Question 622306
Hi, there--
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Specific Weight is defined as weight per unit volume. Here, we are thinking about weight as a force. Weight is not the same thing as mass.
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Specific Weight can be expressed as

γ = ρ*g

where

γ = specific weight in N/m^3 "Newtons per meter-cubed"

ρ = density in kg/m^3 "kilograms per meter-cubed"

g = acceleration of gravity, m/s^2 "meters per second-squared"
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(The acceleration of gravity under normal conditions is 9.807 m/s^2 in SI-units and 32.174 ft/s^2 in imperial units.)
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An Example: The Specific Weight of Water (in S-I units)
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Let γ be the specific weight of water
Let ρ be the density of water, or 1000 kg/m^3
Let g acceleration due to gravity, or 9.807 m/s^2
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γ = ρ*g
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γ = (1000 kg/m^3) (9.807 m/s^2)
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γ = 9807 N/m^3
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You will often see these values converted to kN/m^3, "kilo-Newtons per meter-cubed," where 
1 kN = 1000 N.
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γ = 9.807 kN/m^3
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The specific weight of water in S-I units is 9.807 kN/m^3.
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Hope this helps!
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Ms.Figgy
math.in.the.vortex@gmail.com