A mass of fluid moves in such a way that  each particle describes a circle in one plane  about a fixed axis; show that the equation  of continuity is ∂?/∂t+∂(??)/∂?=0, where  ? is angular velocity of the particle whose  azimuthal angle is ? at time t.

Q: Consider the two-dimensional velocity field given by V = (5+α₁x + b₁y) + (4+ α2x + b²y)), where a₁,…

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Q: Consider the velocity field of Problem 2.18. Plot the streakline formed by particles that passed…

A: Given Data: The velocity of flow is, V→=Bx(1+At)i^+Cyj^. The value of A is, A=0.5 s-1. The value of…

Q: Two concentric cylinders of radii a and b respectively (a > b) have their common axis lying along…

A: In steady laminar flow, the fluid is expected to travel in a circular motion two concentric…

Q: 3. Viscous fluid occupies the region 0 < z<h between two rigid boundaries z = 0 and z = h. The lower…

A: In fluid mechanics, the Navier-Stokes equation is a partial differential equation that describes the…

Q: a particle of mass m moving under the forċe of F a(xi + yj + Zzk). Here a is a ustant. Is the linear…

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Q: Show that the power , necessary to rotate a stirrer (diameter d) with a speed n (s¹) in a fluid of…

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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…

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Q: The three components are as follows: u = 2xt– 3xyz + 6z v = x– yz + 4xyt w = 3x– 5yzt + yz Find the…

A: Let V is the resulatant velocity at any point in a fluid flow. let u,v and w are its components in…

Q: A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown, during the…

A: In order to proceed with the given problem some assumptions need to be taken. The Flow is two…

Q: The sketch shows a flat plate aligned parallel to an incompressible airstream. Assume a velocity…

A: Given Data: flat plate aligned parallel to an incompressible airstream Find: Assume a velocity…

Q: Consider the steady potential flow around the circular cylinder shown in the figure below. At what…

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Q: An unsteady, incompressible, velocity field is given by the following vector: V = (u, v, w) = (−7t…

A: Velocity vector, V→=u,v,w=-7t+3.5xy+2.2yi→+2t+3x-1.6yj→+5+4zk→Point, x,y,z,t=-1,2,1,2

Q: An unsteady, incompressible, velocity field is given by the following vector: V = (u, v, w) = (t +…

A: Given: Let us consider the given velocity field in vector, V→=u,v,w=t+5x-7yi→+-3yj→+2t-4zk→ To find:…

Q: Find the stagnation point in the following two-dimensional velocity field: V=(3+x-y)i + (5+x+y)j

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Q: Thus, the equation of the streamline passing through point (1 m, 2 m) is x² = Determine the…

A: The given equation is of streamlined flow.

Q: The three components are as follows: u = 2xt– 3xyz + 6z v = x– yz + 4xyt w = 3x– 5yzt + yz Find…

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.