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Elliptical Mass

Last modified by
on
May 24, 2024, 2:13:35 PM
Created by
on
May 24, 2024, 2:06:37 PM
`V = pi * "a" * "b" * "h" `
`(a)"semi-major axis"`
`(b)"semi-minor axis"`
`(h)"height of the column"`
`(mD)"Mean Density"`

The Elliptical Mass calculator computes the mass or weight of an ellipse shaped column using the semi-major (a) and semi-minor (b) axes and the height of the column (h).  Note: this is a different that the volume of an ellipsoid (see below)./attachments/163a2ed1-6a7f-11e8-abb7-bc764e2038f2/Elliptical Volume.png

INSTRUCTIONS:  Choose units and enter the following:

  • (a) semi-major axis
  • (b) semi-minor axis
  • (h) height of the column
  • (mD) Mean Density

Volume of Ellipse Shaped Column (V): The calculator returns the volume in cubic meters and the top surface area in square meters.  However these can be automatically converted to compatible units via the pull-down menu next to the resulting answer.

The Math / Science

An elliptical volume is a three dimension object with an elliptical base and top and vertical sides (see diagram above).  This differs from an ellipsoid which is a symmetric curved surface volume with elliptical cross-sections (see diagram below).  The formula for mass or weight of an elliptical volume is:

    M = π•a•b•h⋅mD

where:

In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how "elongated" it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle to arbitrarily close to but less than 1. 

Ellipsoid Calculator

Mean Density Table

Common Mean Densities in Kilograms per Meter Cubed (kg/m3)

Fluids

  • Pure Water - 1,000  
  • Seawater - 1,022  
  • Milk - 1,037 
  • Olive Oil - 860
  • Cement Slurry - 1,442 

Fuels

  • Diesel Fuel - 885 
  • Crude Oil - 870 to 920  
  • Fuel Oil -  890  
  • Ethanol - 789  
  • Gasoline (petrol) - 737 
  • Propane - 493 
  • Liquid Natural Gas - 430 to 470 

Market-Ready Grains

 

Metals

Earthen

  • Concrete - 2,371
  • Dirt - 1,250
  • Fire Clay - 1,362
  • Glass - 2,500
  • Granite - 2,691
  • Sand (dry) - 1,602
  • Sand (wet) - 2,082
  • Sandstone - 2,323

Synthetic

  • Bakelite - 1,362
  • Carbon Fiber - 2,000

Organic

  • Balsa - 170
  • Cork - 240
  • Mahogany - 545
  • Oak - 760
  • Pine - 539
  • Rubber - 1,522
                 Mean Density Lookup Function

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

  • kilograms per cubic meter (kg/m3)
  • grams per cubic centimeter (g/cm3)
  • grams per liter (g/L)
  • pounds per cubic feet (lb/ft3)
  • ounces per cubic inch (oz/in3)
  • pounds per barrel (lb/bbl)
  • pounds per bushel (lb/bu)

If you want to identify a material by its density, use the Density Within Range tool.

Cylinder Calculators

  1. Cylinder Side Area: Computes the surface area of the sides of a cylinder based on height and radius.
  2. Cylinder Surface Area: Computes the total surface area of a cylinder including sides, top and bottom.
  3. Cylinder Volume: Computes the volume of a cylinder based on cylinder height and radius.
  4. Cylinder Volume from Height and Circumference: Computes the volume of a cylinder based on the height and circumference.  It also returns the diameter of the cylinder. 
  5. Cylinder Height: Computes the height of a cylinder based on the volume and radius. 
  6. Cylinder Radius: Computes the radius and diameter of a cylinder based on the volume and height.
  7. Cylinder Weight: Computes the weight, mass and volume of a cylinder based on the height, radius and density.
  8. Cylinder Mass  Computes the mass of a cylinder based on the radius and height and mean density of the cylinder.  
  9. Volume in Horizontal Cylinder: Computes partial volume of a horizontal circular cylinder based on the radius and length of the cylinder and the vertical height of the contents in the cylinder (see diagram).
  10. Cylinder Density: Computes the mean density of a cylinder based on the mass and computed volume from the radius and height.
  11. Slanted Cylinder Surface Area: Computes the surface area of a slanted cylinder based on the radius and side length (L).
  12. Slanted Cylinder Area from Angle: Computes the lateral area (surface area of the sides) of a slanted cylinder based on its radius, height and slant angle (θ).
  13. Slanted Cylinder Volume: Computes the volume of a slanted cylinder based on the radius of the base, side length and slant angle.
  14. Slanted Cylinder Weight: Computes the weight or mass of a slanted cylinder based on the radius, side length, slant angle and density.
  15. Cylinder MoI about Central Axis: Computes the moment of inertia of a cylinder about its central axis based on the mass and radius.
  16. Cylinder MoI about the End: Computes the moment of inertia of a solid circular cylinder of uniform density about an axis along the diameter of the cylinder at one end.
  17. Cylinder MoI Perpendicular to Axis: Computes the moment of inertia of a solid circular cylinder of uniform density about an axis perpendicular to the axis of the cylinder and through the center of mass.
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