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Explain velocity gradient and coefficient ofviscous and gives their units. |
Answer» Solution :Let laminar floe on a horizontal surface as shown in figure Suppose two layer P and Q at distance x and x+dx from stationary surface. The velocity difference dv between two layers separated bydistance dx. `(dv)/(dx)` is know as velocity GRADIENT. Velocity gradient : The difference in velocity between adjacent layers of the fluid is KNOWN as a velocity gradient. Viscous force between two layers depend onfollowing factors . (1)Depends on the area (A) of two contact surface . `FpropA`..... (1) (2) Velocity gradient between two layers `(dv)/(dx)` `Fprop(dv)/(dx)` ......(2) `thereforeFpropA(dv)/(dx)`....(3) `thereforeF=-etaA(dv)/(dx)` .....(4) Here `eta` is known as coefficient of viscosity .Its magnitude depend on the kind of fluid and on temperature. Negative sing indicates viscosityforce , is opposite to the velocity oflayers of fluid. As the temperature increase in liquid `eta` will be decrease while in gas it increases. In equation (4), A=1 unit, `(dv)/(dx)=-1` then `F=eta`. Definitionof coefficient of viscosity : The viscous force acting per unit surface area of contact and per unit velocity gradient between two adjacent layers in a laminar flowis known as the coefficient of viscosity . Unit of coefficient ofviscosity : (1) CGS unit of viscosity is dyne `scm^(-2)` or `gcm^(-1)s^(-1)`. Itis called POISE. `P_(a)*S` MKS unitof viscosity is `Nsm^(-2)` or `KGM^(-1)s^(-1)`.It is called decapoise or poisenile. 1 poisenille `(pl)=Nsm^(-2)` `=(10^(5)"dyne")sxx(10^(2)cm)^(-2)` `=10" dyne"*s*cm^(-2)` =10 poise. (3) Dimensional formula `:[M^(1)L^(-1)T^(-1)]` |
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