slugs per cubic foot (slug/ft3) to pounds per US gallon (lb/gal) conversion

What is the Slug per Cubic Foot?

The slug per cubic foot is the coherent unit of density in the British Gravitational (foot-pound-second) system, expressing the mass in slugs contained in one cubic foot. It is used in aerodynamics and fluid mechanics where the slug keeps Newton's second law consistent in imperial units.

Definition

One slug per cubic foot equals the mass of one slug (14.593903 kg) divided by the volume of one cubic foot (0.028316846592 m³).

$$1\ \text{slug/ft3} = 515.379\ \text{kg/m}^3$$

The slug is defined as the mass that accelerates at 1 ft/s² under a force of 1 pound-force, giving 1 slug = 32.17405 pound-mass = 14.593903 kg. Combined with the cubic foot, this yields 1 slug/ft³ = 515.379 kg/m³.

Origin and History

The slug was introduced in the early twentieth century so that engineers could use pound-force and the foot-second system without a gravitational conversion constant. The unit's name and the gravitational system it belongs to were popularized in British and American engineering practice, particularly aeronautics.

Law and Notable Facts

The slug per cubic foot is a derived unit with no separate statutory definition. It is the natural density unit in imperial fluid dynamics: sea-level standard air density, about 1.225 kg/m³, is roughly 0.002377 slug/ft³, a figure aerospace engineers use constantly.

Real-World Examples and Conversions

• Standard sea-level air (1.225 kg/m³) is about 0.002377 slug/ft³.
• Water (1000 kg/m³) is about 1.940 slug/ft³.
• Seawater (about 1025 kg/m³) is roughly 1.989 slug/ft³.
• 1 slug/ft³ equals 515.379 kg/m³, or 0.515 g/cm³.

What is the Pound per US Gallon?

The pound per US gallon is a US customary unit of mass density, giving the number of avoirdupois pounds contained in one US liquid gallon. It is widely used for fuels, paints, chemicals, and other liquids sold by the gallon in the United States.

Definition

One pound per US gallon equals one avoirdupois pound (0.45359237 kg) in one US liquid gallon (231 cubic inches, or 3.785411784×10⁻³ m³). The result is:

$$1\ \text{lb/gal} = 119.826\ \text{kg/m}^3$$

This uses the US gallon; the imperial (UK) gallon is larger (4.54609 L), so 1 lb per imperial gallon equals about 99.776 kg/m³. Values here refer specifically to the US gallon.

Origin and History

The US gallon descends from the English wine gallon of 231 cubic inches, retained by the United States after Britain redefined its gallon in 1824. Combined with the avoirdupois pound, pounds per US gallon became the standard density and shipping-weight measure for American liquid commerce.

Law and Notable Facts

The US gallon is defined as exactly 231 cubic inches and the pound as exactly 0.45359237 kg, making the conversion exact. A key fact: water weighs about 8.34 lb/gal, the basis of the water-treatment industry's "pounds per million gallons" dosing calculations.

Real-World Examples and Conversions

Water is about 8.34 lb/gal, gasoline roughly 6.0–6.3 lb/gal, and diesel about 7.1 lb/gal. Milk is around 8.6 lb/gal. To convert to kilograms per cubic meter, multiply by 119.826; to kilograms per liter, multiply by 0.119826.