The velocity components in spherical coordinates of the axisymmetric uniform flow of a viscous fluid past a sphere are За = 1⁄2U ( 2 + ²5 - ³ª) 3a) c Up = cos 3a -—-U (2-22-³3-27) 2r Ug = - seno where U is the velocity of the uniform flow and a is the radius of the sphere. Find the Stokes stream function for this flow. Is it a rotational or irrotational flow?

Q: In a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v…

A: to find:the velocity potential function  for the flow fieldthe stream function for the flow…

Q: A two-dimensional incompressible velocity fi eld has u =K (1 - e - ay ), for x ≤ L and 0 ≤ y ≤ ∞.…

A: Write the expression for the continuity equation.

Q: An equation for the velocity for a 2D planar converging nozzle is w = 0 Where U is the speed of the…

A: Given: Velocity in x direction is, u=U1+xL Velocity in y-direction is, v=-UyL

Q: lot the velocity field, potential field, and streamlines. Please explain it in detail.

A:

Q: An irrotational flow in the r-y plane is represented by the potential function 0 = x² + xy – y²,…

A: Given data The potential function of the flow is ϕ=x2+xy-y2.

Q: The stream function of a flow field is ų = Ax3 – Bxy², where A = 1 m-1s1 and B = 3 m1s1. (a) Derive…

A: The velocity along the x axis can be determined as shown below.

Q: A velocity field is given as V (x,y,z,t)=(5xy^2+t) I+ (2z+8) j+18 k. Here x,y and z are in metres…

A:

Q: The stream function for a given 2D flow fields is V = 5x²y – (s/3)y Determine the corresponding…

A: Given data Stream function,ψ = 5x2y  - s3y3 We have to find the corresponding velocity potential.

Q: Given the vector equation below for velocity of a given fluid: V=(0.5+1.2x)i + (-2.0-1.2y)j, derive…

A:

Q: Consider the following velocity potential for two-dimensional flow: $ = 2x – x² + y² a. Show that…

A: Given:Velocity function,φ=2x-x2+y2

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.