Quantity of water or liquid flowing out of a tank through a hole orifice at the bottom of the tank. Mathematical Modelling and Experimental Results.
Application of Integration methods to model quantities that are changing continuously in a non-linear fashion with respect to time.
This work was started as a way to illustrate the power of calculus in mathematical modelling to class 11 and 12 students, when we deal with quantities that are not changing linearly with respect to time or other variable. However the integration methods look slightly complicated and may be suitable only for college level students and fluid mechanics students.
Mathematical Model PDF File
Excel Calculations and Graphs Excel File
Due to friction losses in the orifice, the theoretical flow values will be higher than the actual flow values. So theoretical flow values are multiplied by a term called Coefficient of Discharge to bring it close to actual flow values.
Coefficient of Discharge CD = Actual Flow / Theoretical Flow
This value is approximately around 0.62 to 0.69 for many of the orifices.
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