Weight of Fluid in Spherical Container

The Weight of Fluid in a Spherical Container calculator computes the mass or weight of water or any substance (liquid or loose granular) contained in a spherical container based on the depth of the substance, the diameter of the spherical container and the mean density of the substance.  

INSTRUCTIONS: Choose units and enter the following:

• (d)  Depth of Liquid in Tank.
• (D)  Diameter of Interior of Tank
• (H) Height of Tank
• (mD)  Mean density of the substance in the tank (default for water)

Mass or Weight of Spherical Tank (M):  The mass of the sphere is returned in kilograms.  However this can be automatically converted to other mass and weight units via the pull-down menu.   The calculator also returns the following:

• (M) Weight of Contents in Kilograms
• (CV) Volume of Contents in Liters
• (CxV) Container Max Volume in Liters
• (CxM) Container Max Weight in Kilograms
• (SA)Surface Area of Contents in Square Meters (m²)

Mean Density of Fluids 

Mean density is the average amount of mass within a volume for a substance.  Note, volume of a material is often highly subject to the temperatures, since materials expand as they warm.  For that reason, mean densities of substances are often cited with a set of nominal conditions such as temperature and barometric pressure. 

The formula for mean density is:

μD = V / m

where:

• μD = mean density
• V = Volume in units like gallons or liters
• m = Mass in units like kilograms or pounds

Mean density is also often indicated as the Greek symbol rho (ρ).

The mean density of fluids can be useful since fluids (liquids and gases) conform to the shape of their containers.  This is why it is possible to use the mean density of a substance and the dimensions of its container to estimate the weight/mass of the substance in the container.

The Math/Science

 The spherical tank mass formula:

1.  uses the size of the tank, defined by its inner radius (r), and the depth of the contained material (d), to calculate the volume of the contained substance in the spherical tank.  
2. It then computes the mass by multiplying the volume by the mean density (mD) to provide an estimate of the mass or weight of the contents of the container.  

Other Container Calculators

For similar calculations with other shaped containers, click on the following:

• Volume of a Conic Cylinder 
• Load Weight of a Conic Cylinder 
• Volume of a Capsule (Spherocylinder)
• Load Weight of a Capsule (Spherocylinder)
• Total or Partial Volume  of a Box (Rectangular).  For the partial volume, simply use the depth of substance in the container instead of the total depth of the container.
• Total or Partial Load Weight of a Box (Rectangular).  For the weight of a partial load, simply use the depth of substance in the container instead of the total depth of the container.
• Volume of a Spherical Container
• Total or Partial Load Weight of a Spherical Container. For the total load weight, simply indicated the same value for the measure depth (D) of the substance to equal twice the radius (R) of the container.  (See diagram)
• Volume of a Torispherical Head
• Volume of a Torispherical Tank
• The mean density of many substances, CLICK HERE.

The Mean Density of many substances (metals, mineral, chemicals, gases, woods, agricultural products, liquids and types of earths) can be looked up by CLICKING HERE.
Or you can see these formulas and other useful measurements all combined in one TRUCKING calculator.

Plumbing Calculators

• Rolling Offsets (Run and Travel)  – The Rolling Offset Rolling Offset Lengths Pipe Grading function computes the run and travel length a rolling offset based on the offsets and fittings. (see diagram).
• Pipe Grading - Compute the drop needed over a run to maintain a grade (e.g., 4" over 12')
• Diagonal of a Square - This is a simple calculation to assist in computing the diagonal of a square.
• Diagonal of a Box - This computes the length of the diagonal of a box (T) based on sides of length R, S and U.
• Flow Rate - This computes flow rate based on the total volume and the time it took to accumulate.
• Pipe Flow Volume  - This computes the total volume from a pipe based on the flow rated and the duration of flow.
• Weight of Water in a Tank - Computes the weight of water in a cylindrical tank based on the radius and height (or length).
• Weight of Water in a Pipe - Computes the weight of water or other substances in a pipe based on the dimension and material density.
• Weight of Sea Water in pipe - Computes the weight of sea water in a cylinder based on the radius and height (or length)
• Pressure Head - The Potential Gravity-Fed Water Pressure from a Tank (a.k.a. Pressure Head) based on the height of storage.
• Pipe Volume - Computes the volume in a pipe.
• Pipe Surface Area - Computes the surface area of a pipe.
• Pipe Coating Amount - Computes the volume of coating material for a pipe such as paint, polyethylene, polyurethane, zinc, bitumen, FBE or mortar.
• Volume of Water in a Tank (e.g. hot water tanks),
• Volume of a Spherical Container
• Weight of Water in a Spherical Container
• Volume of Water in Rectangular Tank 
• Weight of Water in a Rectangular Tank
• Capillary Rise - The height of water in a small tube due to capillary force.
• Snow Water Equivalence - The volume of water created by an area and depth of snow.
• Pore Water Pressure - Pressure of uplift from the water table.
• Pipe Stress Budget - Computes the pressure that a pipe can withstand based on the allowable stress, wall thickness and outside diameter.
• Water in Basement Volume: Computes the volume of water in an area such as a basement based on the dimensions and the time required to pump it out based on a sump pump rate.
• Paint for Pipes: Computes the amount of paint needed to cover the exterior surface area of one or more pipes based on the pipe diameter, length, number of coats, number of pipes and the recommended area coverage of the paint. 
• Time to Fill: Computes the amount of time necessary to fill something (e.g., tank or pool) based on the volume and flow rate.
• Pipe Insulation Calc: Computes the number of bags of pipe insulation needed for a run of pipes based on the 12' of length per bag and the length of pipe run to be insulated.