Velocity potential function in the velocity field is given asØ=1axyt:a-Is the flow compressible ?(3p)b-Show the flow...

Velocity potential function in the velocity field is given asØ=1axyt:a-Is the flow compressible ?(3p)b-Show the flow is steady ornot?(3p)c-In this flow field, find the resultant velocity and acceleration and their components at point A(8,8) at time t=1.(5p)d-Find the stream function for this flow.(7p)e-If the particle passing through the point (x0, y0)=(8, 8) is marked at time t=0, determine the location of the particle at time t=4s.(7p)

Expert Solution

Ally Wells answered 11 months ago

The velocity field of a permanent, incompressible and isothermal flow is given by u = a...

The velocity field of a permanent, incompressible and isothermal flow is given by u = a (x^2 - y^2) (1) v = −2axy (2) w = 0 (3) Gravitational acceleration acts on the z axis only. a) Write the Navier-Stokes equations for this flow, canceling the appropriate terms and replacing the non-zero derivatives with their detailed expression. Be sure to indicate clearly your assumptions. (4 points) b) From the result obtained in (a), demonstrate that the pressure field is continuous...

The stream function ?? in a two-dimensional flow field is given as ?? = 4?? −...

The stream function ?? in a two-dimensional flow field is given as ?? = 4?? − 3?? + 7???? (a) Prove that this flow field is irrotational and that it satisfies the continuity equation. (b) Find the potential flow function Ф(??, ??) for this flow field with boundary condition Ф = 0 at x = 2, y = 1.

question 1 : A velocity potential in a two-dimensional flow is given as φ = 3xy2...

question 1 : A velocity potential in a two-dimensional flow is given as φ = 3xy2 – x3 . Find the stream function which is perpendicular to velocity potential question 2 : Write down equations that represents the volume flow rate and the mass flow rate. Show the resultant units of equations in terms of MLT system

1) Distinguish between blood flow rate and blood flow velocity. When an expert in the field...

1) Distinguish between blood flow rate and blood flow velocity. When an expert in the field uses the term blood flow, does that term usually mean rate or velocity? 2) Explain why a heart can keep beating after it has been removed from a living body.

A two-dimensional transient velocity field is given by u = ax(b + ct) v = ey(f+...

A two-dimensional transient velocity field is given by u = ax(b + ct) v = ey(f+ ht) where u is the x velocity component and v, the y component. Find: The trajectory x(t), y(t) if x = x0, y = y0 at t = 0. The streamline that passes through x0, y0 when t=0 and plot it. The acceleration field. a (-) = 5 b (1/s) = 5 c (m) = -1 e (-) = 5 f (1/s) = 5...

Show that {a + b√3 | a, b ∈ Q} is a field (a subfield of...

Show that {a + b√3 | a, b ∈ Q} is a field (a subfield of the field R), but {a + b√3 | a, b ∈ Z} is not a field.

A velocity vector field is given by F (x, y) = - i + xj a)...

A velocity vector field is given by F (x, y) = - i + xj a) Draw this vector field. b) Find parametric equations that describe the current lines in this field. c) Obtain the current line which passes through point (2,0) at time t = 0 and represent it graphically. d) Obtain the representation y = f(x) of the current line in part c).

2. The data of the velocity of a body is given as a function of time...

2. The data of the velocity of a body is given as a function of time in the table below. Determine the value of the velocity at t=16 seconds using: (this is the table) t(s) 0 15 18 22 v(t) 22 24 37 25 a) Newton’s divided difference first order polynomial method. b) Newton’s divided difference second order polynomial method. c) Newton’s divided difference third order polynomial method.

An ideal flow can be described by a velocity potential . What does express? Illustrate (choose...

An ideal flow can be described by a velocity potential . What does express? Illustrate (choose your own flow example) how you with help of the velocity potential and equipotential lines can find the flow direction and if the flow velocity increase, is constant or decrease

Problem 1a: Velocity Selector: Show that with the right ratio of electric to magnetic field strength...

Problem 1a: Velocity Selector: Show that with the right ratio of electric to magnetic field strength a particle of velocity v will proceed through both fields in a straight line at constant speed (hint: you will need an equation containing v. Also: what does the straight line at constant speed give you?). Assume that the angle of the velocity vector relative to the magnetic field vector is 90 degrees. b: Show mathematically that the charge magnitude and sign do not...

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