Question 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfi...
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)....
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...
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...
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1200 kg/m2, Uoo- 20 m/s and cylinder radius R 0.01 m 1 cm and Az 1 m Note: The flow does not cross streamlines, so there is no flow across the side boundaries. Exit (2) NO SCALE Variable u vs y at x2-0 Inlet (1) y- H1 and v 0 constant u Uo constant v0 A) Find mass...
help 1. A 2D inviscid flow field is represented by the velocity potential function: ° = Ax + Bx2 – By2. Where A = 1m/s, B = 15-7, and the coordinates are measured in meters. The flow density is p = 1.2 kg/m3. (a) (2 points) Calculate the velocity field. (b) (2 points) Verify that the flow is irrotational. (c) (2 points) Verify that the flow is incompressible. (d) (2 points) Obtain the expression of stream function. (e) (2 points)...
ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1. The figure below shows the streamlines for the flow past a spinning circular cylinder. In the cylindrical coordinates, the stream function can be written as ψ Uosine (r-7/-Kln (5). where R is the radius of the cylinder. Assuming that the pressure in the far upstream is po. find the pressure distribution on the surface. ME420 Intermediate Fluid Mechanics Name B. Long answer questions (20 points each). 1....
could you please help me with answering all parts of this question. like and comment are rewarded. [7] A3. (a) Draw the streamlines and vortex lines of a Rankine vortex. Indicate which field lines are streamlines and which field lines are vortex lines, and label the vortex core. Explain which region of the flow has zero vorticity, and which region of the flow has non-zero vorticity. (b) A fluid with constant density po, pressure p, and velocity v, satisfies the...
Problem 5 . This question considers uniform random points on the unit disc x2+92 〈 1 (a) A point (X, Y) is uniformly chosen in the unit disc. Find the CDF and PDF of its distance from the origin R X2 +Y2 (b) Compute the expected distance from the origin. (c) Determine the marginal PDF of X and Y (d) Are X and Y independent? (Justify your claims) e) One way to generate uniform random points on this disc is...
Ignore question [1], just need the problem description from it. [1] Water flowing in a pipe is determined to be moving at the velocities given in the diagram below. The higher level is 3 meters above the lower one and the pressure in the lower portion is measured to be 200 kPa. Determine the pressure inside the upper pipe Treat the water as an ideal fluid obeying Bernoulli's equation. Consider the path connecting poin in the lower pipe with point...
Question 1 [40 Points] Liquid mercury at 300 K flows over a flat surface at a free stream velocity 0.15 m/s. The flat plate is smooth with a width of 0.25 m and length 0.5 m and is kept at a uniform temperature of 400 K. The flow is parallel to the longer dimension of the plate. Find out: 1. MINIMUM LOCAL convective heat flux, q min and its location (60%) 2. Total convective heat transfer rate, q (40%) Use...