Partial Volume in a Round Hopper Tank

Hemisphere Dome Tank

Calculate the amount of liquid in a partially filled round hopper tank. This tank has the shape of a cylinder with a truncated cone (funnel) bottom.
This calculator uses inches for measurements.

Approximate weight of Fuel or Water
one US gallon of water = 8.34 pounds.
one US gallon of diesel fuel = 7.1 pounds
one US gallon of gas = 6 pounds

Round Hopper Tank

Top Diameter (T) in
Bottom Diameter (B) in
Height A Cylinder in
Height B Funnel in
Depth of Liquid in
Liquid Weight-Pounds per US Gallon lb/gal US

Results:

Tank Volume and Capacity
Cubic Inches in³
Cubic Feet ft³
Cubic Metres m³
Capacity in US Gallons gal US
Amount of Liquid Inside Tank
In US Gallons gal US
In Imperial Gallons gal Imperial
In Litres L
In Cubic Feet ft³
Weight of Liquid and Fill Amount
Weight of Liquid lbs
To Fill this Tank, Add US gal

Calculator

  1. enter the top diameter (A) of the hopper tank in inches
  2. the cylinder height (A) in inches
  3. the cone (funnel) height (B) in inches
  4. the bottom diameter (B) in inches
  5. the depth of the liquid inside the tank in inches
  6. the weight of the liquid in pounds per US gallon

Results

  1. the volume of the hopper tank in cubic inches
  2. the volume of the tank in cubic feet
  3. the volume of the tank in cubic metres
  4. the total amount of liquid the tank can hold in US gallons
  5. the amount of liquid inside the tank in US gallons
  6. the amount of liquid inside the tank in Imperial gallons
  7. the amount of liquid inside the tank in litres
  8. the amount of liquid inside the tank in cubic feet
  9. the weight of the liquid inside the tank based on lbs/gal US
  10. the amount of liquid it will take to fill this tank in US gallons

Formula
V = 0.5r²(Y-sin(Y))L+d(W-H)
where V is the volume of the cylinder
r half the tanks height
Y=2cos-¹(r-d)/d
d the depth of the liquid inside the tank
W the width of the tank
H the tanks height

V = d*𝝅/3*p²+pa+a²
where V is the volume of the funnel
d the fill height of the liquid
𝝅 = 3.14159265
p diameter @ fill height
a half the tanks'  bottom diameter
Conversions
one cubic inch (in³) = 0.000578703703703704 cubic feet (ft³)
one cubic inch (in³) = 0.000016387064 cubic metres (m³)
one cubic inch (in³) = 0.00432900432900432 gallons (gal) US
one cubic inch (in³) = 0.00360465014990905 gallons (gal) Imperial
one cubic inch (in³) = 0.016387064 litres (L)

The Partial Volume of Liquid in a Tank

Calculate the partial volume of liquid in a tank or container using inches for measurements.

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