volume in horizontal vessel.xls
Description
To find the volume of liquid in a partially filled horizontal cylindrical vessel with hemispherical or elliptical heads, we need to determine the volume of the liquid in the cylindrical portion and the volume in the heads. Here's a stepbystep process to calculate the volume:

Determine the dimensions: a. D = diameter of the cylindrical portion b. L = length of the cylindrical portion c. h = height of the liquid in the vessel

Calculate the volume of liquid in the cylindrical portion (V_cylindrical):
a. Calculate the angle (theta) in radians, using the height of the liquid (h) and the radius (D/2):
theta = 2 * acos((D/2  h) / (D/2))
b. Calculate the area of the circular segment (A_segment) using the angle (theta) and radius (D/2):
A_segment = ((D^2) / 4) * (theta  sin(theta))
c. Calculate the volume of the liquid in the cylindrical portion (V_cylindrical):
V_cylindrical = A_segment * L
 Calculate the volume of liquid in the heads (V_heads):
a. Hemispherical heads: Calculate the volume of the liquid in the hemispherical head using the following formula:
V_hemihead = (1/6) * pi * h^2 * (3*D  h)
The total volume of liquid in the heads (V_heads) = 2 * V_hemihead
b. Elliptical heads (2:1 ellipsoidal heads): Calculate the volume of the liquid in the elliptical head using the following formula:
V_elliphead = (pi * h^2 * (3*D  h)) / 6
The total volume of liquid in the heads (V_heads) = 2 * V_elliphead
 Calculate the total volume of liquid in the partially filled horizontal vessel (V_total):
V_total = V_cylindrical + V_heads
This calculation gives you the total volume of the liquid in a partially filled horizontal vessel with hemispherical or elliptical heads. Note that the calculation assumes a constant crosssectional area of the liquid in contact with the heads, which is an approximation. To obtain a more accurate volume, consider using computational methods or specialized software.
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