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.
The stream function for a certain incompressible flow field is given by the expression Ψ =...
Incompressible fluid flow field
2. (a) An incompressible fluid flow field is given as Vx = x2+y+z2 and Vy=xy+yz+z, what is V?=? that satisfies continuity equation? (b) Plot the 2-D flow field represented by Vx=2y, Vy=4x. First obtain an expression for stream function, and then plot flow lines corresponding to constant stream function values.
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.
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)
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4, determine the stagnation points of the flow, if any. Hint: For stagnation point (W.,Vo,V)-(0,0,0) @s 2
3. Show that the velocity field with components (in spherical coordinates) K,-(4kr-3-2)cosa, pa-(2kr-3 +2)sin θ, ν, 0, k > 0,0 is a possible fluid velocity for an incompressible flow. For k 4,...
Question: 1115 Marks Consider a steady, two-dimensional, incompressible flow field called a source strength Q. Generate an expression for the stream function for this flow. (S Marks) a. , with flow b. Potential flow against a flat plate (Fig. 1a) can be described with the stream function where A is a constant. This type of flow is commonly called a stagnation point flow since it can be used to describe the flow in the vicinity of the stagnation point at...
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...
The stream function for an incompressible, two- dimensional flow field is v-ay-by where a and b are constants. a) Is this an irrotational flow? Governing Equation:
4) Stream function Consider a steady, 2D, incompressible flow with velocity field u(,0, where U, h are constants. Determine the stream function p for this flow. For simplicity take ( 0)0
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1. A 2D inviscid flow field is represented by the velocity potential function: ° = Ax + Bx2 – By2. Where A = 1m/s, B = 15-7, and the coordinates are measured in meters. The flow density is p = 1.2 kg/m3. (a) (2 points) Calculate the velocity field. (b) (2 points) Verify that the flow is irrotational. (c) (2 points) Verify that the flow is incompressible. (d) (2 points) Obtain the expression of stream function. (e) (2 points)...
2. Water flows over a flat surface at 8 m/s, as shown in figure. A pump draws off water through a narrow slit at a volume rate of 0.2 m2/s per meter length of the slit. Assume that the fluid is incompressible and inviscid and can be represented by the combination of a uniform flow and a sink. a) Based on method of superposition, propose a general expression for stream function ψ velocity potential ф, and velocity components of v,...