Compute the vorticity and sketch the velocity and vorticity fields of the following (Note: the following are in cylindrical coordinates): a) The flow in a round tube where the velocity profile is v z =v 0 [1-(r/R) 2] b) An ideal vortex where the velocity is v 0 =Γ /2pi*r. c) Vortex flow where the velocity is v 0= [Γ /2pi*r][1-exp(-r 2 /4vt)]

Question: Using the cylinderical coordinate, find the vorticity for the flow in a round tube where the velocity profile is shown below. And clearly write the direction of the final vector quantity. Using the cylinderical coordinate, find the vorticity for the flow in a round tube where the velocity profile is shown below.

Question: Vorticity is describes the swirling motion in a fluid, and is defined as the curl of velocity ∇×u. (a) Show ∇⋅ω=0. (b) Describe the difference between an irrotational (or free) vortex and a rotational (or rigid body) vortex. Use a diagram for illustration.

Vorticity, w is defined as a curl of velocity, which is a cross product of the "del" operator V = e +e and velocity vector u = uex + vey + Wez Assume we have a 2D flow with the velocity vector given by u = Vø, where ø is a scalar function 3x'y3 Determine z-component of the vorticity vector for this 2D flow by following the steps below: a) Determine the x and y components of the velocity ...

For potential flow due to a line vortex, the vorticity is concentrated along the axis of the vortex. Thus, the problem to be solved for the decay of a line vortex with time due to the viscosity of the fluid is as follows: Here, ω(R, t) is the vorticity, and the total circulation associated with the vortex for any time t ≥ 0 is Γ. Look for a ...

Understand the concept that vorticity in a flow field is related to fluid particle velocity and can be mathematically defined in terms of the rotation vector. View the full answer Previous question Next question

To find the vorticity for the flow in a round tube with the velocity profile , identify and write down the velocity components and make note that the radial and circumferential components are zero. The vortici …

Question: 5. Select the correct relationship between vorticity and angular velocity, and curl of the velocity vector A. Vorticity is half of the angular velocity vector B. Vorticity is equal to the curl of the velocity vector and twice the angular velocity C. Vorticity is not related to angular velocity but is equal to half of the curl of the velocity vector D.

Problem 1 Vorticity is defined as ω ≡ ∇ × u. Show that the divergence of vorticity is zero. Problem 2 Prove that if u 2 = u ⋅ u and ω ≡ ∇ × u for the vector field u, then (u ⋅ ∇) u = 2 1 ∇ u 2 − u × ω. Problem 3 Prove for vectors a and b the following holds (using indicial notation) ∇ ⋅ …

2.7 The velocity field given in Problem 2.3 is called source flow, which will be discussed in Chapter 3. For source flow, calculate: a. The time rate of change of the volume of a fluid element per unit volume. b. The vorticity. Hint: It is simpler to convert the velocity components to polar coordinates and deal with a polar coordinate system.