Question

1. A two-dimensional unsteady velocity field is given by u = x(1 + 2t), v = y. (a) Find the time-varying streamlines which pass through some reference point (xo, yo). Sketch some. (b) Find the equation of the pathline which passes through the point (xo, yo) at t = 0. Sketch this pathline. 2. A two-dimensional velocity field is given by V = (x^2 - y^2 + x)i - (2xy + y)j in arbitrary units. At (x, y) = (1, 2), compute (a) the accelerations ax and ay, (b) the velocity component in the direction ? = 40°, (c) the direction of maximum velocity, and (d) the direction of maximum acceleration. 3. When a valve is opened, fluid flows in the expansion duct of Figure according to the approximation V = iU(1 - x/2L)tanh(Ut/L) Find (a) the fluid acceleration at (x, t) = (L, L/U) and (b) the time for which the fluid acceleration at x = L is zero. Why does the fluid acceleration become negative after condition (b)? 4. A simple flow model for a two-dimensional converging nozzle is the distribution u = Uo(1 + x/L) v = -Uo(y/L) w = 0 Determine if a stream function exists, and, if it does, find an expression for ?(x,y) and sketch the streamline which passes through the point (x, y) = (L/2, L/2). 5. Consider the two-dimensional incompressible velocity potential ? = xy + x^2 - y^2. (a) Is it

          1. A two-dimensional unsteady velocity field is given by u = x(1 + 2t), v = y. (a) Find the time-varying streamlines which pass through some reference point (xo, yo). Sketch some. (b) Find the equation of the pathline which passes through the point (xo, yo) at t = 0. Sketch this pathline.
2. A two-dimensional velocity field is given by
V = (x^2 - y^2 + x)i - (2xy + y)j
in arbitrary units. At (x, y) = (1, 2), compute (a) the accelerations ax and ay, (b) the velocity component in the direction ? = 40°, (c) the direction of maximum velocity, and (d) the direction of maximum acceleration.
3. When a valve is opened, fluid flows in the expansion duct of Figure according to the approximation
V = iU(1 - x/2L)tanh(Ut/L)
Find (a) the fluid acceleration at (x, t) = (L, L/U) and (b) the time for which the fluid acceleration at x = L is zero. Why does the fluid acceleration become negative after condition (b)?
4. A simple flow model for a two-dimensional converging nozzle is the distribution
u = Uo(1 + x/L) v = -Uo(y/L) w = 0
Determine if a stream function exists, and, if it does, find an expression for ?(x,y) and sketch the streamline which passes through the point (x, y) = (L/2, L/2).
5. Consider the two-dimensional incompressible velocity potential ? = xy + x^2 - y^2. (a) Is it

1. A two-dimensional unsteady velocity field is given by u = x(1 + 2t), v = y. (a) Find the time-varying streamlines which pass through some reference point (xo, yo). Sketch some. (b) Find the equation of the pathline which passes through the point (xo, yo) at t = 0. Sketch this pathline.
2. A two-dimensional velocity field is given by
V = (x^2 - y^2 + x)i - (2xy + y)j
in arbitrary units. At (x, y) = (1, 2), compute (a) the accelerations ax and ay, (b) the velocity component in the direction ? = 40°, (c) the direction of maximum velocity, and (d) the direction of maximum acceleration.
3. When a valve is opened, fluid flows in the expansion duct of Figure according to the approximation
V = iU(1 - x/2L)tanh(Ut/L)
Find (a) the fluid acceleration at (x, t) = (L, L/U) and (b) the time for which the fluid acceleration at x = L is zero. Why does the fluid acceleration become negative after condition (b)?
4. A simple flow model for a two-dimensional converging nozzle is the distribution
u = Uo(1 + x/L) v = -Uo(y/L) w = 0
Determine if a stream function exists, and, if it does, find an expression for ?(x,y) and sketch the streamline which passes through the point (x, y) = (L/2, L/2).
5. Consider the two-dimensional incompressible velocity potential ? = xy + x^2 - y^2. (a) Is it

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