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

Types of lubricant , Types of Lubricant: Lubricant is a material which cir...

Types of Lubricant: Lubricant is a material which circulates through the lubrication network to provide lubrication at various points. Lubricants are classified in three forms: Fl

Calculate the maximum shear stress, The square cross sections A and B a...

The square cross sections A and B are shown in Fig Q1, the dimensions b = 80 mm, thickness t = 10 mm. A shear force V is applied at the cross section, calculate the maximum she

Internal combustion engine - thermodynamics, Internal combustion engine - T...

Internal combustion engine - Thermodynamics: Internal combustion engine is popularly known as I.C. engine, is heat engine that converts the heat energy released by the combust

Manufacturing processes, Manufacturing Processes: Importance of Manuf...

Manufacturing Processes: Importance of Manufacturing: The importance of manufacturing is that a gives usable product from the ore of different metals and from different mate

Show the geometric similarity, Q. Show the Geometric Similarity? When m...

Q. Show the Geometric Similarity? When model is required to provide an aid merely for visualisation, scaler reproduction of form is sufficient which is termed Geometric Similar

Steady state conditions and the thermal equilibrium state, What is a differ...

What is a difference between the steady state conditions and the thermal equilibrium state? In steady state condition, temperatures are constant although heat transfer is taking

Theory of machines, procedure to draw velocity and acceleration diagram usi...

procedure to draw velocity and acceleration diagram using relative velocity method

Quasi static process - thermodynamics, Quasi static process - thermodynamic...

Quasi static process - thermodynamics: Thermodynamic equilibrium of a system is very difficult to be realized during the occurrence of a thermodynamic process. 'Quasi-static'

Bicycle frame design, You are required to design the central section of the...

You are required to design the central section of the bicycle frame which consists of the seat tube, top tube, down tube and head tube. You can ignore the seat stays, chain stays a

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