Bottle Coating Amount

Last modified by

on

Mar 27, 2024, 5:06:48 PM

Created by

on

Mar 27, 2024, 4:50:14 PM

V = f (a, b, h_{2}, h_{1}, 1)

$V = f( "a" , "b" , h_2 , h_1 , 1 )$

(a) neck radius

$(a) "neck radius"$

(h 2) neck height

$(h2)"neck height"$

(b) body radius

$(b) "body radius"$

(h 1) body height

$(h1)"body height"$

(t) Coating Thickness

$(t)"Coating Thickness"$

(n) Number of Bottles

$(n)"Number of Bottles"$

Bottle Calculators

Surface Area of a Bottle: This computes the surface area of a bottle shaped object based on the dimensions.
Mass of the Contents of a Bottle: This computes the weight or mass of a bottle shaped object based on the dimensions and the density of its contents.
Volume of a Bottle: This computes the volume of a bottle shaped object based on the dimensions.
Bottle Coating Amount: This computes the volume of material needed to coat the surface area of a bottle shaped object.

The Math

The formula used in this calculator is as follows:

$A = π (a + b) \sqrt{h_{2}^{2} + {(b - a)}^{2}} + 2 \cdot π \cdot b \cdot h_{1} + π \cdot b^{2}$ $A = pi(a+b) sqrt(h_2^2+(b-a)^2) + 2*pi*b*h_1 + pi*b^2$

The surface area (A) includes several geometric shapes: the tapered neck, the cylindrical body and the circular bottom. You can see this in the three components of the formula:

tapered neck (frustum of a cone): $A = π (a + b) \sqrt{h_{2}^{2} + {(b - a)}^{2}}$ $A = pi(a+b)sqrt(h_2^2 + (b-a)^2)$
cylindrical body (cylinder): $A = 2 π \cdot b \cdot h_{1}$ $A = 2pi*b*h_1$
circular bottom (circle): $A = π \cdot b^{2}$ $A=pi*b^2$

NOTES

Geometrically, a bottle shaped object is the combination of right circular cone with a frustum defined by base radius (a) and top radius (b) and height (h₂) in between and a cylinder of radius (b) and height (h₁). The surface area is the sum of the surface of the cone frustum, the cylinder and the circle of the bottom. Note: this leave no surface area for the opening at the top.

Comments
Attachments
Stats

No comments

Bottlesurfacearea-illustration.png

Last 12 Months

This site uses cookies to give you the best, most relevant experience. By continuing to browse the site you are agreeing to our use of cookies.

Bottle Coating Amount

Bottle Calculators

The Math

NOTES

Datasets

Equations and Data Items

Calculators

Equations and Data Items

Collections