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One gaul is defined as the resistance of an airway which, when air (of density 1.2 kg/m 3) flows along it at a rate of one cubic metre per second, causes a pressure drop of one pascal. The gaul has units of N·s 2 /m 8, or alternatively Pa·s 2 /m 6. It uses the same basic equation as its Imperial counterpart, but with slightly different ...
For example, a cube with a side length of 1 meter has a surface area of 6 m 2 and a volume of 1 m 3. If the sides of the cube were multiplied by 2, its surface area would be multiplied by the square of 2 and become 24 m 2. Its volume would be multiplied by the cube of 2 and become 8 m 3. The original cube (1 m sides) has a surface area to ...
The intensity (or illuminance or irradiance) of light or other linear waves radiating from a point source (energy per unit of area perpendicular to the source) is inversely proportional to the square of the distance from the source, so an object (of the same size) twice as far away receives only one-quarter the energy (in the same time period).
By assuming a form of Coulomb's law in which the Coulomb constant k e is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were Q = T −1 L 3/2 M 1/2, [15] which, after substituting his M = T −2 L 3 equation for mass, results in charge having the same dimensions as mass, viz. Q = T −2 L 3.
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed.
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The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m 2), the SI derived unit of area; and the kilogram per cubic metre (kg/m 3 or kg⋅m −3), the SI derived unit of density.