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Flow is driven by rotation of inner cylinder Find the velocity and pressure fields for "Couette...
Consider two concentric, infinitely long cylinders. The cylinders are oriented such that the center-line is along the z-axis, and the radii exist in the r-direction. The inner cylinder has a radius of ra and the outer cylinder has a radius Tb. The inner cylinder rotates with an angular velocity of w whereas the outer cylinder is stationary. There is no pressure gradient applied nor gravity. The fluid contained between the cylinders is assumed to be Netwonian, incompressible, isotropic and isothermal....
Determine from Navier-Stroke equation the velocity profile Couette flow with a constant pressure gradient dp/dx. Couette flow is a laminar flow between parallel plates, one of the plates is at rest while other is moving at a constant velocity U. The separation between the plates is h.
2. (5 points) For a pressure-driven axial flow between long concentric cylinders, find the expression for the velocity profile in the z direction if the inner cylinder is of radius b and outer cylinder is of radius a. This problem relates to flow in an airway or blood vessel in which a central catheter has been placed. solid (a) Show that LILLLLLLLLLLLL where b = Ba and B<1. Confirm that b =0 recovers Eq. (9.45) we learned in class. Eq....
Consider the steady laminar flow between the coaxial cylinders shown below. The inner cylinder rotates with angular velocity Omega and the outer cylinder is stationary. The no-slip condition applies at the inner and outer cylinder surfaces and we are considering the cylinders to be very long in the z-direction, hence we may ignore edge effects near the top and bottom surfaces. a) What are the boundary conditions on the cylinder surfaces at r=R1 , and r= R2 b) Simplify and...
The system IS Initially rotating freely with angular velocity ω1-17 rad s when the inner rod Ais centered length se within he ollow cylinder Bass n he re. Determine the angular velocity of the system (a) if the inner rod A has moved so that a length b/2 is protruding from the cylinder, (b) just before the rod leaves the cylinder, and (c) just after the rod leaves the cylinder. Neglect the moment of inertia of the vertical support shafts...
down A hollow cylinder with inner radius R = 4.45 m rotates with constant angular velocity w around a vertical axis through its center. A small box of mass m = 4.37 kg is placed on the vertical inner surface of the cylinder and rotates with it. The coefficient of static friction between the box and the inner surface is p = 0.272, and the frictional force f between the box and the inner surface keeps the box from sliding...
5*) Find the angular velocity of the Earth due to its daily rotation and express it in radians per second. Then use it, and a model of the Earth as a solid sphere of mass M= 5.97 × 1024 kg and radius R = 6.37 × 106 m, to estimate the angular momentum of the Earth due to its rotation around its axis. (The result should be of the order of 1033 kg m2/s. This is called the Earth’s “intrinsic”...
Page 5 Nane: Johnson, Perri NN: 35 1000 omawork 10 10.5 Aoni cous fuid is contained betwen two infinitely vertical, concentric cylinders. The outer cylinder has a radius fixedd rotates with an angular velocity o. The inner cylinder is and has a radius r. The Navier-Stokes equations can be used As utain an exact solution for the velocity distribution in the gap. that the flow in the gap is axisymmetric (neither velocity Fluid nor pressure are functions of angular position...
2. A circular shaft is mounted in a bearing as shown. There is a small gap between the stationary inner shaft and the outer rotating bearing filled with a viscous, incompressible Newtonian fluid. The shaft turns with a constant rotation rate ω (in rad/sec) due to the downward motion of the attached weight pulling on the cord attached to a the outer bearing (see figure) of radius R Hint: If the gap between the shaft and bearing is small compared...
Consider incompressible, steady, inviscid flow at vertical velocity vo though a porous surface into a narrow gap of height h, as shown. Assume that the flow is 2D planar, so neglect any variations or velocity components in the z direction. Find the x-component of velocity, assuming uniform flow at every x location. Find the y-component of velocity. Find an expression for the pressure variation, assuming that the pressure at the outer edge of the gap is Parm (hint: we can...