Consider a vortex filament of strength in the shape of a closed circularloop of radius R.Consider also a straight line through the center of the loop, perpendicular to the plane of the loop. Let A be the distance along this line, measured from the plane of the loop. Obtain an expression for the velocity at distance A on the line, as induced by the vortex filament.

Consider a vortex filament of strength in the shape of a closed circularloop of radius R.Consider also a straight line through the center of the loop, perpendicular to the plane of the loop. Let A be the distance along this line, measured from the plane of the loop. Obtain an expression for the velocity at distance A on the line, as induced by the vortex filament.

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.

Chapter6: Forced Convection Over Exterior Surfaces

Section: Chapter Questions

Problem 6.34P

See similar textbooks

Similar questions

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.
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
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 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.
Consider the geometry sketched. The velocity of the upper plate is 200 ft/s, and the two plates are separated by a distance of 0.01 in. The fluid between the plates is air. Assume incompressible flow. The temperature of both plates is the standard sea level value of 519◦R.(a) Calculate the velocity in the middle of the flow.(b) Calculate the shear stress.(c) Calculate the maximum temperature in the flow.(d) Calculate the heat transfer to either wall.(e) If the lower wall is suddenly made adiabatic, calculate its temperature.
The gases coming out of the steam boiler are discharged from a chimney with a rectangular area of 15x20 ft at a constant speed of 50 ft / s. The flue line is 250 ft long and there are 2 bends at 90 degrees. The temperature of the gases is constant at 180 F and an average pressure of 1 atm. Its physical properties are the same as the air in the same conditions. Calculate the pressure difference and required power in the flue line.
As discussed in class, rotor wheel turbines are commonly used in hydroelectric power plants to generate electric power. In the Pelton wheel design below with radius r = 2 m, a high speed water jet (with Vj = 50 m/s and flow rate 10 m3 /s) impinges on buckets making an angle β=160 degrees, forcing the wheel to rotate at constant angular speed ω = 150 revolutions per minute. Calculate the power delivered to the rotor if there are 10 jets as described above surrounding the Pelon wheel.
Explain, with the use of sketch diagrams or a paper model, why the aerodynamic fore on a blade hass to be resoled twice to obtain the accelerating force in a wind turbine rotor.
A liquid of density ρ fl ows through a 90 ° bend as shown inFig. and issues vertically from a uniformly poroussection of length L . Neglecting pipe and liquid weight,derive an expression for the torque M at point 0 required tohold the pipe stationary.
Example: A fan of diameter 0.7 m running 1500 rpm delivers 140 m3/min of air at 15C against 75 mm of water total pressure when the total effeciency is 86%. Determine the volume of air delivered, total pressure and power consumed, if (a) the air temperature is 50C. (b) the air temperature is 50C and the fan speed is 1700 rpm. (c) the same conditions as (b) but a 0.6 m diameter, geometrically similar fan is used.
The steady plane flow in Fig. has the polar velocitycomponents υθ = Ωr and υr = 0. Determine the circulationΓ around the path shown.
A multi-rotor propeller has a geometric pitch angle of 9 degrees at a point 0.11 m from the shaft. If the inflow velocity at this point is 3 m/s and the propeller is spinning at 2,000 RPM, what is the local angle of attack?