Answered: Consider a vortex filament of strength…

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.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.3P: Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK,...

See similar textbooks

Related questions

Q: The airflow network produces suction on the block mass (shown in figure). Which fluid mechanic…

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

Q: For the Couette flow of Fig., calculate the linear strain rates in the x- and y-directions, and…

A: The data given is, Distance between the parallel plates = h The equation of the steady,…

Q: Find the location of the stagnation point for the flow due to a vortex +T at (2a,0) and a vortex -…

Q: The wing of the Fairchild Republic A-10A twin-jet close-support airplane is approximately…

A: Reynold's number: It is a dimensionless number it is the ratio of the inertia force to the opposing…

Q: With the aid of diagram, derive an expression for continuity of a two dimensional flow .State…

A: According to the continuity equation, the product of area and velocity of flow is constant. It is…

Q: The lift on a spinning circular cylinder in a freestream with a velocity of 22 m/s and at standard…

Q: The lift on a spinning circular cylinder in a freestream with a velocity of 30 m/s and at standard…

A: Given data: Free stream velocity of air, V∞=30 m/s. At sea level conditions, density of air,…

Q: Write the equation for conservation of mass for unsteady and non-uniform flow. Briefly explain what…

A: The equation for unsteady and non-uniform flow is given below, ∑m˙in=∑m˙out+dmcvdt

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

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: What is momentum? How its related to Newton's second law of motion? Also explain how to calculate…

A: Linear momentum denoted by p is defined as product of mass of system by it's velocity. p=mV kgm/s…

Q: For fully developed laminar flow, you have found previously that that the average velocity is ½ of…

A: We have given; U=Vc1-rR1/5 Vc = centerline velocity. Uav=∫0RU(2πr)dr∫0R(2πr)dr Uav=∫U dA∫dA

Q: Perform the convective on velocity vectors u in cylindrical coordinates : Du/Dt

A: Given question: We have to find DU/Dt in cylindrical coordinates. The given question is related to…

Q: Do gases usually have a constant specific weight? What increases in altitude is necessary in the…

Q: Figure I exhibits the front view of a finite wing of span 'b' with a bound vortex at the center and…

A: It is asked to find the velocity from the vortex strength

Q: Using the irrotational flow approximation, calculate and plot the nondimensional static pressure…

A: Consider two points one at far away distance from the cylinder and other on the surface of the…

Q: A journal bearing 120 mm in diameter and 60 mm long has a diametral clearance of 0.20 mm. The…

Q: may be derived using fluid parameters.

Q: Problem 4: Vorticity of flow A two-dimensional velocity is given by the equation: v = 6yi +6xj Is…

Q: A cylindrical tank of radius rrim = 0.354 m rotates about its vertical axis. The tank is partially…

A: Given data: The radius of rim, Rrim = 0.354 m. The speed of rim, Vrim = 3.61 m/s. As the angular…

Q: A marine vehicle tows a hollow cylinder of 760 mm diameter and 5.5 m length. The cylinder is fully…

A: Given: The speed of marine vehicle, v = 6 knot = 3.086 m/s The diameter of cylinder, d = 760 mm The…

Q: Problem 1. For uniform flow over a flat plate, a useful approximation for the z-component of…

A: Given the profile uU=2yδ-yδ2δ=cx12

Q: Prove: For a sphere in unrestricted three-dimensional flow the added mass (also known as the…

Q: Outside an inner, intense-activity circle of radius R , a tropicalstorm can be simulated by a…

A: (a) Given velocity potential function is The tangential velocity can be determined as,

Q: 2- Determine stream function and velocity potential for combination of a horizontal uniform flow…

Q: Present and validate how Stokes Law is used to analysing fluid behaviour and measure the viscosity…

A: A fluid's viscosity is a measure of its resistance to deformation at a particular rate. A fluid…

Q: What are the classifications of uinachinery according to flow direction?

Q: A source with strength 0.25 m2/s and a vortex with strength 1 m2/s (counter-clockwise) are located…

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: A windmill is operating in a 10m/s wind that has a density of 1.2kg/m3. The diameter of the windmill…

A: Write the given values along with the suitable variables.

Q: Write down the streamfunction for an isotropic line source of strength 2rm in a unifor stream of…

Q: 2. Consider the boundary-layer momentum equation for steady incompressible flow in two dimen- sions:…

A: At the stationary solid surface,∂u∂y=0(no slip condition)Thus the equation reduces…

Q: A semi-cylindrical concrete structure having a radius of 3 m and length of 5 m is rested on ground.…

Q: A jet of ethylene exists a 40 mm diameter nozzle into still air at 300K and 1 atm. Compare the…

Q: Consider the displacement of oil by water from a capillary tube with radius of 25 microns. Assume…

A: given data σ = 30 x10-3 N/mRadius = 25 μm = 25 ×10-6mDiameter = 50 ×10-6mDensity of water = 1…

Concept explainers

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.

Question

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

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The steady plane flow in Fig. has the polar velocitycomponents υθ = Ωr and υr = 0. Determine the circulationΓ around the path shown.
Using the following streamline pattern, draw an appropriate control volume on the topside of the airfoil and describe how the airfoil creates a lift force based on the equations for conservation of mass and momentum.
The entrance flow between two parallel plates (gap h) has a velocity that varies linearly at the entrance and develops into a fully parabolic profile at the exit. What is the relationship between the maximum velocity at the entrance and that at the exit? You can show by symmetry that the maximum velocity is attained at the mid-plane between the two plates.
A positive line vortex K is trapped in a corner, as inFig. Compute the total induced velocity vector atpoint B, (x, y) = (2a, a), and compare with the inducedvelocity when no walls are present.
A horizontal pipe of diameter 25cm has a constriction of diameter of 5cm. The velocity of the water in the pipe is 1cm/s and the pressure is 10⁵ Pa. Calculate the velocity and pressure in the constriction. Include an illustration or drawing of the situation
A sink of strength 20 m2/s is situated 3 m upstream of a source of 40 m²/s in a uniform stream. It is found that, at a point 2.5 m from both source and sink, the local velocity is normal to the line joining the source and sink. Find the velocity at this point and the velocity of the uniform stream. Locate any stagnation points and sketch the flow field.
Using the irrotational flow approximation, calculate and plot the nondimensional static pressure distribution on the surface of a circular cylinder of radius a in a uniform stream of speed V∞. Discuss the results. The pressure far away from the cylinder is P∞.
The lift on a spinning circular cylinder in a freestream with a velocity of 30 m/s and at standard sea level conditions is 6 N/m of span. Calculate the circulation around the cylinder
Outside an inner, intense-activity circle of radius R , a tropicalstorm can be simulated by a polar-coordinate velocitypotential ϕ ( r , θ ) = U o R θ , where U o is the wind velocity atradius R . ( a ) Determine the velocity components outsider = R . ( b ) If, at R = 25 mi, the velocity is 100 mi/h and thepressure 99 kPa, calculate the velocity and pressure atr =100 mi.
A Savonius rotor can be approximatedby the two open half-tubes in Fig mounted ona central axis. If the drag of each tube is similar to thatin Table 7.2, derive an approximate formula for therotation rate Ω, as a function of U, D, L, and the fluidproperties (ρ, μ).
A cart with frictionless wheels and a large tank shoots water at a deflector plate, turning it by angle ? as sketched. The cart tries to move to the left, but a cable prevents it from doing so. At the exit of the deflector, the water jet area Ajet, its average velocity Vjet, and its momentum flux correction factor ?jet are known. Generate an expression for the tension T in the cable in terms of the given variables.
A slender missile is flying at Mach 1.5 at low altitude. Assume the wavegenerated by the nose of the missile is a Mach wave. This wave intersectsthe ground 559 ft behind the nose. At what altitude is the missileflying?