(i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 coefficient of viscosity of the liquid (\u03b7)<\/p>\n\n\n\n
(ii) density of the liquid (r)<\/p>\n\n\n\n
(iii) diameter of the tube (D)<\/p>\n\n\n\n
Let vc <\/sub>= k \u03b7a<\/sup> rb<\/sup> Dc<\/sup><\/p>\n\n\n\n where k is a dimensionless constant. Writing the above equation in dimensional form, we get<\/p>\n\n\n\n [M0<\/sup>LT-1<\/sup>] = [ML-1<\/sup>T-1<\/sup>]a<\/sup> [ML-3<\/sup>]b<\/sup> [L]c<\/sup><\/p>\n\n\n\n [M0<\/sup>LT-1<\/sup>] = [Ma + b <\/sup>L-a – 3b + c<\/sup>T – a<\/sup>]<\/p>\n\n\n\n Equating powers of M, L and T, we get<\/p>\n\n\n\n a + b = 0<\/p>\n\n\n\n – a – 3b + c = 1<\/p>\n\n\n\n – a = -1<\/p>\n\n\n\n On solving, we get a = 1, b = -1, c = -1<\/p>\n\n\n\n \u2234 vc<\/sub> = k \u03b7 r-1<\/sup> D-1<\/sup> = Clearly, the critical velocity vc<\/sub> will be large if \u03b7 is large, and p and D are small. So, we can conclude that<\/p>\n\n\n\n (i) The flow of liquids of higher viscosity and lower density through narrow pipes tends to be streamlined.<\/p>\n\n\n\n (ii) The flow of liquids of lower viscosity and higher density through broad pipes tends to become turbulent, because in that case the critical velocity will be very small.<\/p>\n","protected":false},"excerpt":{"rendered":" Critical velocity The critical velocity of a liquid is that limiting value of its velocity of flow upto which the flow is streamlined and above which the flow becomes turbulent. The critical velocity vc of a liquid flowing through a tube depends on (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 coefficient of viscosity of the liquid (\u03b7) (ii) density of the … Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[69],"_links":{"self":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/330"}],"collection":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/comments?post=330"}],"version-history":[{"count":1,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/330\/revisions"}],"predecessor-version":[{"id":331,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/posts\/330\/revisions\/331"}],"wp:attachment":[{"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/media?parent=330"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/categories?post=330"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/successrouter.com\/articles\/wp-json\/wp\/v2\/tags?post=330"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}k \u03b7 \/ r D<\/p>\n\n\n\n