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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/ft^{3}. 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/sec^{2}, m/s^{2}

*ρ* = density lbm/ft^{3}, kg/m^{3}

*g _{c}* = gravitational constant ft/sec

^{2}, n.a.

If the gravitational acceleration is 32.2 ft / sec^{2}, as it is
almost everywhere on earth, the specific weight in lbf / ft^{3} will be numerically equal to the density in lbm/ft^{3}. This
concept is demonstrated in Example 1.

Example 1

What is the sea level (g = 32.2 ft/sec^{2}) specific weight
(in lbf / ft^{3}) of liquids with densities of (a) 1.95 slug / ft^{3}and (b) 58.3 lbm / ft^{3} ?

Solution

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

*γ = g · ρ = ( 32.2 ft / sec ^{2} ) ( 1.95 slug / ft^{3} )*

*γ = ( 32.2 ft / sec ^{2} ) ( 1.95 lbf-sec^{2} / ft-ft^{3} ^{} )*

*γ =** 62.8 lbf / ft ^{3}*

(b) From Eq. 1b,

*γ = ρ ( g / g _{c} ) = ( 58.3 lbm / ft^{3} ) ( 32.2 ft / sec^{2} / 32.2 lbm-ft/ lbf-sec^{2} )*

*γ = 58.3 lbm / ft ^{3}*

Reference

Civil Engineering Reference Manual, Fifteemth Edition

Michael R. Lindeburg, PE

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