linear interpolation, which is a method that (generally) incurs in little error.
To learn more please watch the video till end and if you have a question just ask in the comments section.
If you like the video, please SUBSCRIBE and don't forget to press the bell 🔔, 👍like, comment and share. ---------------------------
---------------------------
▶️Watch More Videos:
---------------------------
#interpolation #linearinterpolation #thermodynamics #Engineeringuniversity #problemsolving #EngineeringHack #steamtables #saturatedmixture #engineeringsolutions #engineeringaustralia #engineering #saturatedliquid #propertytables #steamtables #university #saturatedvapor #qualitygas #puresubstance
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