GIVEN Water flowing from the oscillating slit shown in Fig. E4.3a produces a velocity field given by V = u sin[w(t - y/v)] + voj, where uo. o, and are constants. Thus, the y component of velocity remains constant (v = v) and the x component of velocity at y = 0 coincides with the velocity of the oscillating sprinkler head [u = 1₁ sin(ot) at y = 0]. FIND (a) Determine the streamline that passes through the origin at 1 = 0; at t = m/2w. (b) Determine the pathline of the particle that was at the ori- gin at t = 0; at 1 = 7/2w. (c) Discuss the shape of the streakline that passes through the origin.

GIVEN Water flowing from the oscillating slit shown in Fig. E4.3a produces a velocity field given by V = u sin[w(t - y/v)] + voj, where uo. o, and are constants. Thus, the y component of velocity remains constant (v = v) and the x component of velocity at y = 0 coincides with the velocity of the oscillating sprinkler head [u = 1₁ sin(ot) at y = 0]. FIND (a) Determine the streamline that passes through the origin at 1 = 0; at t = m/2w. (b) Determine the pathline of the particle that was at the ori- gin at t = 0; at 1 = 7/2w. (c) Discuss the shape of the streakline that passes through the origin.

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

te
(a)
Mo
Pathlines of
particles at origin
at time
0
Oscillating
sprinkler head
1-x/200
1
■FIGURE E4.3
1-0
2x
-2ugleo
xvje
11
Pathline
0
Streamlines
through origin
x/200
2ugler
Streaklines
through origin
at time

EXAMPLE 4.3 Comparison of St
GIVEN Water flowing from the oscillating slit shown in
Fig. E4.3a produces a velocity field given by V =
u sin[w(ty/v)] + voj, where o, o, and are constants.
Thus, the y component of velocity remains constant (v = v)
and the x component of velocity at y = 0 coincides with the
velocity of the oscillating sprinkler head [u= u, sin(ot) at
y = 0].
FIND (a) Determine the streamline that passes through
the origin at t = 0; at t = 7/2w.
(b) Determine the pathline of the particle that was at the ori-
gin at t = 0; at f = m/2w.
(c) Discuss the shape of the streakline that passes through
the origin.

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