Find the equation of motion (Navier Stokes) for a viscous fluid between two rotating concentric cylinders (axle andshaft). The inner cylinder has the radius roand rotates at angular speed wo. The outer cylinder has the radius R and is stationary. Write down each vectorcomponent of the equation in a separate line and use reasonable assumptions to simplify the equation, especially thederivatives.Be sure to use cylindrical coordinates for the convective operator and the other derivatives.

Answered: Find the equation of motion (Navier…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Dentrance x=0 uentrance FIGURE P4-21 u(x) lexit x = L Dexit 4-22 For the velocity field of Prob. 4-21, calculate the fluid acceleration along the diffuser centerline as a function of x and the given parameters. For L = 1.56 m, uentrance = 22.6 m/s, and exit = 17.5 m/s, calculate the acceleration at x = 0 and x = 1.0 m. Answers: 0, -96.4 m/s²
4. Consider steady flow of water through an axisymmetric garden hose nozzle (see Fig). Along the center line of the nozzle, the water speed increases from uentrance to Uexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle. Write an equation for centerline speed u(x), based on the parameters given here, from x=0 to x=L. Dentrance Dexit Hentrance Hexit u(x) x=L
Solve using Euler's law the boundary representation model for the below-mentioned diagram.
4s-1, Given the velocity field V = Axî – Ayĵ, where A %3D (a) Sketch the velocity field. (you can do this by hand or use software of your choice)
4-17 Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4-16. The pressure field is given by P = Po 2U,bx + b°(x² + y°) where P, is the pressure at x = 0. Generate an expression for the rate of change of pressure following a fluid particle.
The Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case of a moving and/or deforming control volume, we write the RTT as follows: d pb dV + pbV-ñ dA dt dt dB sys where Vr is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of each additive term in the equation and verify that the equation is dimensionally homogeneous. Show all your work. (Hint: Since B can be any property of the flow-scalar, vector, or even tensor—it can have a variety of dimensions. So, just let the dimensions of B be those of B itself, {B}. Also, b is defined as B per unit mass.)
Consider how the new geometry in this problem affects the math/boundary condition/derivation. Both equations are listed!
A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the…
Engine oil at 60°C rotates as a rigid body about the z-axis in a spinning cylindrical container. There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r). (Hint: P = Patm everywhere on the free surface. The flow is rotationally symmetric about the z-axis.)
The velocity potential for non-viscous two-dimensional and uncompressed water flow in Cartesian coordinates is given as D= -(3x²y - y³) a) Find the corresponding current function. b) Find the pressure difference between points (1,2) and (4,4). Omit the height difference
Ex:O How many Potenhially defferent mixed tensors forder two ca be defined by faking the auer Product of s and T twice 7 Ok / tten Contraching s
(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахis

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