In chemistry, the volume fraction φ_i is defined as the volume of a constituent V_i divided by the volume of all constituents of the mixture V prior to mixing:

Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%.

The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients).

The sum of all volume fractions of a mixture is equal to 1:

The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

Volume percent

Volume percent is a common expression of a solution's concentration. It is the volume fraction expressed with a denominator of 100, and thus is defined as:

A vol (French for "flight") is a once-obscure heraldic symbol consisting of a pair of outstretched, usually plumed bird's wings, which are connected together at their shoulders without having any bird's body in the middle.

The French Armée de l'Air, one of the world's first air forces, adopted a vol for its cap badge, rather than the eagle used by many other air forces. In France, the eagle is associated with the Napoleonic empire.

Cap badges

Many European countries have an eagle as the main charge of the heraldic shields of their respective monarchies: Germany, Austria-Hungary, and pre-revolutionary Russia all used some derivative of this bird in their badge. Poland did too, and even kept its badge under Communist rule, because Poland did not have a king since the partition of Poland late in the eighteenth century, so the symbol was merely nominal. In America, the cap badge of the US Air Force is the Great Seal of the United States, which also includes an eagle. But its use for the US Air Force derives from that service's derivation from the US Army, which also had the same badge.

Vol. 4 is the fourth studio album by English heavy metal band Black Sabbath, released in September 1972. It was the first album by Black Sabbath not produced by Rodger Bain; guitarist Tony Iommi assumed production duties. Patrick Meehan, the band's then-manager, was listed as co-producer, though his actual involvement in the album's production was minimal at best.

Recording

In June 1972, Black Sabbath reconvened in Los Angeles to begin work on their fourth album at the Record Plant Studios. The recording process was plagued with problems, many due to substance abuse issues. In the studio, the band regularly had large speaker boxes full of cocaine delivered. While struggling to record the song "Cornucopia" after "sitting in the middle of the room, just doing drugs",Bill Ward feared that he was about to be fired from the band. "I hated the song, there were some patterns that were just horrible", Ward said. "I nailed it in the end, but the reaction I got was the cold shoulder from everybody. It was like 'Well, just go home, you're not being of any use right now.' I felt like I'd blown it, I was about to get fired". According to the book How Black Was Our Sabbath, Bill Ward "was always a drinker, but rarely appeared drunk. Retrospectively, that might have been a danger sign. Now, his self-control was clearly slipping." Iommi claims in his autobiography that Ward almost died after a prank-gone-wrong during recording of the album. The Bel Air mansion the band was renting belonged to John DuPont of the DuPont chemical company and the band found several spray cans of gold DuPont paint in a room of the house; finding Ward naked and unconscious after drinking heavily, they proceeded to cover the drummer in gold paint from head to toe.