3. Consider the one-dimensional, incompressible flow through the circular channel shown. The velocity at section 1 is given by U=Uo+ U₁ sin(@ot), where Uo= 20 m/s, U₁ = 2 m/s, and o 0.3 rad/s. The channel dimensions are L-1 m, R₁-0.4 m, and R₂-0.2 m. Determine the particle acceleration at the channel exit. Plot the results as a function of time over a complete cycle. On the same plot, show the acceleration at the channel exit if the channel is constant area, rather than convergent, and explain the difference between the curves. X1 L X2 R₂

3. Consider the one-dimensional, incompressible flow through the circular channel shown. The velocity at section 1 is given by U=Uo+ U₁ sin(@ot), where Uo= 20 m/s, U₁ = 2 m/s, and o 0.3 rad/s. The channel dimensions are L-1 m, R₁-0.4 m, and R₂-0.2 m. Determine the particle acceleration at the channel exit. Plot the results as a function of time over a complete cycle. On the same plot, show the acceleration at the channel exit if the channel is constant area, rather than convergent, and explain the difference between the curves. X1 L X2 R₂

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 two-dimensional flow (x-y plane) is given by u =x +yt and v = - y+xtwhere u and y are the components of the velocity in the x and ydirections respectively, and t is time.A. Is this flow incompressible? Show how you reached yourconclusion.B. Determine the time rate of change of u an v for the fluid particlewhich is located at (x,y) = (2,2) at t = 2 seconds.
Flow through a converging nozzle can be approximated by a one-dimensional velocity distribution u=vo (1+2). For the nozzle shown below, assume that the velocity varies linearly from u = vo at the entrance to u = 3v, at the exit. Compute the acceleration at the entrance and exit if vo=10m/s and L = 1m. x=0 X u= :326 x=L
1. For a flow in the xy-plane, the y-component of velocity is given by v = y2 −2x+ 2y. Find a possible x-component for steady, incompressible flow. Is it also valid for unsteady, incompressible flow? Why? 2. The x-component of velocity in a steady, incompressible flow field in the xy-plane is u = A/x. Find the simplest y-component of velocity for this flow field.
Q1) One dimensional steady fluid flow along x axis is shown in figure. The velocities at point O and X2 as from uo= 3 m/s and u2= 12 m/s. Assuming that the velocity is varying linearly with the distance through x axis, Uo= 3 m/s U2= 12 m/s X, +0.10 m- a) Calculate accelerations at O, X, and X2 points. (15) b) Determine the flow is incompressible or not. (10) 0.20 m-
A flat plate of width L= 1 m is pushed down with a velocity wall resulting in the drainage of the fluid between the plate and the wall as shown in the figure. Assume two-dimensional incompressible flow and that the plate remains parallel to the wall. The average velocity, Uvg of the fluid (in m/s) draining out at the U = 0.01 m/s towards a instant shows in the figure is (correct to three decimal places). Plate d = 0.1 m Uavg Wall
The Bernoulli's equation is valid for steady, inviscid, and incompressible flows with constant acceleration of gravity. Consider flow on a planet where the acceleration of gravity varies with height so that g = go cz, where go and c are constants. Integrate "F = ma" along a streamline - to obtain the equivalent of the Bernoulli's equation for this flow.
3. A circular cylinder of radius a is fitted with two pressure sensors to measure pressure at 0 = 180° and at 150°. The intent is to use this cylinder as a stream velocimeter, i.e. a device to determine the velocity of a stream by measuring the pressures at the two taps. The fluid is incompressible with a density of p. Figure for Part (a) U Figure for Part (b) 30 a) Using potential flow approximation, derive a formula for calculating U from the measured pressure difference at the two pressure taps. Note that for accurate measurement, the velocimeter must be aligned to have one of the taps exactly facing the stream as shown in the figure. (Ans: 2|Aptaps|/p ) b) Suppose the velocimeter has been misaligned by ổ degrees so that the two pressure taps are now at 180° + 8 and 150° + 8. Derive an expression for the percent error in stream velocity measurement. Then, calculate the error for 8 = 5°,10° and –10°. (Ans: [2/(sin2(150 + 8) – sin²(180 + 8) )– 1] × 100 )
3. The velocity components of a two-dimensional incompressible fluid flow are prescribed as v=-3x²² u=-1 i) Determine the stream function. ii) Using excel plot the stream function for y=-5 and y=-20 from x = 0 to x = 5.
A two dimensional, steady, incompressible and potential flow field of water (ρ=1000 kg/m3) is given with velocity components u and v. If the velocity component, u is given as u=2xy m/s with the magnitude of maximum pressure in the field as 52108 Pa. a) At x=+1 m and y=+2 m point, what is the magnitude of the velocity component v (in m/s)? (Please use 2 decimal digits in your answer) b) At x=+1 m and y=+2 m point, what is the magnitude of dynamic pressure (in Pa)? (Please do not use any decimal digit in your answer) c) At x=+1 m and y=+2 m point, what is the magnitude of static pressure (in Pa)? (Please do not use any decimal digit in your answer)
In a 2D dimension incompressible flow , if the fluid velocity components are given by u = x-4y , v = -4x then stream function y is given by
1-Consider the flow of a fluid in rectangular coordinates VX=XY2, VY=-X2Y, VZ=0 and ρ=xy. Make sure the velocity and density represent a physically possible flow. Remarks: For resolution, use the continuity equation. Furthermore, it is important to look in the literature for what flow is possible from the continuity equation together with the substitution of rectangular coordinate values.
The velocity field of a flow is given by V= axyi + by^2j where a = 1 m^-1s^-1 and b = - 0.5 m^-1s^-1. The coordinates are in meters. Determine whether the flow field is three-, two-, or one-dimensional. Find the equations of the streamlines and sketch several streamlines in the upper half plane