จะหาปริมาตรน้ำมัน ในถังทรงกระบอก (วางในแนวนอน)ได้อย่างไร ถ้าทราบความสูงของน้ำมันในถังทรงกระบอกแล้ว แล้วจะเอาสูตรไปเขียนโปรแกรมง่ายๆได้อย่างไรบ้างเช่นในเอกเซล หรือโปรแกรมอื่นๆก็ได้ ขอบคุณครับ
Area chord ABC = Area sector OACB Area triangle OAB
Angle AOB = 2*arccos [(R-h)/R] (This number must be in radian, not degree)
Sector area
Area OACB = 0.5*R^2*Angle AOB (remember area of the circle = Pi*R^2)
Area OACB = 0.5*R^2*2*arccos[(R-h)/R] = R^2*arccos[(R-h)/R]
Triangle area
Area OAB = 0.5*R^2*sin (angle AOB)
Area OAB = 0.5*R^2*sin (2*arccos [(R-h)/R] )
Area OAB = 0.5*R^2*2*sin(arccos [(R-h)/R] )cos(arccos [(R-h)/R] )
Area OAB = R^2*sin(arccos [(R-h)/R] )[(R-h)/R]
Area OAB = R*(R-h)*sin(arccos [(R-h)/R] )
Area OAB = R*(R-h)*[sqrt(2Rh h^2)/R]
Area OAB = (R-h)*sqrt(2Rh h^2)
Area chord ABC
Area ABC = R^2*arccos[(R-h)/R] - (R-h)*sqrt(2Rh h^2)
Volume of the liquid in horizontal cylinder
Volume = Area ABC*length of horizontal cylinder
Volume = R^2*L*arccos[(R-h)/R] L*(R-h)*sqrt(2Rh h^2)
To program it in Microsoft(R) EXCEL
Access Visual Basic first then type in the following code (note that we have to convert Arccos to the function recognised by the program in term of Arctan). Do not include ......... in your program, I put it here for the indentation only.
Function HRZCyl(L, R, h)
.........x = (R - h) / R
.........HRZCyl = R ^ 2 * L * (Atn(-x / Sqr(-x * x + 1)) + 2 * Atn(1)) - L * (R - h) * (2 * R * h - h ^ 2) ^ 0.5
End Function
Then in the EXCEL spreadsheet enter the following
for cylinder radius (R) 50 cm, height from the side of cylinder (h) 10 cm, and horizontal length (L) of 200 cm.
=HRZCyl(200, 50, 10)
The function should give you 81750.55 cm^3.
