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Function FDOUB(X As Single, Y As Single, xo As Single, yo As Single, KAPPA As Single)
    ' Functions for the Stream function due to elementary flows.
    ' This is based on equation 6.96 on page 308 in the fluids pdf
    ' This REAL function returns the stream function at X,Y due to a
    ' Doublet of strength KAPPA located at XO,YO.
    Dim Pie As Single
    
    ' Assign the value of pi to the variable Pie
    Pie = Application.Pi()
    
    ' Calculate the stream function due to a doublet using the given formula
    FDOUB = -KAPPA * (1# / (2# * Pie)) * (Y - yo) / ((X - xo) ^ 2 + (Y - yo) ^ 2)
End Function



Function Fpsands(X As Single, Y As Single, x0 As Single, y0 As Single, hat As Single) As Single
' Functions for the Stream function due to elementary flows.
 
' This REAL function returns the stream function at x,y due to a
' source or a sink of strength hat located at x0,y0
' This is based on equation 6.83 on page 303 in the fluids pdf
    Dim Pie As Single, A As Single, B As Single
    Pie = Application.Pi()
    B = X - x0
    A = Y - y0
    If Y > 0 Then
' The Atan2 function gives the correct answer if the y value is greater than zero,
' that is, first and second quadrants.
    Fpsands = (hat / (2# * Pie)) * (Application.Atan2(B, A))
Else
' This equation corrects the atan2 problem when y is less than zero,
' that is the third and fourth quadrants
    Fpsands = (hat / (2# * Pie)) * ((2# * Pie) + (Application.Atan2(B, A)))
End If

End Function


Function fvortex(X As Single, Y As Single, x0 As Single, y0 As Single, gamma As Single) As Single
' Functions for the Stream function due to elementary flows.
' This is based on equation 6.91 on page 306 in the fluids pdf.
' This REAL function returns the stream function at x,y due to a
' vortex of strength gamma located at x0,y0
 
    Dim Pie As Single, lan As Single
    Pie = Application.Pi()
    fvortex = (gamma / (2# * Pie)) * Application.Ln((((X - x0) ^ 2) + _
    ((Y - y0) ^ 2)) ^ 0.5)
 
End Function


Function UniformFlowStreamFunction(X As Single, Y As Single, U As Single, alpha As Single) As Single
    ' Function for the stream function of uniform flow
    ' ? = U * (y * Cos(a) - x * Cos(a))
    
   UniformFlowStreamFunction = U * (Y * Cos(alpha) - X * Cos(alpha))
End Function


Function SumOfResults(X As Variant, Y As Variant, x01 As Single, y01 As Single, KAPPA As Single, _
                      x02 As Single, y02 As Single, hat As Single, x03 As Single, _
                      y03 As Single, gamma As Single, U As Single, alpha As Single) As Double
                        
    
    ' Sum up the results
    SumOfResults = FDOUB(X(i, 1), Y(i, 1), x01, y01, KAPPA) + Fpsands(X(i, 1), Y(i, 1), x02, y02, hat) + fvortex(X(i, 1), Y(i, 1), x03, y03, gamma) + UniformFlowStreamFunction(X(i, 1), Y(i, 1), U, alpha)
    

End Function

Sub CalculateAndPlaceResult()

    'Variables for FDOUB
    Dim X as Integer
    Dim Y as Integer
    Dim x01 As Single
    Dim y01 As Single
    Dim KAPPA As Single
    
    'Variables for Fpsands
    Dim x02 As Single
    Dim y02 As Single
    Dim hat As Single
    
    'Variables for fvortex
    Dim x03 As Single
    Dim y03 As Single
    Dim gamma As Single
    
    'Variables for UniformFlowStreamFunction
    Dim U As Single
    Dim alpha As Single
    
    'Assign Values to each variable
    Y = Range("D13:D38").Count
    X = Range("E12:O12").Count
   
    'FDOUB
    x01 = Range("J7").Value
    y01 = Range("J8").Value
    KAPPA = Range("J6").Value
    
    'Fpsands
    x02 = Range("F7").Value
    y02 = Range("F8").Value
    hat = Range("F6").Value
    
    'fvortex
    x03 = Range("L7").Value
    y03 = Range("L8").Value
    gamma = Range("L6").Value
    
    'UniformFlowStreamFunction
    U = Range("D6").Value
    alpha = Range("D7").Value
    For I = X To 1 Step -1
		For J = Y To 1 Step -1
			Cells(J+12,I+4).value = SumOfResults(I, J, x01, y01, KAPPA, x02, y02, hat, x03, y03, gamma, U, alpha)
End Sub
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