Homework Answers
The pressure distribution is obtained using Bernoulli's Equation applied on the surface and a point far upstream, which is given by:
where ρ is the density of the fluid and vs is the velocity on surface.
In order to apply the Bernoulli Equation the velocities at the surface was required. The velocities were found using the relation between the stream function and velocities given by:
Then the substitution r=R is made to obtain the velocity on the surface, this results in radial term becoming zero.
This velocity is then substituted back into the Bernoulli equation to obtain the pressure distribution.
The pressure distribution is obtained as a function of θ as:
Refer to the images below for further understanding.
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2. (30 points) The figure below shows the streamlines for the flow past a spinning circular cylin...
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 coo...
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....
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...
The potential function, ф, of the flow past a corner is provided by the following equation,...
The potential function, ф, of the flow past a corner is provided by the following equation, where n is a constant that depends on the angle between the two walls (see Figure below) 600 Figure 2: Stream function in proximity of two walls at an angle of 60° . Determine the stream function, ψ, associated to the potential function and discuss the relationship between ψ and φ. . Determine the constant n corresponding to an angle of 60° between the...
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...
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)....
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that i...
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that is moving with a uniform steady velocity Uk far from the cylinder; the cylinder axis is in the z-direction The cylinder is also spinning on its axis with constant angular velocity, Ω2, where x, у and z are the usual Cartesian unit vectors We wish to model this 2D flow using an inviscid approximation. This is achieved by first calculating...
don’t us excel please Problem 3. (30 points) From inviscid potential flow analysis, as a uniform stream approaches...
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 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...
2. -1 points My Notes Ask Your Teacher The figure below shows, in cross section, three...
2. -1 points My Notes Ask Your Teacher The figure below shows, in cross section, three solid cylinders, each of length L and uniform charge Q. Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius. Cylinder Gaussian Rank the Gaussian surfaces according to the electric field at any point on the surface, greatest first. (Use only >orsymbols. If any elements are equal, show their equality in alphabetic order - for example: a>b-c.)...
The figure below shows a circular wire loop of radius R = 4,5 m that carries...
The figure below shows a circular wire loop of radius R = 4,5 m that carries a constant clockwise current of 7 = 2.02 A and it have a cons ant mass per length of 1 = 0.003 kg/m. Below the fixed horizontal line in the figure there is a constant magnetic field of strength B = 0.1 T that is pointing into the page and above this fixed horizontal line there is no magnetic field. No B Here No...
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....
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...
The potential function, ф, of the flow past a corner is provided by the following equation, where n is a constant that depends on the angle between the two walls (see Figure below) 600 Figure 2: Stream function in proximity of two walls at an angle of 60° . Determine the stream function, ψ, associated to the potential function and discuss the relationship between ψ and φ. . Determine the constant n corresponding to an angle of 60° between the...
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...
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)....
Consider a circular cylinder of radius a whose central axis is stationary. The cylinder is surrounded by a fluid that is moving with a uniform steady velocity Uk far from the cylinder; the cylinder axis is in the z-direction The cylinder is also spinning on its axis with constant angular velocity, Ω2, where x, у and z are the usual Cartesian unit vectors We wish to model this 2D flow using an inviscid approximation. This is achieved by first calculating...
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...
2. -1 points My Notes Ask Your Teacher The figure below shows, in cross section, three solid cylinders, each of length L and uniform charge Q. Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius. Cylinder Gaussian Rank the Gaussian surfaces according to the electric field at any point on the surface, greatest first. (Use only >orsymbols. If any elements are equal, show their equality in alphabetic order - for example: a>b-c.)...
The figure below shows a circular wire loop of radius R = 4,5 m that carries a constant clockwise current of 7 = 2.02 A and it have a cons ant mass per length of 1 = 0.003 kg/m. Below the fixed horizontal line in the figure there is a constant magnetic field of strength B = 0.1 T that is pointing into the page and above this fixed horizontal line there is no magnetic field. No B Here No...
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