a/ Derive (i.e. “find the equation”) the velocity potential for a doublet; that is, derive Equation...
a/ Derive (i.e. “find the equation”) the velocity potential for a doublet; that is, derive Equation (3.88). Hint: The easiest method is to start with Equation (3.87) for the stream function and extract the velocity potential.
b/ Consider the nonlifting flow over a circular cylinder. Derive ( “find”) an expression for the pressure coefficient at an arbitrary point (r, θ) in this flow, and show that it reduces to Equation (3.101) on the surface of the cylinder.
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a/ Derive (i.e. “find the equation”) the velocity
potential for a doublet; that is, derive Equation...
Start with the stream functions of a uniform horizontal flow Var sin θ and of the doublet k sin θ...
Start with the stream functions of a uniform horizontal flow Var sin θ and of the doublet k sin θ 2π a) Derive the streamfunction for the flow over a cylinder b) Find expression for velocity field (u, v) c) Plot the velocity magnitude on the surface for all angels (r-R, θ) d) Plot the velocity magnitude directly above the cylinder (r> R, t/2) e) Plot pressure on the surface for all angels (r-R, θ)
Start with the stream functions...
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...
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 1 (40 points) From potential flow theory, the combination of a doublet and a uniform flow gives the flowfi...
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...
QUESTION 2 In an experiment to measure approaching uniform flow, U.to a non-rotating circular cylinder as...
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...
Understand how to find the equation of motion of a particle undergoing uniform circular motion. Consider...
Understand how to find the equation of motion of a particle undergoing uniform circular motion. Consider a particle--the small red block in the figure--that is constrained to move in a circle of radius R. We can specify its position solely by θ(t), the angle that the vector from the origin to the block makes with our chosen reference axis at time t. Following the standard conventions we measure θ(t) in the counterclockwise direction from the positive x axis. (Figure 1)...
Now evaluate the mass and momentum into and out of the CV shown with 1.0s y Rs 1.5 at (2) Let p 1...
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...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Start with the stream functions of a uniform horizontal flow Var sin θ and of the doublet k sin θ 2π a) Derive the streamfunction for the flow over a cylinder b) Find expression for velocity field (u, v) c) Plot the velocity magnitude on the surface for all angels (r-R, θ) d) Plot the velocity magnitude directly above the cylinder (r> R, t/2) e) Plot pressure on the surface for all angels (r-R, θ)
Start with the stream functions...
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 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...
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...
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...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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