Given the potential function,
Derive the velocity components as follows:
At point A,
Using Bernoulli's theorem to get the pressure field obtained directly from the velocity field gives:
Similarly, at point B,
Therefore, pressure differences between points A and B would be:
Name: Problem 4 (20 pts). The velocity potential for a cylinder rotating in a uniform stream of fluid is 2TT where U, a, Г are constants. The density of the flow is , and gravitational force is n...
a) Derive the general stream function of a potential flow around a cylinder of radius R given the stream functions Y of a uniform flow and a doublet are uniformUy 'doublet where Uis the speed of the uniform flow and C is the strength of the doublet. (5 marks) b) Find the specific stream function assuming the streamline on the surface of the cylinder is Ψ-0 (5 marks) c) Find the velocities at two points (-3R, 0 and (-2R, 0)....
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...
Fluid Mechanics Problem Problem 3: Determine the velocity distribution between two parallel plates where there is a pressure gradient applied and the top plated is moving the velocity of U. Also if possible, calculate the stream function and velocity potential. (20 points) dpldx<o Continuity equation Ou OW ?NCZ Navier-Stokes equation Ouolu op l1
QUESTION 2 In an experiment to measure approaching uniform flow, U.to a non-rotating circular cylinder as shown in Figure Q2, a small hole is to be drilled at the stagnation point on the cylinder surface. (a) Determine the location of the drilled hole on the cylinder surface using potential flow theory by combining a doublet with a uniform flow. (3.5 marks) (b) Determine the theoretical pressure distribution expression on the cylinder surface, Pc and plot or sketch a graph of...
Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfield around a cylinder. The resulting velocity potential for the flow is given by: A cos Ur cos e The resulting velocity field in cylindrical coordinates is given by - = 4 r ae ar where e, and eo are the unit vectors in cylindrical polar coordinates, Uo is the free-stream velocity and A an arbitrary parameter. a) (10 points) Determine...
don’t us excel please Problem 3. (30 points) From inviscid potential flow analysis, as a uniform stream approaches a cylinder of radius R along the symmetry line AB in the figure, the velocity has only one component: u(x)U for 0<xs-R where U, is the stream velocity far from the cylinder. a. Using EXCEL, plot u(x) along AB from -0.4<x<-0.05 when R-0.05 m and U,-4 m/s. Label axes with variables and dimensions and add a title to the plot. Since the...
Consider the flow field represented by the velocity potential φ = Ax+Bx2−By2, where A = 1 m/s, B = 1 s−1, and the coordinates are measured in meters. Obtain expressions forthe velocity field and the stream function. Using water as the working fluid, calculate the pressure difference between the origin and the point (x,y) = (1,2). What is the volume flow rate (per unit depth) between streamlines passing through these two points?
Home looking Files X Exam2(2).pdf + Exam2%20(2).pdf 4/4 3. An incompressible, viscous fluid with density, p, flows past a solid flat plate which has a depth, b, into the page. The flow initially has a uniform velocity U... before contacting the plate. After contact with the plate at a distance x downstream from the leading edge, the flow velocity profile is altered due to the no-slip condition. The velocity profile at location is approximated to have a linear shape, u...