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1) For a uniform flow with Uw making an angle of a with the horizontal plane;...
Consider stagnation point flow for which the Cartesian velocity components are given by u = Ax...
Consider stagnation point flow for which the Cartesian velocity components are given by u = Ax and v = -Ay a. Determine the stream function y b. Determine the velocity potential
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stre...
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines)...
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...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a sour...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink in a uniform stream, separated by a fixed distance. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink...
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)....
6.102 The flow field for a plane source at a distance h above an infinite wall...
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
2. The ends of uniform rod AB can slide along the horizontal floor and the inclined plane. At the...
2. The ends of uniform rod AB can slide along the horizontal floor and the inclined plane. At the instant shown, the end A is moving at a constant velocity of 2.5 to the left. Using the concept of the instantaneous center of zero velocity, determine (a) the angular velocity of the rod and (b) the velocity of end B of the rod. Also determine the acceleration of the mass center of the rod, G, which is located at the...
Advanced Fluid Mechanics Determine the streamfunction and velocity potential for uniform flow of strength U over a p...
Advanced Fluid Mechanics
Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points.
Determine the streamfunction and velocity potential for uniform flow of strength...
A jet of water impacts a flat plane oriented at an angle as shown. The flow...
A jet of water impacts a flat plane oriented at an angle as
shown. The flow is in the horizontal xy plane. The cross-sectional
area of the jet is 1.7 in2 and the velocity is 16 ft/s. The angle θ
is 67°.
Assume negligible friction. This assumption lets you (1) use
the Bernoulli equation to determine v2 and v3, and (2) determine
the direction of the force apriori (no friction means no shear
along the surface of the plate):
(a)...
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...
Consider stagnation point flow for which the Cartesian velocity components are given by u = Ax and v = -Ay a. Determine the stream function y b. Determine the velocity potential
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of a Half Body. This is a source in a uniform stream. 1. Visualize the Flow Net (the streamlines and velocity potential lines)...
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...
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink in a uniform stream, separated by a fixed distance. 1. Visualize the Flow Net (the streamlines and velocity potential lines) 2. Determine an expression for the velocity field. Note that the book uses cylindrical coordinates here
Construct expressions for the stream function and velocity potential of flow around a circular cylinder. This is a source and a sink...
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)....
6.102 The flow field for a plane source at a distance h above an infinite wall aligned along the x axis is given by 20[x2 + y - 12|xi +(y-hil 9 2;[xi + (y + hil * 29x2 + (y + h) 21 where q is the strength of the source. The flow is irrotational and incompressible. Derive the stream function and velocity potential. By choosing suitable values for 4 and h, plot the streamlines and lines of constant velocity...
2. The ends of uniform rod AB can slide along the horizontal floor and the inclined plane. At the instant shown, the end A is moving at a constant velocity of 2.5 to the left. Using the concept of the instantaneous center of zero velocity, determine (a) the angular velocity of the rod and (b) the velocity of end B of the rod. Also determine the acceleration of the mass center of the rod, G, which is located at the...
Advanced Fluid Mechanics
Determine the streamfunction and velocity potential for uniform flow of strength U over a point source and sink of equal strength, m, located on the x-axis at +/-b (the source is at-b with the sink at +b, where b is not small). Write expressions for the u and v velocity components, and draw streamlines of the flow. Determine the location(s) of any and all stagnation points.
Determine the streamfunction and velocity potential for uniform flow of strength...
A jet of water impacts a flat plane oriented at an angle as
shown. The flow is in the horizontal xy plane. The cross-sectional
area of the jet is 1.7 in2 and the velocity is 16 ft/s. The angle θ
is 67°.
Assume negligible friction. This assumption lets you (1) use
the Bernoulli equation to determine v2 and v3, and (2) determine
the direction of the force apriori (no friction means no shear
along the surface of the plate):
(a)...
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...
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