Stoke\u2019s Law is a mathematical equation that expresses the settling velocities of the small spherical particles in a fluid medium. The law is derived considering the forces acting on a particular particle as it sinks through the liquid column under the influence of gravity. The force that retards a sphere moving through a viscous fluid is directly proportional to the velocity and the radius of the sphere, and the\u00a0fluid\u2019s viscosity.<\/p>\n\n\n\n
Sir George G. Stokes, an English scientist, clearly expressed the viscous drag force F as:<\/p>\n\n\n\n Where r is the sphere radius, \u03b7 is the fluid viscosity, and v is the sphere\u2019s velocity.<\/p>\n\n\n\n From Stoke\u2019s Law viscosity equation, we know that viscous force acting on a sphere is directly proportional to the following parameters:<\/p>\n\n\n\n Mathematically, this is represented as<\/p>\n\n\n\n F \u221d \u03b7 a r b v c<\/p>\n\n\n\n Now let us evaluate the values of a, b and c.<\/p>\n\n\n\n Substituting the proportionality sign with an equality sign, we get(1)<\/p>\n\n\n\n F = k \u03b7 a r b v c<\/p>\n\n\n\n Here, k is the constant of proportionality which is a numerical value and has no dimensions.<\/p>\n\n\n\n Writing the dimensions of parameters on either side of equation (1), we get[MLT\u20132<\/sup>] = [ML\u20131<\/sup>T\u20131<\/sup>]a<\/sup> [L]b<\/sup> [LT-1<\/sup>]c<\/sup><\/p>\n\n\n\n Simplifying the above equation, we get[MLT\u20132<\/sup>] = Ma <\/sup>\u22c5 L\u2013a+b+c<\/sup> \u22c5 T\u2013a\u2013c<\/sup> (2)<\/p>\n\n\n\n According to\u00a0classical mechanics, mass, length and time are independent entities.<\/p>\n\n\n\n Equating the superscripts of mass, length and time respectively from equation (2), we get<\/p>\n\n\n\n a = 1 (3)<\/p>\n\n\n\n \u2013a + b + c = 1 (4)<\/p>\n\n\n\n \u2013a \u2013c = 2 or a + c = 2 (5)<\/p>\n\n\n\n Substituting (3) in (5), we get<\/p>\n\n\n\n 1 + c = 2<\/p>\n\n\n\n c = 1 (6)<\/p>\n\n\n\n Substituting the value of (3) & (6) in (4), we get<\/p>\n\n\n\n \u20131 + b + 1 = 1<\/p>\n\n\n\n b = 1 (7)<\/p>\n\n\n\n Substituting the value of (3), (6) and (7) in (1), we get<\/p>\n\n\n\n F = k \u03b7 r v<\/p>\n\n\n\n The value of k for a spherical body was experimentally obtained as<\/p>\n\n\n\n 6 \u03c0<\/p>\n\n\n\n Therefore, the viscous force on a spherical body falling through a liquid is given by the equation.<\/p>\n\n\n\n F = 6 \u03c0 \u03b7 r v<\/p>\n\n\n\n In the case of raindrops, initially, it is due to the gravity that it accelerates. As the velocity increases, the retarding force also increases. Finally, when viscous force and the\u00a0buoyant force\u00a0is equal to the force due to gravity, the net force becomes zero, and so does the acceleration. The raindrop then falls with a constant velocity. Thus, in equilibrium, the terminal velocity\u00a0vt<\/sub>\u00a0<\/em>is given by the equation<\/p>\n\n\n\n v t = 2 a 2<\/sup> ( \u03c1 \u2212 \u03c3 ) g \/9 \u03b7<\/p>\n\n\n\n and <\/p>\n\n\n\n \u03c3 <\/p>\n\n\n\n are sphere and fluid mass densities, respectively.<\/p>\n\n\n\n From the equation above, we can infer that the\u00a0terminal velocity\u00a0depends on the square of the radius of the sphere and is inversely proportional to the viscosity of the medium.<\/p>\n\n\n\n Stokes\u2019s law finds application in several areas such as:<\/p>\n\n\n\n What is Stoke\u2019s Law? Stoke\u2019s Law is a mathematical equation that expresses the settling velocities of the small spherical particles in a fluid medium. The law is derived considering the forces acting on a particular particle as it sinks through the liquid column under the influence of gravity. The force that retards a sphere moving […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[665],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3256"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=3256"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/3256\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=3256"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=3256"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=3256"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}F=6\u03c0\u03b7rv<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n Stoke\u2019s Law Derivation<\/h2>\n\n\n\n
Terminal Velocity Formula<\/h3>\n\n\n\n
Stoke\u2019s Law Applications<\/h2>\n\n\n\n