Consider a two-dimensional ?ow with velocity
components 
.Find expressions for the
vorticity and the strain rate tensor.
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Consider a two-dimensional ?ow with velocity
components
.Find expressions for the
vorticity and the strain rate...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are u = ln hie) v = created where C is a constant. Is the flow irrotational?
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in...
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in the x-direction is 1.8 s−1. Calculate the linear strain rate in the y-direction. The linear strain rate in the y-direction is
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in...
Consider a steady, two-dimensional, incompressible flow field in the x-y plane. The linear strain rate in the x-direction is 1.65 s−1. Calculate the linear strain rate in the y-direction. The linear strain rate in the y-direction is s−1
Consider a velocity field given by: Axi 2 a) Find the strain rate and rotation rate...
Consider a velocity field given by: Axi 2 a) Find the strain rate and rotation rate tensors
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field...
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field is given by 2ry (a) (5 points) Is this flow incompressible? b) (10 points) Use the x-momentum equation to determine ap/aa (e) (10 points) Use the y-momentum equation to determine ap/dy (d) (5 points) Use the above results to integrate and solve for p(x, y). Evaluate constant of integration by setting p(0,0- Pa as a condition (e) (45 Bonus points) Determine the viscouas stress...
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj....
. Consider the following two dimensional velocity field ~v(x, y) = −xy3ˆi + y 4 ˆj. (a) Sketch a figure of the streamlines for this flow field. Include arrows on your streamlines to indicate the direction of the flow. (b) Is this flow field incompressible or compressible? Show all work. (c) Derive an expression for the vorticity vector ~ζ for this flow field. (d) Is this flow field rotational or irrotational? Provide some evidence in support of your answer
1. A general equation for a steady, two-dimensional velocity field that is linear in both spatial...
1. A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is h) where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. a) Calculate the x- and y-components of the acceleration field b) What relationship must exist between the coefficients to ensure that the flow field is incompressible? c) Calculate the linear strain rates in the x- and y-directions. d) Calculate the shear...
Problem #5 Consider a steady, incompressible, inviscid two-dimensional flow in a corner, the stream function is...
Problem #5 Consider a steady, incompressible, inviscid two-dimensional flow in a corner, the stream function is given by, -xy a) Obtain expressions for the velocity components u and v b) If the pressure at the origin, O, is equal to p o obtain an expression for the pressure field Sketch lines of constant pressure c)
A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions...
A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is -(u,v)-(U+a+by)+(Va+b,y)j where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. a) Calculate the x- and y-components of the acceleration field. b) What relationship must exist between the coefficients to ensure that the flow field is incompressible? c) Calculate the linear strain rates in the x- and y directions. d) Calculate the shear...
(30p) Consider a two-dimensional strain state defined by 612 = € and all normal strains zero....
(30p) Consider a two-dimensional strain state defined by 612 = € and all normal strains zero. Write the strain and the stress tensors in this coordinate system (use Hooke's law). The shear modulus is G. Find the principal strains and the principal directions of strain. Write the stress and strain tensors in these principal directions. Are these also the principal directions of stress? You don't need to solve the eigenvalue problem for stress to answer this question. Find the effective...
Question 1 (10 points) Rotational Flow and Vorticity The velocity components for a two-dimensional flow are u = ln hie) v = created where C is a constant. Is the flow irrotational?
Consider a velocity field given by: Axi 2 a) Find the strain rate and rotation rate tensors
3. (30 points) Consider a two-dimensional flow of a Newtonian fluid in which the velocity field is given by 2ry (a) (5 points) Is this flow incompressible? b) (10 points) Use the x-momentum equation to determine ap/aa (e) (10 points) Use the y-momentum equation to determine ap/dy (d) (5 points) Use the above results to integrate and solve for p(x, y). Evaluate constant of integration by setting p(0,0- Pa as a condition (e) (45 Bonus points) Determine the viscouas stress...
1. A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is h) where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. a) Calculate the x- and y-components of the acceleration field b) What relationship must exist between the coefficients to ensure that the flow field is incompressible? c) Calculate the linear strain rates in the x- and y-directions. d) Calculate the shear...
Problem #5 Consider a steady, incompressible, inviscid two-dimensional flow in a corner, the stream function is given by, -xy a) Obtain expressions for the velocity components u and v b) If the pressure at the origin, O, is equal to p o obtain an expression for the pressure field Sketch lines of constant pressure c)
A general equation for a steady, two-dimensional velocity field that is linear in both spatial directions (x and y) is -(u,v)-(U+a+by)+(Va+b,y)j where U and V and the coefficients are constants. Their dimensions are assumed to be appropriately defined. a) Calculate the x- and y-components of the acceleration field. b) What relationship must exist between the coefficients to ensure that the flow field is incompressible? c) Calculate the linear strain rates in the x- and y directions. d) Calculate the shear...
(30p) Consider a two-dimensional strain state defined by 612 = € and all normal strains zero. Write the strain and the stress tensors in this coordinate system (use Hooke's law). The shear modulus is G. Find the principal strains and the principal directions of strain. Write the stress and strain tensors in these principal directions. Are these also the principal directions of stress? You don't need to solve the eigenvalue problem for stress to answer this question. Find the effective...
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