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A 2-D (x and y) velocity field varies with space and time and can de descibed...
Given that the magnetic field varies as a function of time B = 175 sin (2...
Given that the magnetic field varies as a function of time B = 175 sin (2 pi t) Teslas, what is the expression for the electric field as a function of time?
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).
The nozzle in the figure is shaped such that the velocity of flow varies linearly from...
The nozzle in the figure is shaped such that the velocity of flow varies linearly from the base of the nozzle to its tip. At the base, diameter is D and x=0, and at the tip, diameter is d and x=L. The velocity at any distance x is assumed to be the same over the cross section. The velocity at the base is 2t (ft/s) and at the tip is 5t (ft/s), where t is tiime in seconds (s). L...
The velocity field of a flow is given by V = (2+1) x y2 i +...
The velocity field of a flow is given by V = (2+1) x y2 i + (3+2) t j m/s where x and y is in meter and t in seconds. Determine the following at point (1, 2) and t= 3 s: 1. The fluid speed. 2. The angle between the velocity vector and the positive x 3. Locations (if avaliable) of any stagnation point for this flow field? 4. The local acceleration, then classiffy the flow . 5. The...
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y=...
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y= +2 x axis 77 X =- (x,y) = (0,0) y axis a) what is the stream function for the entire field b) what is the velocity potential function for the entire field c) what is the u velocity component for the entire field d) what is the v velocity component for the entire field e) what is the velocity along both walls (can be...
The vector position of a particle varies in time according to the expression r = 8.20...
The vector position of a particle varies in time according to the expression r = 8.20 i-5.60p j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) x m/s Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) X m/s2 (c) Calculate the particle's...
2. A velocity field is proposed to be x + y x + y (a) Is...
2. A velocity field is proposed to be x + y x + y (a) Is this a possible incompressible flow? (b) If so, find the pressure gradient Vp assuming a frictionless air flow with the z-axis vertical. Use ρ= 1.23 kg/m3, and assume ğ--gk . (5 pt)
Let (X, d) be a discrete space and let (Y, d′) be any metric space. Prove...
Let (X, d) be a discrete space and let (Y, d′) be any metric space. Prove that any function f : (X, d) → (Y, d′) is continuous. (Namely, any function from a discrete space to any metric space is continuous.)
Given the velocity field V = 101 +(x² + y2); - 2xy k [m/s] a) b)...
Given the velocity field V = 101 +(x² + y2); - 2xy k [m/s] a) b) c) Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of(x,y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m? d)
A steady, incompressible, two-dimensional (in the x-y plane) velocity field is given by V = (0.523-1.88x...
A steady, incompressible, two-dimensional (in the x-y plane) velocity field is given by V = (0.523-1.88x + 3.94y) i + (-2.44 + 1.26x + 1.88y) j . Calculate the acceleration at the point (x,y-(2, 3) The acceleration components are ax Acceleration components at (2, 3) are
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).
4. A source is located at (x,y) = (-3,+2) next to a corner as shown. y= +2 x axis 77 X =- (x,y) = (0,0) y axis a) what is the stream function for the entire field b) what is the velocity potential function for the entire field c) what is the u velocity component for the entire field d) what is the v velocity component for the entire field e) what is the velocity along both walls (can be...
The vector position of a particle varies in time according to the expression r = 8.20 i-5.60p j where r is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (Use any variable or symbol stated above as necessary.) x m/s Determine the acceleration of the particle as a function of time. (Use any variable or symbol stated above as necessary.) X m/s2 (c) Calculate the particle's...
2. A velocity field is proposed to be x + y x + y (a) Is this a possible incompressible flow? (b) If so, find the pressure gradient Vp assuming a frictionless air flow with the z-axis vertical. Use ρ= 1.23 kg/m3, and assume ğ--gk . (5 pt)
Given the velocity field V = 101 +(x² + y2); - 2xy k [m/s] a) b) c) Is the flow steady or unsteady? Is this motion kinematically possible for an incompressible fluid? Do you think that velocity field can represent a potential flow at specific positions of(x,y)? What is the acceleration of a particle at position (x, y, z) = (3, 1, 0) m? d)
A steady, incompressible, two-dimensional (in the x-y plane) velocity field is given by V = (0.523-1.88x + 3.94y) i + (-2.44 + 1.26x + 1.88y) j . Calculate the acceleration at the point (x,y-(2, 3) The acceleration components are ax Acceleration components at (2, 3) are
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