Problem N-S 2 A velocity field is described by the following equations: 10y -10x u = and w=0 x2+y2 ' x²+y2' (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m³, and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.

Problem N-S 2 A velocity field is described by the following equations: 10y -10x u = and w=0 x2+y2 ' x²+y2' (a) Is this flow compressible or incompressible? (b) Find the pressure gradient. Assume frictionless flow in the z-axis, the density is 1.2 kg/m³, and the z-axis is aligned with gravity. Also assume the normal and shear effects are negligible.

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

Assumptions The flow is steady. The flow is incompressible. The flow is two-dimensional in the x-y plane V = (u, v) = (U, + bx) ỉ - byj %3D We are to calculate the material acceleration for a given velocity field. (None = b( U, +bx) a. y b? y = b( U, +by) ax b2 x (Uo +bx) = b y a, II
HW2_Q3. Streamline. For the velocity field V¯=4î+ where A = 2m?s, and the coordinates are measured in meters. (a). Obtain an equation for the flow streamline that passes through the point (x, y) = (1, 3). Select one: a. y = x O b. y = C*x O c. y = C*(1/x) d. y = x + C e. y = C*(x^2)
6. Problem We want to know the velocity component of a fluid flow normal to a given surface: v, = v"n. Compute the normal velocity u, for the following normal vector and flow vector. ) --E- 3.0 v = m/s V3 1.0
1 (a) If a flow field is compressible, what can you say about the material са derivative of density? What about if the flow field is incompressible? Explain your answer.
g Figure 3: Fluid flows between two infinite plates A viscous, incompressible steady fluid flows between two infinite, vertical, parallel plates distance h apart, as shown in Figure 3. Use the given coordinates system and assume that the flow is laminar, fully developed (30), and planar (w = 0,0). Assume that pressure and gravity are not negligible. (a) Simplify the contnuity equation and show that v = 0. (b) Using the y-momentum equation show that pressure is a function of a only. (c) Find the velocity distribution u(y) in terms of u, g, h, p and d (d) Find the wall shear stress of the flow.
For the flow field described by V = 2xyi − 3y2j. (a) Is the flow field incompressible? (b) Is the flow field steady? (c) Is the flow field two- or three-dimensional? (d) Find the angle the streamline makes that passes through the point (3, −2). (e) Find the acceleration of the flow field.
Q1 (a) If a flow field is compressible, what can you say about the material derivative of density? What about if the flow field is incompressible? Explain your answer.
For a two-dimensional incompressible flow field given by - Ajxi - vi , where A> 0, which one of the following statements is FALSE? A. It satisfies continuity equation B. It is unidirectional when x 0 and y → o. C. Its streamlines are given by x = y. D. It is irrotational
(2) Consider the following fluid velocity fields: F(x,y) = (x,y), F(x,y)=(-x, y), F(x,y) = (y, 0). (a) Plot the three fields as glyphs. Which of these vector fields represent an expansion, a compression and a shear flow? (b) Calculate the divergence of the three fields V F. Can you relate the value of the divergence with the nature (compression, expansion or shear of the flow)? (c) Calculate the circulation V x F and relate it with the nature of the flow.
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.
Problem 3: Obtaining the stream function from velocity components The steady state, incompressible flow field for two-dimensional flow is given by the following velocity components: V =16y-x and v, =16x + y %3D Determine the equation for the stream function and make sure continuity is satisfied.