Consider the following steady, three-dimensional velocity field in Cartesian coordinates: V → = ( u , v , w ) = ( a x 2 y − b ) i → + c x y 2 j → + d x 2 y k → where a , b , c , and dare constants. Under what conditions is this flow field incompressible?
Consider the following steady, three-dimensional velocity field in Cartesian coordinates: V → = ( u , v , w ) = ( a x 2 y − b ) i → + c x y 2 j → + d x 2 y k → where a , b , c , and dare constants. Under what conditions is this flow field incompressible?
Solution Summary: The author explains the condition for which the flow field is incompressible. Write the equation for the three dimensional velocity field in Cartesian coordinates.
Consider the following steady, three-dimensional velocity field in Cartesian coordinates:
V
→
=
(
u
,
v
,
w
)
=
(
a
x
2
y
−
b
)
i
→
+
c
x
y
2
j
→
+
d
x
2
y
k
→
where
a
,
b
,
c
, and dare constants. Under what conditions is this flow field incompressible?
3.) 15.40 – Collar B moves up at constant velocity vB = 1.5 m/s. Rod AB has length = 1.2 m. The incline is
at angle = 25°. Compute an expression for the angular velocity of rod AB, ė and the velocity of end A of the
rod (✓✓) as a function of v₂,1,0,0. Then compute numerical answers for ȧ & y_ with 0 = 50°.
2.) 15.12 The assembly shown consists of the straight rod ABC which passes through and is welded to the
grectangular plate DEFH. The assembly rotates about the axis AC with a constant angular velocity of 9 rad/s.
Knowing that the motion when viewed from C is counterclockwise, determine the velocity and acceleration of
corner F.
500
Q3: The attachment shown in Fig.3 is made of
1040 HR. The static force is 30 kN. Specify the
weldment (give the pattern, electrode
number, type of weld, length of weld, and leg
size).
Fig. 3
All dimension
in mm
30 kN
100
(10 Marks)
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