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

Velocity acquired by block - system released from rest, Velocity acquired b...

Velocity acquired by block - system released from rest: T wo blocks shown in the figure given below, have masses A = 20N and B = 10N and the coefficient of friction between

Find velocity of the vehicle, Find velocity of the vehicle: A car hav...

Find velocity of the vehicle: A car having mass 400kg is moving with velocity of 20m/sec. A force of 200N that acts on it for 2 mins. Find velocity of the vehicle: (1) W

Determine the deflection under the loads, Determine the deflection under th...

Determine the deflection under the loads: Determine the deflection under the loads as shown in Figure Solution ∑ F y   = 0, so that R A + R B  = 80 + 20 = 100 k

Determine the amount of air circulated per minute, An air refrigerator oper...

An air refrigerator operates between the pressure limits of 1 bar and 5 bar. The temperature of the air entering the compressor and expansion cylinder are 15 o C and 25 o C respect

Determine the wire drawing - cold drawing processes, Determine the Wire Dra...

Determine the Wire Drawing - cold drawing processes Similar to above process bars are first pickled, washed and coated to prevent any oxidation. After this rods are passed t

Types of belt drive used for power transmission, Q. Explain the types of be...

Q. Explain the types of belt drive used for power transmission? Also derive the velocity ratio of them. Sol:   There are mainly three types of belt drive: (1) Open belt driv

Describe polythionic acid corrosion, Q. Describe Polythionic Acid Corrosion...

Q. Describe Polythionic Acid Corrosion? Although it is not typically thought of as high temperature corrosion, polythionic acid stress corrosion cracking occurs in areas where

Illustration of cam, Illustration of CAM A cam rotating at consisted an...

Illustration of CAM A cam rotating at consisted angular velocity operates an oscillating follower. Draw cam profile for the given data: Angular displacement of the follower

Newton law of motion - third law, Newton law of motion - Thir d Law F...

Newton law of motion - Thir d Law Force of action and reaction between the bodies which are interacting are equal in magnitude, opposite in direction and have same line of ac

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