Consider the following steady, three-dimensional velocity field in Cartesian coodinates: V → = ( u , v , w ) = ( a x y 2 − b ) i → − 2 c y 3 j → + d x y k → , where a , b, c and d are constants. Under what conditions is this flow field incompressible?
Consider the following steady, three-dimensional velocity field in Cartesian coodinates: V → = ( u , v , w ) = ( a x y 2 − b ) i → − 2 c y 3 j → + d x y k → , where a , b, c and d are constants. Under what conditions is this flow field incompressible?
Solution Summary: The author explains the condition for the incompressible fluid. Write the expression of the three-dimensional velocity field in Cartesian coordinates.
Consider the following steady, three-dimensional velocity field in Cartesian coodinates:
V
→
=
(
u
,
v
,
w
)
=
(
a
x
y
2
−
b
)
i
→
−
2
c
y
3
j
→
+
d
x
y
k
→
, where a, b, c and d are constants. Under what conditions is this flow field incompressible?
PROBLEM 3.23
3.23 Under normal operating condi-
tions a motor exerts a torque of
magnitude TF at F. The shafts
are made of a steel for which
the allowable shearing stress is
82 MPa and have diameters of
dCDE=24 mm and dFGH = 20
mm. Knowing that rp = 165
mm and rg114 mm, deter-
mine the largest torque TF
which may be exerted at F.
TF
F
rG-
rp
B
CH
TE
E
1. (16%) (a) If a ductile material fails under pure torsion, please explain the failure
mode and describe the observed plane of failure.
(b) Suppose a prismatic beam is subjected to equal and opposite couples as shown
in Fig. 1. Please sketch the deformation and the stress distribution of the cross
section.
M
M
Fig. 1
(c) Describe the definition of the neutral axis.
(d) Describe the definition of the modular ratio.
using the theorem of three moments, find all the moments, I only need concise calculations with minimal explanations. The correct answers are provided at the bottom
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