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Incompressible fluid flow field
2. (a) An incompressible fluid flow field is given as Vx =...
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)
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the...
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the corresponding stream function and sketc h the stream lines. Specify the line of (solid Boundaries) and plot all possible streamlines.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 -...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj,...
A two dimensional incompressible flow is given by the velocity field V = 3yi + 2xj, in arbitrary units. Does this flow satisfy continuity? If so, find the stream function ψ(x,y) and plot a few streamlines, with arrows.
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y...
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
The stream function for a certain incompressible flow field is given by the expression Ψ =...
The stream function for a certain incompressible flow field is given by the expression Ψ = -Ur sin θ + qθ/2π. (a) Obtain an expression for the velocity field. (b) Find the stagnation point(s) where | V | = 0.
W The stream function « in a two-dimensional flow field is given as Q = 4x...
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature, flowing radially between...
Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature, flowing radially between two porous cylindrical shells with inner and outer radii xR and R (a) Show that the equation of continuity leads to V C/r where C is a constant (b) Simplify the components of the equation of motion to obtain the following expressions for the modified-pressure distribution: ds dr dz (c) Integrate the expression for dP/dr above to get (d) Write out all the nonzero...
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x...
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x - x’y) m/s and v = (xy? - 2y - x®/3) m/s a) Determine the velocity and acceleration at point P (1, 3). (1 point) b) Is the flow physically possible? (Proof needed) (1 point) c) Obtain an expression for the stream function. () (1 point) d) What is the discharge between the streamlines passing through (1, 3) and (2, 3). (1 point) e)...
ABCD plesse!!!! 3B.11 Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature,...
ABCD
plesse!!!!
3B.11 Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature, flowing radially between two porous cylindrical shells with inner and outer radii KR and R. (a) Show that the equation of continuity leads to v, C/r where C is a constant. (b) Simplify the modified pressure distribution: the components of the equation of motion to obtain the following expressions for (3B.11-1) dz
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)
ents of a steady state, incompressible two dimensional flow is given by u 2y determine the corresponding stream function and sketc h the stream lines. Specify the line of (solid Boundaries) and plot all possible streamlines.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
6. An Eulerian flow field is characterized by the stream function in Cartesian coordinates below: y = vzt where a is a positive constant. • Sketch the streamlines for the given flow field in the xy-plane at a given time, t. Be sure to specify the direction of the streamlines in your plot. Determine if the fluid in the flow field is incompressible. Determine if the flow field is irrotational. If so, find the corresponding velocity potential and sketch a...
W The stream function « in a two-dimensional flow field is given as Q = 4x – 3y + 7xy (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function 0(x, y) for this flow field with boundary condition Q = 0 at x = 2, y = 1.
Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature, flowing radially between two porous cylindrical shells with inner and outer radii xR and R (a) Show that the equation of continuity leads to V C/r where C is a constant (b) Simplify the components of the equation of motion to obtain the following expressions for the modified-pressure distribution: ds dr dz (c) Integrate the expression for dP/dr above to get (d) Write out all the nonzero...
1) The velocity components in a 2-D incompressible flow are expressed as; u =(y/3 + 2x - x’y) m/s and v = (xy? - 2y - x®/3) m/s a) Determine the velocity and acceleration at point P (1, 3). (1 point) b) Is the flow physically possible? (Proof needed) (1 point) c) Obtain an expression for the stream function. () (1 point) d) What is the discharge between the streamlines passing through (1, 3) and (2, 3). (1 point) e)...
ABCD
plesse!!!!
3B.11 Radial flow between two coaxial cylinders. Consider an incompressible fluid, at constant temperature, flowing radially between two porous cylindrical shells with inner and outer radii KR and R. (a) Show that the equation of continuity leads to v, C/r where C is a constant. (b) Simplify the modified pressure distribution: the components of the equation of motion to obtain the following expressions for (3B.11-1) dz
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