We shall now look at the velocity field: v = v_xi + v_yj = xyi +...
We shall now look at the velocity field:
v = v_xi + v_yj = xyi + yj
a) Find the streamlines (hint: solve a separable differential equation), and draw them by hand (find stagnation points).
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Describing Velocity Fields and Stream Lines A velocity field is given by, V= -yi + xj...
Describing Velocity Fields and Stream Lines A velocity field is given by, V= -yi + xj a) Remark on the dimensionality, directionality and steadiness of the flow b) Calculate the equation for the stream lines c) Sketch (by hand) the streamlines through point x=2, y=0 and x=3, y=0 d) Describe in words what the flow pattern look like? Which of the following situations does the flow look like: Flow over a cylinder, flow into an acute corner, flow into 90...
The following velocity field exists inside a room of size 10m × 10m: u = 0.1(−xi...
The following velocity field exists inside a room of size 10m × 10m: u = 0.1(−xi + yj)m/s a) Draw the rectangular region, and depict the velocity distribution inside using arrows vectors. You may use a software of your choice to do this if you wish. (b) Compute the equations of the streamlines, and sketch them on top of your arrows. Do the streamlines make sense?
(1 point) An object of mass 5 kg is given an upward initial velocity of 16...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
General Instructions: All of these problems rely on mathematical equations to describe velocity a...
General Instructions: All of these problems rely on mathematical equations to describe velocity and acceleration fields. However, you should take some time looking at the equations for V to determine how velocity depends on x and y in each flowfield. For example, think about how u and v vary as x and y increase or decrease, or change from positive to negative. This ability to "vize"the flowfield will be very useful. Problem 1 your work and provide clear hand-written sample...
Solve for the equation of a streamline in a flow with velocity field u = cx,...
Solve for the equation of a streamline in a flow with velocity field u = cx, v = -cy, where c is a positive constant. The solution should have the form y = f(x). Using the axes given below, sketch representative streamlines for this flow
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It...
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It is approximated by u 3x2y x +10 It is also known that the v-velocity is zero along the line y-0. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, v, for this flow c) Determine the location of any stagnation points in the flow (stagnation means -0) d) Calculate the acceleration field (a and ay)...
Consider the following steady, two-dimensional velocity field: V(u,v) = (0.51 + 2.1x)i + (−3.4 – 2.1y)j...
Consider the following steady, two-dimensional velocity field: V(u,v) = (0.51 + 2.1x)i + (−3.4 – 2.1y)j where V(u,v) is the velocity field vector and i and j are the standard unit vectors. The locations of the stagnation points are:
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It...
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It is approximated by u 3x2y x 10 It is also known that the v-velocity is zero along the line y-O. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, 11, for this flow c) Determine the location of any stagnation points in the flow (stagnation means V-0) d) Calculate the acceleration field (ax and ay)...
The y component of velocity in a steady, incompressible flow field in the xy plane is...
The y component of velocity in a steady, incompressible flow field in the xy plane is v = -Bxy3, where B = 0.7 m-3 · s-1, and x and y are measured in meters. (a) Find the simplest x component of velocity for this flow field. (b) Find the equation of the streamlines for this flow (use C as constant).
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4, determine the stagnation points of the flow, if any. Hint: For stagnation point (W.,Vo,V)-(0,0,0) @s 2
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
(1 point) An object of mass 5 kg is given an upward initial velocity of 16 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -50, where v is the velocity of the object in m/sec. Assume gravitational constant is g = 9.8m/seca. Set up the differential equation for this scenario: v' = m/sec Solve the differential equation for the equation of motion: The equation is both...
General Instructions: All of these problems rely on mathematical equations to describe velocity and acceleration fields. However, you should take some time looking at the equations for V to determine how velocity depends on x and y in each flowfield. For example, think about how u and v vary as x and y increase or decrease, or change from positive to negative. This ability to "vize"the flowfield will be very useful. Problem 1 your work and provide clear hand-written sample...
. An experimentalist has measured the u-velocity component of a steady, two- imensional flow field. It is approximated by u 3x2y x +10 It is also known that the v-velocity is zero along the line y-0. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, v, for this flow c) Determine the location of any stagnation points in the flow (stagnation means -0) d) Calculate the acceleration field (a and ay)...
6. An experimentalist has measured the u-velocity component of a steady, two- dimensional flow field. It is approximated by u 3x2y x 10 It is also known that the v-velocity is zero along the line y-O. a) Find an expression for the v-velocity in the entire field b) Find an expression for the streamfunction, 11, for this flow c) Determine the location of any stagnation points in the flow (stagnation means V-0) d) Calculate the acceleration field (ax and ay)...
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4, determine the stagnation points of the flow, if any. Hint: For stagnation point (W.,Vo,V)-(0,0,0) @s 2
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
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