GEC BHARUCH FLUID FLOW OPERATION CHEMICAL ENGINEERING SEM:3

PREPARED BY 140140105018: HARDIK B VAGADIA 140140105019: HARSHIL H HARSORA 140140105020: RAVI A KACHA 140140105021: KANETIYA JAYDEEP

REYNOLDS NUMBER: Osborne Reynolds (English, 1842-1912): “The internal motion of water assumes one or other of two broadly distinguishable forms – either the elements of the fluid follow one another along lines of motion which lead in the most direct manner to their destination, or they eddy about in sinuous paths the most indirect possible” “Laminar” “Turbulent”

Reynolds made an experiment the 22nd of February 1880 (at 2 pm). He varied the speed of the flow, the density of the water (by varying the water temperature), and the diameter of the pipe. He used colorants in the water to detect the transition from Laminar to Turbulent.

He found that when The flow becomes turbulent More in general, the ratio with L typical length scale of the flow, is called “Reynolds number”. The critical value of the transition from laminar to turbulent flow changes with the type of flow

Reynolds number is very important in fluid mechanics The flow behaves in two different ways for low and high Reynolds numbers. For Low Reynolds numbers the flow is Laminar A laminar flow is characterized by smooth, orderly and slow motions. Streamlines are parallel and adjacent layers (laminae) of fluid slide past each other with little mixing and transfer (only at molecular scale) of properties across the layers. A small perturbation does not increase with time. The flow is regular and predictable.

For high Reynolds numbers the flow is turbulent Turbulent flows are highly irregular, three-dimensional, rotational, and very diffusive and dissipative. A small perturbation increases with time. They cannot be predicted exactly as function of time and space. Only statistical averaged variables can be predicted.

A high Reynolds number means that the inertial terms in the equation of motion are far greater than the viscous terms. However, viscosity cannot be neglected, because of the no-slip boundary condition at the interface.

Critical velocity The velocity at which the flow changes from laminar to turbulent is known as the critical velocity. Reynolds further found that the critical velocity for the transition from laminar to turbulent flow depends on the diameter of the pipe,the average velocity of the flowing fluid, the density and velocity of the fluid.

The equation of Reynolds number D=diameter of the pipe,m u=average velocity,m/s =density of fluid,kg/ =viscosity of the fluid,kg/(m*s) The Reynolds number is a dimensionless group and magnitude is independent of the unit used provide that the consistent units are used.

The Reynolds number is the ratio of the inertia force to the viscous force. The inertia force is proportional to and the viscous force is proportional to u/D. Reynolds number is useful tool to determine the nature of flow weather laminar or turbulent.

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