**Momentum Conservation using the Shell Balance Approach**To apply the shell balance approach for momentum conservation, sketch a control volume in Cartesian coordinates. Clearly indicate all fluxes and forces in your diagram. Using this shell balance, derive the following momentum conservation equations:**Equations:**- **x-motion:** \[ \rho \left( u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} \right) = -\frac{\partial p}{\partial x} + \mu \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \right) + B_x \]- **y-motion:** \[ \rho \left( u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} \right) = -\frac{\partial p}{\partial y} + \mu \left( \frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} \right) + B_y \]**Explanation of Terms:**- \( \rho \): Density of the fluid- \( u, v \): Velocity components in the x and y directions, respectively- \( p \): Pressure- \( \mu \): Dynamic viscosity- \( B_x, B_y \): Body forces in the x and y directionsThese equations represent the conservation of momentum in a fluid, accounting for convection, diffusion, and external forces.

Answered: Image /qna-images/answer/cda7a42a-3767-42ef-b7d4-522e2e61ec89.jpg

Use the Shell Balance approach for Momentum conservation, create a sketch of a control volume in Cartesian coordinates, and indicate all fluxes and forces in your sketch. Use this Shell Balance to derive the following Momentum conservation equations. x-motion: p(u y-motion: p(u ax +v) = - + μ (3+0) + Bx ax +v) = − ² +μ (0²2² +0²2) - - + By

Use the Shell Balance approach for Momentum conservation, create a sketch of a control volume in Cartesian coordinates, and indicate all fluxes and forces in your sketch. Use this Shell Balance to derive the following Momentum conservation equations. x-motion: p(u y-motion: p(u ax +v) = - + μ (3+0) + Bx ax +v) = − ² +μ (0²2² +0²2) - - + By

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

See similar textbooks

Similar questions

When a valve is opened, a certain fluid flows through the choke duct or valve (see figure), according to the relationship: V= V (1 + x/L) i Determine a) If the flow is stationary or transient. b) The acceleration (ax) of the fluid applying Euler's approach. c) The position of the particle as a function of time at x = 0 and t = 0. d) Determine the acceleration of the particle as a function of time.
a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.
please solve in 20 mins . i need help i will give you positive feeback
Can I have help filling the blanks(when applicable) in the following? Please add a description of the way you thought to fill the blank. Thank you!
A missile is fired and a radar on the ground shows that the missile follows the law of movement r(t) = 5 (V₁² +25' VP² +25² arctan ¹). Answer what is proposed below: (A)) Find the speed, acceleration and shaking of the missile. (B) Find the curvature and torsion of the missile trajectory in t = 2 (C) Find the mobile frame (T, N, B) in t = 1. (D) What is the length of the path traveled by the missile from its launch in t = 0 to its impact in t=10
An object of mass m falling vertically in a resisting fluid under linear resistance force F= -ev. Find the velocity as a function of time in term of terminal speed v and characteristic time (t). p 3:11
Kindly give a detail and corrrect solution with proper explanation. I will give like else dislike
Consider the velocity field represented by V = K (yĩ + xk) Rotation about z-axis is
10 m 1 m 1 m/s Figure 2 Electricity transmission tower Consider 2D, incompressible, steady flow in a vertical channel at a Reynolds number of 100. This channel flow is shown schematically in the figure below. The figure is not drawn to scale. NEGLECT GRAVITY for the sake of simplicity. Channel length 1 and width w are 10 m and 1 m, respectively, as shown in the figure. Assume thickness= 1 m in the z-direction. The velocity is constant at the inlet, in the y-direction and equal to 1 m/s. The Reynolds number is defined as Re . pvw fl where v is the average velocity at any cross-section. Take p = 1 kg/m3 and adjust μ to get the desired Reynolds number. The absolute pressure at the outlet is 1 atm. Note that the cross-section is a square of 1m by 1m. Contrast this to the laminar pipe flow considered earlier where the cross-section was circular. When the cross-section is square or rectangular, this type of a flow is referred to as a channel flow. When the cross-section is circular, the…
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
Problem 1 Given a steady flow, where the velocity is described by: u = 3 cos(x) + 2ry v = 3 sin(y) + 2?y !! !! a) Find the stream function if it exists. b) Find the potential function if it exists. c) For a square with opposite diagonal corners at (0,0) and (47, 27), evaluate the circu- lation I = - f V.ds where c is a closed path around the square. d) Calculate the substantial derivative of velocity at the center of the same box.
t = 0