Couette flow

In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The configuration often takes the form of two parallel plates or the gap between two concentric cylinders. The flow is driven by virtue of viscous drag force acting on the fluid, but may additionally be motivated by an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like flow in lightly loaded journal bearings, and is often employed in viscometry and to demonstrate approximations of reversibility. This type of flow is named in honor of Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century. In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The configuration often takes the form of two parallel plates or the gap between two concentric cylinders. The flow is driven by virtue of viscous drag force acting on the fluid, but may additionally be motivated by an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like flow in lightly loaded journal bearings, and is often employed in viscometry and to demonstrate approximations of reversibility. This type of flow is named in honor of Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century. Couette flow is frequently used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. The simplest conceptual configuration finds two infinite, parallel plates separated by a distance h {displaystyle h} . One plate, say the top one, translates with a constant velocity U {displaystyle U} in its own plane. Neglecting pressure gradients, the Navier–Stokes equations simplify to where y {displaystyle y} is a spatial coordinate normal to the plates and u ( y ) {displaystyle u(y)} is the velocity distribution. This equation reflects the assumption that the flow is uni-directional. That is, only one of the three velocity components ( u , v , w ) {displaystyle (u,v,w)} is non-trivial. If y originates at the lower plate, the boundary conditions are u ( 0 ) = 0 {displaystyle u(0)=0} and u ( h ) = U {displaystyle u(h)=U} . The exact solution can be found by integrating twice and solving for the constants using the boundary conditions.A notable aspect of the flow is that shear stress is constant throughout the flow domain. In particular, the first derivative of the velocity, U / h {displaystyle U/h} , is constant. (This is implied by the straight-line profile in the figure.) According to Newton's Law of Viscosity (Newtonian fluid), the shear stress is the product of this expression and the (constant) fluid viscosity.