Question: The velocity components for a fluid flow are given as follow: z(x-2)2 u = ty...

Question: The velocity components for a fluid flow are given as follow: z(x-2)2 u = ty w = xy (t is time) t+1 a.) Is the flow incompressible or not? b.) How many dimensions does the flow have? c.) Is the flow irrotational or rotational? d.) Find the local acceleration of the flow along x-direction at the points A(x,y,z,t)=A(0,1,1,4); B(x,y,z,t)=B{2,2,1,0)? e.) Find the convective acceleration of the flow along y-direction at the points A(x.y,z,t)=A(0,1,1,4); B(x,y,z,t)=B(2,2,1,0)?

Expert Solution

samet mamat answered 2 years ago

The velocity components of an incompressible, two-dimensional velocity field are given by the equations u=y^2-x(1+x) v=y(2x+1)...

The velocity components of an incompressible, two-dimensional velocity field are given by the equations u=y^2-x(1+x) v=y(2x+1) (a)Show that the flow satisfies continuity. (b) Determine the corresponding stream function for this flow field. (c) Determine if the flow is irrotational.

A fluid flow field is given by v = x^2yi + y^2zj-(2xyz + z^2)k. Prove that...

A fluid flow field is given by v = x^2yi + y^2zj-(2xyz + z^2)k. Prove that it is a case of possible steady in compressible flow. Calculate the velocity and acceleration at the point (2,1,3).

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

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A fluid has velocity components of u=(8t2)m/s and v=(8y+3x)m/s, where x and y are in meters...

A fluid has velocity components of u=(8t2)m/s and v=(8y+3x)m/s, where x and y are in meters and t is in seconds. Part A Determine the magnitude of the velocity of a particle passing through point (1 m, 1 m) when t = 2 s. V= Part B Determine the direction of the velocity of a particle passing through point (1 m, 1 m) when t = 2 s. θv= Part C Determine the magnitude of the acceleration of a particle...

Given a function φ(z) with z = x+iy let U(x, y) = ½ [φ(x+iy) +...

Given a function φ(z) with z = x+iy let U(x, y) = ½ [φ(x+iy) + φ(x-iy)] and V(x, y) = i/2 [φ(x+iy) –φ(x-iy)] A) For φ(z) = z2 find U and V and their induced vector fields E =▼U and F =▼V also show that ▼2U = ▼2V = 0 B) Repeat for f(z) = z3 C) For f(z) = ln z we get U(x, y) = ½ ln (x2+y2) and V(x, y) = arctan (y/x) Find ▼U (electrostatic...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to...

Let X and Y be random variable follow uniform U[0, 1]. Let Z = X to the power of Y. What is the distribution of Z?

Velocity field for this system is: V=[X^2-(yz^1/2/t)]i-[zy^3+(x^1/3z^2/t^1/2)j+[-x^1/3t^2/z*y^1/2]k find the components of acceleration for the system.

Velocity field for this system is: V=[X^2-(y*z^1/2/t)]i-[z*y^3+(x^1/3*z^2/t^1/2)j+[-x^1/3*t^2/z*y^1/2]k find the components of acceleration for the system.

2. Suppose utility for a consumer of cereal (x) and milk (z) is U = min(x,...

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Fluid X is flowing in a circular pipe with a constant velocity ν (m/s). The fluid...

Fluid X is flowing in a circular pipe with a constant velocity ν (m/s). The fluid is cooled by a jacket kept at constant temperature, Tj. Fluid velocity is plug shaped , in other words uniform at radial positions. Assume that temperature is uniform in radial positions because of turbulent flow conditions; ρ and Cp of the fluid are constants. The inlet temperature (at z=0) is constant and uniform at To (To>Tj). Assume that thermal conduction of heat along the...

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

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