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: The velocity field in which this particle flows is given as V = (y/5)i + (2t/5)j. Plot the pathline…

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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: 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: 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: The velocity distribution in the boundary layer is given by :u/U=(y/δ)^0.23 where u is the velocity…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: The motion of a very viscous fluid in the two-dimensional (wedge) region −α < φ can be described, in…

A: Here the motion of a very viscous fluid in 2d (wedge) given region -x&lt;ϕ&lt;x, can be described in…

Q: The x and y components of velocity for 2D flow are u=6y ft/s, and ??=3 ft/s, where y in feel.…

A: Given data: u=6y ft/s v =3 ft/s Need to determine the  equation of streamline.

Q: he vertical air velocity is much sma

A: GIVEN: Use the continuity equation ∇ · u to argue that the vertical air velocity is much smaller…

Q: If the speed component in the fluid is u=x?+2y, v=+) -+3y W= 2z V =-+y all wrongs -. in(x) Int2) c =…

A: Solution:

Q: 5.14 The velocity field within a laminar boundary layer is repre- AU y 4 3/2J, where A= 141 sented…

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Q: (b, b) (b > 0) at the time of interest in a semi-infinite (y > 0) two-dimensional inviscid fluid. A…

A: given data;two ideal vortices with ideal circulation are located atX1=(-b,b)and…

Q: A wave in deep water has the following characteristics: HO=3.z m, T=7.y sec (Bathymetries are…

A: GivenT=7sH=3mZ=-2mTo find:-Orbital horizontal and vertical velocities

Q: 3. Two ideal vortices with ideal circeulation I are located at x1 = (-b, b) and x2 = (b, b) %3D (b >…

A: Similar to vorticity circulation is a primary characterization of rotation of flow in fluid…

Q: Find the stream lines and path lines of the particles of the two dimensional velocity field…

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Q: Explain the fundamental reason for shear viscosity oxz bị along the x-axis with velocity v(z). How…

A: Shear viscosity's primary function is to oppose the flow of fluid from one layer to another.

Q: The disk rotates by an axial with angular velocity ω. Space between disks And the static surface is…

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Q: For a steady flow, the velocity field is V = (-2² + 3y) i + (2zy) j. The magnitude of the…

A: Given, V → = -x2 + 3y i^ + (2xy) j^   X and Y components of velocity is given by, u = -x2 + 3yv =…

Q: Determine the vorticity for the velocity field, u = 3x + 2y ,v = 5x – 3y %3D |

A: The components of the velocity field are given as, u=3x+2yv=5x-3y

Q: In deriving the continuity equation, we assumed, for simplicity,that the mass fl ow per unit area on…

A: Solution : Consider a cuboid of dimension dx ,dy &amp;  dz as shown in figure below :

Q: For a constant tensor, Ajk prove that V(A x, x )= (Ay + Ay )x,.

A: Steps:               a) The component of symmetric tensor M(μν) and anti - symmetric tensor M[μν]…

Q: The value of b,

A: Given; The velocity field of an incompressible flow is given in question: Where, a1=2…

Q: A motion is described by the linear (in a) function p(a,t) = F(t)a with det F(t) = 1+t for all…

A: In field theories, a Lagrangian Density is utilised. Lagrangian density throughout space. In…

Q: The velocity field in a two-dimensional, unsteady flow is given by V(x, y,t) = 2xy²j + 3xyĵ m/s· The…

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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: 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: In deriving the vorticity equation, we have used the identity V × (VP) = 0. Show that this identity…

A: The objective of the question is to verify the vector identity V cross (VP) = 0 for any scalar…

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: If the velocity field is given by u =x -y +x and v=- (2xy + y), determine o and y. и

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Q: u = x,v = - y The equation of continuity is satisfied صواب O خطأ

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Q: 1. Find the velocity at a point (4, 3, 1) after 2 sec. for a three dimensional flow given by Eq.1. ?…

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

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Q: Question 1 Determine the pathline and the streamline which pass through the origin at t = 0 for the…

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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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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.