Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4—16. A fluid particle ( A ) is located at x = x A and y at time t = 0 (Fig. P4—54). At some later time i. the fluid particle has moved downstream with the flow to some new location x = x A , y = y A , as shown in the figure. Generate an analytical expression for the -location of the fluid particle at arbitrary time t in terms of its initial y-location and constant b. In other words, develop an expression for. (Hint: We know that v = d y particle following a fluid particle. Substitute the equation for u, separate variables, and integrate.)
Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4—16. A fluid particle ( A ) is located at x = x A and y at time t = 0 (Fig. P4—54). At some later time i. the fluid particle has moved downstream with the flow to some new location x = x A , y = y A , as shown in the figure. Generate an analytical expression for the -location of the fluid particle at arbitrary time t in terms of its initial y-location and constant b. In other words, develop an expression for. (Hint: We know that v = d y particle following a fluid particle. Substitute the equation for u, separate variables, and integrate.)
Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4—16. A fluid particle (A) is located at x = xAand y at time t = 0 (Fig. P4—54). At some later time i. the fluid particle has moved downstream with the flow to some new location
x
=
x
A
,
y
=
y
A
, as shown in the figure. Generate an analytical expression for the -location of the fluid particle at arbitrary time t in terms of its initial y-location and constant b. In other words, develop an expression for. (Hint: We know that
v
=
d
y
particle
following a fluid particle. Substitute the equation for u, separate variables, and integrate.)
A steady, incompressible, two-dimensional velocity field is given by V-›= (u, ? ) = (2xy + 1) i-›+ (−y2 − 0.6) j-› where the x- and y-coordinates are in meters and the magnitude of velocity is in m/s. The angular velocity of this flow is (a) 0 (b) −2yk-› (c) 2yk-› (d ) −2xk-› (e) −xk-›
3.3 Starting with a small fluid element of volume dx dy dz, derive the
continuity equation (Eq. 3.4) in rectangular cartesian coordinates.
In a certain region of steady, two-dimensional, incompressible flow, the velocity field is given by V-› = (u, ? ) = (ax + b) i-› + (−ay + cx) j-›. Show that this region of flow can be considered inviscid.
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