This question is from the subject "Fluid Mechanics" 3. A velocity field v= ui + vj + wk is given as: u = x+2y+ 3z + 4r°,v = xyz +1 andw = (x+y)z² +2r.Determine: (a) the local acceleration, (b) the convective acceleration and (c) the total accelerationat the point P(1,1,1,2).

Answered: Image /qna-images/answer/f4b4f614-8cdd-4aad-9920-d8a94c887b43.jpg

3. A velocity field v= ui + vj + wk is given as: u =x+2y+3z + 4r°, v = xyz +t and w = (x+ y)z +21. Determine: (a) the local acceleration, (b) the convective acceleration and (c) the total acceleration at the point P(1,1,1,2).

3. A velocity field v= ui + vj + wk is given as: u =x+2y+3z + 4r°, v = xyz +t and w = (x+ y)z +21. Determine: (a) the local acceleration, (b) the convective acceleration and (c) the total acceleration at the point P(1,1,1,2).

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

In Cartesian coordinates (x, y, x), the velocity of a three-dimensional flow in x and an incompressible motion in three directions in the x and z directions are given below. u=3.x.y2 w=4.y.z2 If only the numerical magnitude of the speed in (1,2,1) coordinates is 15 speed units a) What is the Velocity expression in the y direction b) what are the acceleration components in the three directions c) Calculate the resultant acceleration at point (3,1,2)
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?
4. A steady, incompressible, and two-dimensional velocity field is given by the following components in the xy-plane: Vxu = 2.65 + 3.12x + 5.46y = Vy= =v=0.8+ 5.89x² + 1.48y = Calculate the acceleration field (find expressions for acceleration components ax and ay and calculate the acceleration at the point (x,y) = (-1,3).
(3a)The first time derivative of vector A cross vector B is equal to the first time derivative of vector B cross vector A. The first time derivative of vector A cross vector B is equal to the first time derivative of vector B cross vector A. True False (b) Suppose you're interested in the first time-derivative of velocity vector v(t) = (5t2)i + (2t)j. Which of the following expressions represents the first time-derivative of two times v(t)? Suppose you're interested in the first time-derivative of velocity vector v(t) = (5t2)i + (2t)j. Which of the following expressions represents the first time-derivative of two times v(t)? (10t)i + (2)j (20t)i + (4)j (10)i (5/3)(t3)i + (t2)j
5. The velocity field of an incompressible flow is given by V = (a1x + a2y + azz) i + (b1 x + b2y + b3 z)j + (c1x + c2y + c32)k, where a1=2 and c3=-4. The value of b2 is
Problem#1 Given: Within a certain region the Eulerian components of velocity are as follows: v, =-A(x'+xy')e v, = A(x'y+y')e- v, = 0 %3! Where A and k are constants. Required: Determine the following at the coordinate location (1,1,0): a) The Eulerian acceleration vector b) The Lagrangian acceleration vector
two-dimensional velocity field u =xt + 2y and v =xt^2- yt x=1 meter y= 1 meter and t= 1 second Find the acceleration where it is.?
The velocity component in the y-direction is given as v = 3x - 4y for the steady, inviscid and two- dimensional flow of an incompressible fluid. The only body force is the gravity, g, and it acts in the negative y-direction. The density of the fluid is p. For an irrotational flow, determine a) The velocity component in the x-direction, if it is zero at the origin b) The acceleration vector: ) and c) The pressure field, if the pressure is Po at the origin d) The stream function(
1. Stagnation Points A steady incompressible three dimensional velocity field is given by: V = (2 – 3x + x²) î + (y² – 8y + 5)j + (5z² + 20z + 32)k Where the x-, y- and z- coordinates are in [m] and the magnitude of velocity is in [m/s]. a) Determine coordinates of possible stagnation points in the flow. b) Specify a region in the velocity flied containing at least one stagnation point. c) Find the magnitude and direction of the local velocity field at 4- different points that located at equal- distance from your specified stagnation point.
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
You are surfing, but the waves are lame so you paddle back to shore. The waves are pushing you directly to the shore, but you are paddling at an angle, so that you get closer to where you parked your car. The waves are pushing you 10 ft/sec, and you are paddling 45◦ to the right at a speed of 5 ft/sec.(a) Draw a to scale vector diagram of this situation. Your diagram should include the vector describing the velocity from the waves, and the vector describing the velocity from your paddling. Label the scale of your drawing.(b) On your drawing above, use the two given vectors to make a scale draw- ing of their resultant vector. Then use the scale of your drawing to estimate the magnitude of the resultant. Show the calculation of using the scale. (c) Using the vector addition technique learned in this course, determine the magnitude and direction of the resultant vector exactly by resolving the original two vectors into their x and y components, and using these components to construct the…
Numerical Problem: Round off your final answers into 2 decimals only. a) The velocity vector in a fluid flow is given as V = 1xt- 12x?yj + 3tk. Find the resultant velocity and acceleration of a fluid particle at (1,3,4) at time t=1. b) Determine the third component of velocity such that they satisfy the continuity equation: v = 3y and w = 1ryz?. c) Find the convective acceleration at the middle of a pipe which converges uniformly from 0.2 m diameter to 0.12 m diameter over 2 m length. The rate of flow is 30 liters per second.