Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P4-16). A simple approximate velocity field for this flow is V → = ( v , v ) = ( U 0 + b x ) i → − b y j → Where U o is the horizontal speed at x = 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components a x and a y and (2) as acceleration vector
Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P4-16). A simple approximate velocity field for this flow is V → = ( v , v ) = ( U 0 + b x ) i → − b y j → Where U o is the horizontal speed at x = 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components a x and a y and (2) as acceleration vector
Solution Summary: The author describes the acceleration of fluid particles passing through a converging duct.
Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P4-16). A simple approximate velocity field for this flow is
V
→
=
(
v
,
v
)
=
(
U
0
+
b
x
)
i
→
−
b
y
j
→
Where Uo is the horizontal speed at x = 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components axand ay and (2) as acceleration vector
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
In a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v = –2 ft/s.Determine the corresponding stream function and velocity potential for this flow field. Sketch theequipotential line φ = 0 which passes through the origin of the coordinate system. Could you answer and explain every step please
3.3 Starting with a small fluid element of volume dx dy dz, derive the
continuity equation (Eq. 3.4) in rectangular cartesian coordinates.
Consider the following steady, three-dimensional velocity field in Cartesian coordinates: V-› = (u, ?, w) = (axz2 − by) i-› + cxyz j-› + (dz3 + exz2)k →, where a, b, c, d, and e are constants. Under what conditions is this flow field incompressible? What are the primary dimensions of constants a, b, c, d, and e?
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