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The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m-1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through, A , and a unit vector normal to the area, n ^ {\displaystyle {\hat {\mathbf {n} }}} .
Suppose the pipe has radius r = 2 cm = 2 × 10 −2 m. The area is then =. To calculate the mass flux j m (magnitude), we also need the amount of mass of water transferred through the area and the time taken. Suppose a volume V = 1.5 L = 1.5 × 10 −3 m 3 passes through in time t = 2 s.
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...
This means the greater the hydraulic radius, the larger volume of water the channel can carry. Based on the 'constant shear stress at the boundary' assumption, [ 6 ] hydraulic radius is defined as the ratio of the channel's cross-sectional area of the flow to its wetted perimeter (the portion of the cross-section's perimeter that is "wet"):
V is the total wetted volume of the channel, S is the total wetted surface area. This definition is reduced to 4 A P {\displaystyle {\frac {4A}{P}}} for uniform non-circular cross-section channels, and 2 R {\displaystyle 2R} for circular pipes.
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter ) ( D {\displaystyle D} ) is twice the equivalent radius.
In fluid dynamics, Sauter mean diameter (SMD) is an average measure of particle size.It was originally developed by German scientist Josef Sauter in the late 1920s. [1] [2] It is defined as the diameter of a sphere that has the same volume/surface area ratio as a particle of interest.