Air flows downward toward an infinitely wide horizontal flat plate. The velocity field is given by V → = ( a x i ^ − a y j ^ ) ( 2 + cos ω t ) , where a = 5 s −l , ω > = 2 π s −1 , x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in s. Obtain an algebraic equation for a streamline at t = 0. Plot the streamline that passes through point (x, y) = (3, 3) at this instant. Will the streamline change with time? Explain briefly. Show the velocity vector on your plot at the same point and time. Is the velocity vector tangent to the streamline? Explain.
Air flows downward toward an infinitely wide horizontal flat plate. The velocity field is given by V → = ( a x i ^ − a y j ^ ) ( 2 + cos ω t ) , where a = 5 s −l , ω > = 2 π s −1 , x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in s. Obtain an algebraic equation for a streamline at t = 0. Plot the streamline that passes through point (x, y) = (3, 3) at this instant. Will the streamline change with time? Explain briefly. Show the velocity vector on your plot at the same point and time. Is the velocity vector tangent to the streamline? Explain.
Air flows downward toward an infinitely wide horizontal flat plate. The velocity field is given by
V
→
=
(
a
x
i
^
−
a
y
j
^
)
(
2
+
cos
ω
t
)
,
where a = 5 s−l, ω > = 2 π s−1, x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in s. Obtain an algebraic equation for a streamline at t = 0. Plot the streamline that passes through point (x, y) = (3, 3) at this instant. Will the streamline change with time? Explain briefly. Show the velocity vector on your plot at the same point and time. Is the velocity vector tangent to the streamline? Explain.
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.
The expression for stream function is described by y = x ^ 3 - 3x * y ^ 2 . Indicate whether the flow is rotational or irrotational. Determine the value or velocity potential o, if it exists.
1. The components of velocity in a flow field are given byu=x2+y2+z2v=xy+yz+z2w=-3xz- 0.5z2+4a) Determine the volumetric dilatation rate and interpret the result.b) Determine an expression for the rotation vector. Is this an irrotational flow field?
The velocity for the 2-dimensional flow is defined by V =(3y2 i+4xj) m/s, where y is in meters. Determine the equation of the streamline that passes through point (2 m, 1 m).
only HANDWRITTEN answer needed ( NOT TYPED)
Chapter 2 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
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