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Additional resources for Mildenhall: Multi-mission Task Force
Integration of the normal and shear stresses on the surface of the fluid sphere yields the total hydrodynamic force exerted by the fluid on the viscous sphere as follows: FD = 2paUmc 3l + 2 . 96) The corresponding drag coefficient for the viscous sphere in Stokes flow becomes CD = 8 ( 3l + 2 ) 2FD . 97) The last expression yields the so-called Stokes drag for a solid sphere CD = 24/Rer and for an inviscid bubble CD = 16/Rer. The corresponding expressions for the drag force are FD = 6πaUμc for the solid sphere and FD = 4πaUμc for the inviscid bubble.
A general characterization of particle size distribution is monodisperse and polydisperse. In a monodisperse mixture, the particles’ sizes are close to a single size and typically, the standard deviation of the sizes is less than 10% of the mean size. In a polydisperse mixture, there is a wide range of particle sizes. Particle, drop, and bubble size distributions can also be classified as discrete or continuous. The continuous size distribution derives from the discrete distribution as the sampling interval approaches zero.
The continuous cumulative distribution is obtained from the integral of the continuous frequency distribution as follows: d ò Fn (d ) = f n (x)dx. 37) 0 12 1. 5 Continuous number frequency distribution of a sample of particles. 5. 6. The cumulative distribution of a uniform (constant) continuous distribution is a straight line. All cumulative distribution functions approach the value 1, as the particle size approaches the maximum size. It must be noted that measurements of size data for particles generate discrete distributions.