2. (Problem 2.5) For steady flow through a conical nozzle of length L, the velocity in the direction of flow,x direction, is approximately√x =Uo (1-1)-2where Uo is the velocity at the entrance to the nozzle.(a) Determine the acceleration in the x direction at x = 1 m for Uo = 5 m s¹ and L = 2 m.(b) The velocity given by the above equation is approximate. Identify two locations along thenozzle where the velocity will not be correct.

Answered: Image /qna-images/answer/c5e3c4bb-8dc1-4b31-bc96-e7b9f1dfe97f.jpg

Answered: 2. (Problem 2.5) For steady flow…

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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5. A sprinkler rotates around fixed Point C. The nozzle on Arm A has broken off. So, water exits Arm A in the radial direction, relative to the sprinkler at 2 m/s and the radial velocity of the water is increasing at 0.5 m/s². The sprinkler arms are rotating around Point Cat = 6 rad/s, and because the nozzle has broken, it is decelerating with Ö= -1 rad/s². At that moment, what are the radial (vr) and theta (ve) components of velocity of the water exiting the sprinkler at Point A? b. Express the velocity vector in rectangular coordinates, in terms of i and j unit vectors. a. Y X view from the top 0.1 m 8 = 6 rad /s Ö= -1 rad/s² A *w = 2 m/s *w = 0.5 m/s²
The rocket in vertical flight is being tracked by radar.At an instant, the radar readings are:
2) Caryn purchases an electronic telescope that automatically extends and rotates the lens to focus on incoming meteors in a meteor shower. In this instance, the telescope tube is elevating and extending 0.5m, L = 0.2 , L = deg at the same time. At a given instant, Ⓒ = 45°, 0 = 10 = constant, L = S -0.3 m/s². a. Find the magnitude of the velocity v (in m/s) of the lens at point 'P'. [Ans. to Check: |v| = 0.3296 b. C. Find the acceleration a (in m/s²) of the lens at point 'P'. [Ans. to Check: |a| = 0.357] Express v and a in terms of the unit vectors i and j (cartesian coordinates).
Ex.5.3 The position of a particle moving along the x-axis is described by x = t3 – 108t in. where t is the time in sec. For the time interval t = 0 to t = 10 s (a) plot the position, velocity and acceleration as a function of time (b) find the displacement of the particle and (c) determine the distance traveled by the particle. -
2. The velocity components expressed in m/s in a fluid flow is known to be: 2 u= 2yzt v=xy W=4xzt² Find the acceleration of a fluid particle at point, P (2m,1m,1m) when time is 2 s.
7. Find the convective acceleration at the middle of a pipe which converges uniformly from 0.6 m diameter to 0.3 m diameter over 3 m length. The rate of flow is 40 lit/s. If the rate of flow changes uniformly from 40 lit/s to 80 lit/s in 40 seconds, find the total acceleration at the middle of the pipe at 20th second. [Ans. .0499 m/s² ; .11874 m/s]
3. a. An incompressible, inviscid fluid flows steadily past a ball of radius R, as shown in the figure below. According to a more advanced analysis of the flow, the fluid velocity along streamline A-B is given by R3 V = u(x)i = v. 1+ x3 where V is the upstream velocity far ahead of the sphere. Determine the acceleration experienced by fluid particles as they flow along this streamline.
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.
Q1 A balloon is rising vertically above a level, straight road at a constant rate of 1 ft sec. Just when the balloon is 65 ft above the ground, a bicycle moving at a constant rate of 17 ft sec passes under it. How fast is the distance s(t) between the bicycle anoballoon increasing 3 sec later?
For the steady flow through a conical nozzle, the axial velocity is approximately given by Uo u = (1-)* where U, is the entry velocity, and L is the distance from the inlet plane to the apparent vortex of the cone. i. Derive the general expression for the axial acceleration. ii. Determine the acceleration at x=0 and x = 1.0m if Uo = 5 m/s and L=2m
3. The equation v-v =2as gives the final velocity (v.) of a body which started with an initial velocity (v.) and received an acceleration (a) for a distance (s). Show that all three terms have the same dimensions and that the equation is dimensionally correct. Lv where h, is head loss, 2Dg 4. Determine if the equation is dimensionally homogeneous h,- f is a dimensionless resistance coefficient, L is length, D is diameter, v is velocity, and g is acceleration due to gravity.
Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. Part (a) What is the speed of the roller coaster, in meters per second, at the top of the loop if the radius of curvature there is 15 m and the downward acceleration of the car is 1.3g? Note that g here is the acceleration due to gravity. Part (b) The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track. Part (c) If it actually starts 3.5 m higher than your answer to the previous part (yet still reaches the top of the loop with the same velocity), how much energy, in joules, did it lose…

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