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 o...
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....
Consider two concentric, infinitely long cylinders. The cylinders are oriented such that the center-lines are along the z-axis, and the radii exist in the r-direction. The inner cylinder has a radius of r, and the outer cylinder has a radius rb. The inner and outer cylinders are stationary. Gravity exists in the negative z- direction, whereas a constant pressure gradient exists in the positive z-direction. The fluid contained between the cylinders is assumed to be Netwonian, incompressible, isotropic and isothermal....
An incompressible Newtonian fluid is contained between two long concentric cylinders of radii AR (< 1) and R, as shown in the figure. The inner cylinder rotates with an angular velocity Ω (a) Compute the velocity distribution between the cylinders. End effects caused by (b) Compute the torque required to hold the outer cylinder stationary. (8 Pts)
An incompressible Newtonian fluid is contained between two long concentric cylinders of radii AR (
Navier-Stokes Equation:
An incompressible Newtonian liquid is confined between two
concentric cylinders of infinite length—a solid inner cylinder of
radius RA and a hollow outer cylinder of radius RB. The inner
cylinder rotates at angular velocity ω and the outer cylinder is
stationary. The flow is steady, laminar, and two-dimensional in the
r-θ plane. The flow is rotationally symmetric, meaning that nothing
is a function of the coordinate θ. The flow is also circular so
that ur=0 everywhere.
Found Uθ=...
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...
4. Consider the situation of radial flow between two concentric cylinders. The outer cylinder has a radius of R and the inner cylinder has a radius KR. Assume flow is only in the radial direction and assume v, = v(r). Use the continuity equation and the relevant momentum balance equations to derive an expression for the pressure difference Pi-Po between the outer and inner cylinders as a function of the volumetric flow rate with L being the length of the...
An infinitely long cylinder with axis aloong the z-direction and
radius R has a hole of radius a bored parallel to and
centered a distance b from the cylinder axis
(a+b<R). The charge density is uniform and total
charge/length
is placed on the cylinder. Find the magnitude and direction of the
electric field in the hole.
Thankfully, you were able to reconnect your air tube before you lost consciousness. After such a stressful situation, you decided to take a vacation. On your vacation, you are sitting on a beach on Earth drinking a cocktail (a non-alcoholic one, of course). It's one of those fancy drinks with a straw, as shown below on the left. As an engineer who is fascinated by fluid flow, you start wondering about the velocity profiles within the fluid that you create...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗ . The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗ =2I0πa2[1−(ra)2]k^forr≤a=0forr≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. A)Using Ampere's law, derive an expression for the magnitude of the magnetic field...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...