Consider a vortex filament of strength  in the shape of a closed circularloop of radius R. Obtain an expression for the velocity induced at thecenter of the loop in terms of  and R.

Q: Q/A uniform flow with a velocity of 4 m/s is flowing over a source placed at the origin. The…

A: Given: Uniform velocity (U)=4m/sStagnation points= (-0.35,0)

Q: Draw the diagram of the dimensionless velocity profile and 11 for the boundary layer on the surface…

A: To discuss the dimensionless velocity profile in a boundary layer under a pressure gradient, we need…

Q: this is not simple couette flow! the walls on the side have an effect on the velocity profile, but…

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Q: A conveyer belt is installed in a process industry to move the product from bottom to top. An…

A: Question (A) part is Solved here. For Other Part ,Please Post this Question Again.

Q: The velocity components for idealised flow along a right angled wall is given by u = 4 x m/s, v = -4…

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Q: 3- Determine stream function and velocity potential for combination of a horizontal uniform flow…

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Q: The energy distribution in the boundary layer over the free of a spilliway was observed to be :…

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Q: At point A in Fig.  is a clockwise line vortex ofstrength K =12 m2/s. At point, B is a line source…

A: Given data Clock wise vortex strength at A K = 12 m2/sec Line source strength at B m = 25m2/sec…

Q: A positive line vortex K is trapped in a corner, as inFig.  Compute the total induced velocity…

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Q: 38. Equation III..3.13 for steady flow simplifies to V pV = 0. What other con- dition should exist…

A: The continuity equation is a mathematical statement of the principle of conservation of mass.…

Q: Please expand the energy equation for the unsteady Cylindrical flow.

A: In this problem, it is asking about to expand the unsteady energy equation for cylindrical flow.

Q: Please expand the energy equation for the unsteady Cylindrical flow.

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Q: Consider steady, incompressible, laminar, fully developed, planar Poiseuille flow between two…

A: The flow between the two horizontal plates is constant, incompressible, laminar and fully developed.…

Q: A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind…

A: (a) The variation of the with x can be expressed as, The density as a function of x can be…

Q: Consider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and…

A: Given that :Flow is two dimensional flowVelocity field terms are given u=1v=2ytAsking to calculate…

Q: Please expand the energy cquation for the unsteady Cylindrical flow.

A: In this problem, it is asking to write the energy equation for the unsteady cylindrical flow and…

Q: A cylinder having a radius of 1 ft is immersed in air (density of 0.076 lbm/ ft’) having a uniform…

A: Draw a diagram showing the streamlines around the cylinder.

Q: An instrument popular in the beverage industry is the targetflowmeter in Fig. A small flat disk is…

A: (a) Target flowmeters measures the flow, particularly measuring the amount of the force exerted by…

Q: 5. Consider Poiseuille flow through a tube. Use the more general bound- ary condition for slip which…

A: Here we have Given data  The poiseuile law states that the flow of liquid  depends on  the following…

Q: e whether the flow is rotational or irrotational using an expression for the vorticity of the flow…

A: The key difference between rotational flow and irrotational flow lies in the presence or absence of…

Q: The Rankine body of revolution in Fig.  is 60 cm longand 30 cm in diameter. When it is immersed in…

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Q: The dynamic equilibrium in circular pipe flow: Velocity profile in laminar flow CExplain in detail,…

A: Explaining velocity distribution in laminar flow in a circular pipe.

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

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Q: Consider a potential flow describing a uniform flow around a rotating cylinder. It is rotating such…

A: Given:The two stagnation points are  apart.The function is .The fluid density is .The upstream…

Q: Flow separation: Using sketch, briefly describe the phenomena of flow separation at an arterial…

A: Flow seperation occurs at an arterial bifurcation region.And we have to discuss about it.

Q: Derive the Continuity Equation by considering a stream-tube of flow through a conduit.

A: Continuity equation This equation describes the conservation of mass during the fluid flow in the…

Q: Find the location of the stagnation point and the equation of the dividing streamline. What are the…

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Q: Consider the laminar flow of an incompressible fluid over a flat plate at y-0.

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Q: In the figure belowa 3D-wing is represented by a single horse shoe vortex with ro = 9 m²/s. The span…

A: according to the given figure and data

Q: Problem9 The entrance flow between two parallel plates (gap h) has a velocity that varies linearly…

A: In a laminar flow between two parallel plates, the velocity profile is symmetric about the mid-plane…

Q: For an incompressible flow on xz-plane, write down the continuity equation. Define an appropriate…

A: Given: The flow takes place on XZ plane. And the flow is incompressible so the density will remains…

Q: If stream function for steady flow is given by y = (y* – x*), determine whether the flow is…

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Q: Derive stoke's stream function?Also solve a numerical related to this?

A: For the steady flow ψ=fx,y After differentiation of ψ with respect to x and y The velocity component…

Q: A tornado in atmospheric air is simulated by a CCW free vortex as a potential flow field. The…

A: Given: The velocity measured at r1= 1 m from the center is v1=60 m/s, Air density ρ= 1 .0 kg/m3.…

Q: 5. Consider a Pitot probe in high-speed flow.(a) Give the value of the stagnation pressure to the…

A: Given question is explained below :Explanation:a) For a Pitot probe in high-speed flow with a Mach…

Q: Write down the Bernouli,s equation for a steady incompressible flow and identify the resulting terms

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Q: 4. The equation for the axial velocity of a vortex ring is U(0, R) = 4л -log(8R/a) where a is the…

A: Write the equation for axial velocity of vortex ring. U0,R=Γ4πlog8Ra     ...... (1)

Q: For the Taylor-Couette flow between concentric cylinders discussed in class, derive an  expression…

A: Given data : In a Two concentric cylinder inside cylinder is rotating with angular velocity of Ω and…

Q: whether the function o represents the velocity potential %3D x2+y2 lar incompressible 2D flow, and…

A: ∅=cxx2+y2 c=2Now for φ to represent velocity potential of incompressible 2D flow…

Q: The velocity components for idealised flow along a right angled wall is given by u = 4 x m/s, v = -4…

A: Given:u=4x m/sv=-4y m/sw=0 m/sx=(1,2,1) cm

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.