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.
Velocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 s
This problem will show you how to obtain the pathline and the streamline for a velocity field. A velocity field is given by u=(ax_1 t)i −(bx_2)j , where a=0.1^s−2 and b=1s^−1.
(a) For the particle that passes through the point (x1,x2) = (1,1) at instant t = 0, get the equation of the pathline during the interval from t = 0 to t = 3s. Plot it roughly by hand(b) Get the equations of the streamlines through the same point at the instants t = 0,1, and 2s. Plot it roughly by hand
A two dimensional, steady, incompressible and potential flow field of water (ρ=1000 kg/m3) is given with velocity components u and v. If the velocity component, u is given as u=2xy m/s with the magnitude of maximum pressure in the field as 52108 Pa.
a) At x=+1 m and y=+2 m point, what is the magnitude of the velocity component v (in m/s)? (Please use 2 decimal digits in your answer)
b) At x=+1 m and y=+2 m point, what is the magnitude of dynamic pressure (in Pa)? (Please do not use any decimal digit in your answer)
c) At x=+1 m and y=+2 m point, what is the magnitude of static pressure (in Pa)? (Please do not use any decimal digit in your answer)
Chapter 2 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
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