Find the differential equation, Mechanical Engineering

Assignment Help:

Find the Differential Equation

Flow problems where the Reynolds number is very, very small (Re<<1) are called "creeping flow." These problems are of special interest because, unlike many other fluid mechanics problems, they can often be solved analytically. The underlying reason for this is that the Navier-Stokes equation contains a non-linear term. However, if the Reynolds number is so small that it approaches zero, this non-linear term also approaches zero and effectively disappears from the equation.

(a) The space between two coaxial cylinders is filled with an incompressible fluid at constant temperature. The radii of the inner and outer wetted surfaces are κR and R, respectively. The inner and outer cylinders are rotated with a steady angular velocity of Ωi and Ωo, respectively, where these are sufficiently slow such that creeping flow may be assumed. Find the differential equation and boundary conditions that may be solved to find the velocity distribution in the fluid. (Note: You are not being asked to solve this equation!)

 (b) Repeat for the analogous problem of concentric spheres.


Related Discussions:- Find the differential equation

Shear stress, write the assumption made in derivetion of shear stress produ...

write the assumption made in derivetion of shear stress produced in circular shaft subjected to torsion

High speed circuit-carburettor in high speed condition , High Speed Circuit...

High Speed Circuit : The speed of motorcycle is further increased by raising the throttle valve. In this condition, fuel and air enter through main passage and main jet as can be

Principle of energy conversion, Q.   Describe the principle of energy conve...

Q.   Describe the principle of energy conversion. Show that the reaction of coupling magnetic field on the electrical or mechanical system is essential for the electro - mechanical

The progressive liberalization , The progressive liberalization of the nor...

The progressive liberalization of the norms for foreign investment and import of technology appear to have benefited the automobile sector with production of total vehicles increa

Explain principal process for abrasive jet cutting machines, Explain Princi...

Explain Principal Process for Abrasive Jet Cutting Machines Abrasive particles are fed from the hopper in to the mixing chamber by regulating device as shown in figure.

Thermodynamics, show that work is a path function and not a point funtion ?...

show that work is a path function and not a point funtion ?

Explain the importance of jigs and fixtures, Explain the Importance of jigs...

Explain the Importance of jigs and fixtures: Enhance productivity. Rapid production work. Reduces manufacturing costs. Complex and heavy components can be

Feed speed-spindle rpm-cutting time material removal rate, A hole of 25 mm ...

A hole of 25 mm diameter and 62.5 mm depth is to be drilled. The suggested feed is 1.25 mm/rev.and the cutting speed is 60 m/min. Assume the clearance height is 5 mm. Determine: f

Evaluate the shaft diameter on strength basis, The layout of a transmission...

The layout of a transmission shaft carrying two pulley C and B and supported on bearings A and D is shown in figure. Power is supplied to the shaft by means of vertical belt on pul

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd