At a certain point in its motion, the force on the body would cancel out and the body suffers no further change in velocity. Under the acceleration, the body’s velocity keeps on increasing and from equation (5), consequently, the retarding force keeps increasing. Let us suppose that an object is moving in a viscous liquid under the force of gravity. Where a is the radius of the sphere and v is the velocity of motion of the body. Stokes discovered the expression for retarding force an object moving in a medium for viscosity : The viscous drag experienced by any object in a viscous medium is seen to be proportional to the velocity of the body in the fluid. Scaling and the law of similarity help in the design of vehicles such as cars, planes, and other fast-moving vehicles so that the smooth motion of the vehicles is not disturbed by the turbulence in the medium, in which they move.įor the flow of liquids in tubes, the characteristics of Reynolds number values are: Viscous Drag and terminal velocity: Turbulence manifests as noise in blood flow through arteries, where it enables blood pressure measurement. Weather in parts of the world is conditioned by ocean currents of large proportions. This aspect is used for benefit in certain cases where it may be needed, like, in the kitchen mixie. Turbulence results in the rapid mixing of composition and energy of the medium. When the critical velocity is exceeded in any situation, turbulence sets in and this leads to energy dissipation, mostly as heat. For example, if oil and water are pumped through tubes of identical shapes and cross-sections, the flow becomes turbulent at approximately the same value of R e, for the suitable combinations. Geometrically, similar flows become turbulent at the same values of R e for the different combinations of and v C. The experimental results may be assumed to hold for the real situation also. The technical importance of this number is that the resistance of a medium to the motion of the body, of any shape, may be ascertained by using a scaled-down model under lab conditions, with the same liquid. In the case of motion of bodies through viscous media, the number obeys the ‘law of similarity’.Hence, geometrically similar bodies have similar streamlined flow in the same liquid. See More: Continuity equation Applications of viscosity It is a much-used critical number that looks like the ratio of the inertial force per unit area to the viscous per unit area. This law has passed several rigorous experimental tests and found to be valid. In the case of an obstacle like a sphere, for instance, it could be the diameter of the sphere and for flow through a tube, it could be the diameter of the tube. ’d’ may be taken to stand for the typical dimension of the obstacle or boundary to fluid flow. Where is the coefficient of viscosity and is the density of the liquid,d is the diameter of the tube carrying the fluid? ’R e’ is called Reynold’s number and from a dimensional analysis of the equation, we see that it is just a number. Osborne Reynolds demonstrated that the critical velocity of a liquid is given by a relation of the form: The liquid flow could then have eddies and great turbulence. There is no more laminar flow and flow lines of different layers shall cross each other. A liquid inflow, more particularly through a tube, may experience streamlined or laminar flow as the velocity is increased, till a certain value, the critical value,v c at which the steady flow is disturbed.
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