The x and y components of velocity for 2D flow are u = 3 m/s and v = 9x2 m/s, where x is in meter. Determine the equation of the streamlines (y) and plot the graph of the streamline when y = 0 for the range of -10 <=x <= 10 and -10 <= y <= 10
The velocity components of a particle in the flow field are defined by : u= 3 m/s and v = (6t) m/s, ∙where t is in seconds. Plot the path line for the particle if it is released from the origin when t = 2 sec. Also draw the streamline for this particle ∙when t = 2 s.
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x - x’y) m/s and v = (xy? - 2y - x®/3) m/s a) Determine the velocity and acceleration at point P (1, 3). (1 point) b) Is the flow physically possible? (Proof needed) (1 point) c) Obtain an expression for the stream function. () (1 point) d) What is the discharge between the streamlines passing through (1, 3) and (2, 3). (1 point) e)...
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
Advanced Fluid Mechanics Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points. Determine the streamfunction and velocity potential for uniform flow of strength...
The components of a velocity field are given by u = x + y, and v = xy3 + 81 and w = 0. Determine the location of the stagnation point (V = 0) in the flow field where y is positive
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...
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).
Problem 3. A 2D velocity field for an incompressible Newtonian fluid is given by u 12xy-62.3, u = 18x2y-4y3, where the velocity has unit m/s and x and y are in meters. (a) Determine the normal stresses ơzz and ơuy, and shear stress Try at the point x-1 m, y 1 m, where the pressure at this point is 6 kPa and dynamic viscosity is 1 Pa.s. (b) Sketch the magnitude and direction of the stress components.
Find the flow rate Q when the flow velocity distribution u (m / s) in the pipeline with radius R (m) as shown in the figure below is expressed by the following equation as a function of the distance y (m) from the inner wall surface. However, U is the maximum flow velocity (m / s) in the central axis of the pipeline, and the flow velocity distribution u is symmetrical with respect to the central axis of the pipeline,...
For the following velocity field: V -2yi 9y2j m/s a) Determine whether the flow is one, two or three dimensional b) Calculate the velocity components at the point (0.5,3.5) c) Develop an equation for the streamline passing through the same point as part b The velocity components are: