Kinetic energy of a fluid flow can be computed byI pv - vdV, where p(z, y, z) and v(x, Y, z)are the pointwise fluid density and velocity, respectively. Fluid with uniform density 1 flows in the6domain bounded by a? + z? = 3 and 0 < y < -. The velocity of parabolic flow in the givendomain is v(z, y, z) = (3 – a2 – z)j. Find the kinetic energy of the fluid flow.Yanıt:

Kinetic energy of a fluid flow can be computed by /pv. vdV, where p(x, y, z) and v(r, y, z) are the pointwise fluid density and velocity, respectively. Fluid with uniform density 1 flows in the domain bounded by a? + z2 3 and 0 < y<-. The velocity of parabolic flow in the given %3D domain is v(r, y, z) = (3 - a?- 2)j. Find the kinetic energy of the fluid flow. %3D Yanıt:

Kinetic energy of a fluid flow can be computed by /pv. vdV, where p(x, y, z) and v(r, y, z) are the pointwise fluid density and velocity, respectively. Fluid with uniform density 1 flows in the domain bounded by a? + z2 3 and 0 < y<-. The velocity of parabolic flow in the given %3D domain is v(r, y, z) = (3 - a?- 2)j. Find the kinetic energy of the fluid flow. %3D Yanıt:

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

A nozzle is designed to move a liquid from V1 velocity to V2 in a linear fashion. The linear relationship here is V = ax + b and a and b are constant. As the flow is constant with V1 = 10 m / s at x1 = 0 and V2 = 25 m / s at x2 = 1m; a) local (local) acceleration, b) Convective acceleration (convective acceleration), c) Determine the acceleration of the liquid at the points x1 = 0 and x2 = 1 m.
p) A mass of fluid is in motion so that the lines of motion lie on the surface of coaxial cylinders. Show that the equation of continuity is partial differential ap 1 a 5(pvo) + əz - (ρυ.) 0 r d0 where (v,, vg, vz) are the components of velocity in cylindrical co-ordinates and p is the density.
3.1. The velocity at a point in a fluid for a one-dimensional flow may be given in the Eulerian coordinates by u == AxBt. Show that x = f(x, t) in the Lagrange coordinates can be obtained from the Eulerian system. The in- itial position of the fluid particle is designated by x) and the initial time to = 0 may be assumed.
4. The velocity vectors of three flow fileds are given as V, = axĩ + bx(1+1)}+ tk , V, = axyi + bx(1+t)j , and V3 = axyi – bzy(1+t)k where coefficients a and b have constant values. Is it correct to say that flow field 1 is one-, flow filed 2 is two-, and flow filed 3 is three-dimensional? Are these flow fields steady or unsteady?
Question 2 (Potential flow) a) The velocity component of an incompressible and 2-dimensional flow is given by Determine i. ii. iii. u = -x + 4y v = 2x - y The resultant velocity at point (-1m, 1m) The stream function The velocity potential
Tp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…
1. The potential function of fluid flow motion is given by, [(x+c)2+y²7 p = log la-e)2+y². a) Prove that, fluid is incompressible, b) Find the velocity field, c) Find the geometric location of the providing IV? = constant. %3D
Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flow
1. Answer the following questions: (a) What is the physical meaning of the following: D a +V.v at Dt where V is the velocity vector of the flow field. (b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting by the fluid on a surface element ds (with unit normal în ) computed? Give your answer in vector notation and also in index notation. What is the physical meaning of Ty ? (c) Write down the work done on a material volume of fluid by the viscous surface force in vector notation and also in index notation. (d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (with unit normal în ) in vector notation and also in index notation.
Which of the following situations is INCORRECTLY paired to its probable type of flow? Select one: O a. Flow of currents in Manila Bay: UNIFORM O b. Flow in a natural river during a flood event: UNSTEADY O c. Flow of water in a laboratory flume with constant discharge: STEADY O d. Flow in a converging pipe: NON-UNIFORM Consider the velocity field, V the magnitude of the y-component of the acceleration, ay in m/s², at point (2,1) in the velocity field? Answer: = · (x² + y² − 4)i + (xy — y)j, where x and y are in m and V is in m/s. What is - Consider the velocity field, V = (x − 2y)i — (2x + y)j. What is the value of the velocity potential function at the point (2,3)? Answer:
The two components of the velocity vector are given as Vx = –ay/(x2+ y2)1/2 and Vy = ax/(x2+ y2)1/2 where a is a constant in cm/s. Find the vorticity of a fluid element located at x = y = 1 cm. [Ans.: 1.41a k ].
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.