Specific Weight Formula and Review

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Specific Weight Formula and Review

Specific Weight Review and Formula

Specific weight (unit weight), ", is the weight of fluid per unit volume. The use of specific weight is most often encountered in civil engineering projects in the United States, where it is commonly called “density.” The usual units of specific weight are lbf/ft³. Specific weight is not an absolute property of a fluid, since it depends not only on the fluid, but on the local gravitational field as well.

Eq. 1a
SI
γ = g · ρ

Eq. 1b
Imperial
γ = ρ ( g / g_c )

Where

g = gravity ft/sec², m/s²
ρ = density lbm/ft³, kg/m³
g_c = gravitational constant ft/sec², n.a.

If the gravitational acceleration is 32.2 ft / sec², as it is almost everywhere on earth, the specific weight in lbf / ft³ will be numerically equal to the density in lbm/ft³. This concept is demonstrated in Example 1.

Example 1

What is the sea level (g = 32.2 ft/sec²) specific weight (in lbf / ft³) of liquids with densities of (a) 1.95 slug / ft³and (b) 58.3 lbm / ft³ ?

Solution

(a) Equation 1a can be used with any consistent set of units, including densities involving slugs.

γ = g · ρ = ( 32.2 ft / sec² ) ( 1.95 slug / ft³ )

γ = ( 32.2 ft / sec² ) ( 1.95 lbf-sec² / ft-ft³ )

γ = 62.8 lbf / ft³

(b) From Eq. 1b,

γ = ρ ( g / g_c ) = ( 58.3 lbm / ft³ ) ( 32.2 ft / sec² / 32.2 lbm-ft/ lbf-sec² )

γ = 58.3 lbm / ft³

Reference

Civil Engineering Reference Manual, Fifteemth Edition
Michael R. Lindeburg, PE