The theory of the equilibrium and motion of fluids / By Thomas Webster.

  • Webster, Thomas, 1810-1875.
Date:
[1836]
Catalogue details

Licence: Public Domain Mark

Credit: The theory of the equilibrium and motion of fluids / By Thomas Webster. Source: Wellcome Collection.

    222/238 (page 210)
    V2 and the preceding becomes i>2 = V2(l - e' 2ks) Sr Sr The constant k = --; 2k- — . 16 a 8 a Let the sphere be double the density of the fluid, then r = and let the sphere have descended p 2 through a space equal to 16 diameters. Then s = 82a; .*. k = e~2l!s = e-6 = 4^, nearly. Hence v* = T2(l - 555); .*. v=F(l-L)9 Gr, by the time that a sphere of twice the density of the fluid has descended through 16 diameters, which, when the particles are small in an insensible space, the velocity is within -8-J-0th of the terminal velocity, and may after that be considered as moving uniformly. /(l — The terminal velocity V = \/---, and substi¬ tuting the preceding values , V= V k ]6ag , which varies as the square root of the diameter of the sphere. Hence it appears that the smaller the sphere the sooner it acquires its terminal velocity, and the less that velocity is when acquired. If then any small spherical bodies, as small dust, descend in water, or condensed vapour, as very small rain, descend in air, the velocity will be uniform and almost imperceptible. 159. Prop. To determine the motion of an air- bubhle ascending in a fluid.