The velocity field for a line some in the r θ plane (Fig. P4-43) is given by u r = m 2 π u θ = 0 Where m is the line source strength. For the case with in m / ( 2 π ) = 1.5 m 2 / s , plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.
The velocity field for a line some in the r θ plane (Fig. P4-43) is given by u r = m 2 π u θ = 0 Where m is the line source strength. For the case with in m / ( 2 π ) = 1.5 m 2 / s , plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V = 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.
The velocity field for a line some in the
r
θ
plane (Fig. P4-43) is given by
u
r
=
m
2
π
u
θ
=
0
Where m is the line source strength. For the case with in
m
/
(
2
π
)
=
1.5
m
2
/
s
, plot a contour plot of velocity magnitude (speed). Specifically, draw curves of constant speed V= 0.5, 1.0, 1.5, 2.0, and 2.5 m/s. Be sure to label these speeds on your plot.
The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
A linear system is one that satisfies the principle of superposition. In other words, if an input u₁
yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-
bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.
Using this fact, determine the output y(t) of the following linear system:
given the input:
P(s) =
=
Y(s)
U(s)
=
s+1
s+10
u(t) = e−2+ sin(t)
=e
The manometer fluid in the figure given below is mercury where D = 3 in and h = 1 in. Estimate the volume flow in the tube (ft3/s) if the flowing fluid is gasoline at 20°C and 1 atm. The density of mercury and gasoline are 26.34 slug/ft3 and 1.32 slug/ft3 respectively. The gravitational force is 32.2 ft/s2.
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