Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

Consider a gas bubble rising in a liquid - filled tube. If the bubble volume ( V B ) and tube radius ( R T

Consider a gas bubble rising in a liquid-filled tube. If the bubble volume (VB) and tube radius (RT) are such that VB13
RT, then the bubble will be highly elongated. Assume that the bulk of the bubble forms a cylinder of radius RB and length L, as shown inthe figure). The liquid film between the bubble and tube wall is expected to be very thin )=(RT-RBRB. Consequently, local rectangular coordinates can be used in the film, as shown in the figure). It is convenient to fix the coordinate origin on the wall.
Assuming that the flow in the liquid film is fully developed and that the bubble dimensions are known, derive an expression for the steady rise velocity of the bubble, U. State any additional assumptions that are needed. (Hint: The bubble velocity is not uniform, so that the velocity at the gas-liquid interface differs from U, the mean value for the bubble.)
The X-momentum P(dUxdt+UxdUxdx+dUxdy=-dPdx+(d2Uxdx2+d2Uxdy2.Then0=-dPdx+d2Uxdy2.
The y momentum is0=-dPdy.TheboundaryconditionsaredUxdy(x,y=H)=0, and Ux(x,y=0)=0.
image text in transcribed

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

Chemical Engineering Design And Analysis An Introduction

Authors: T. Michael Duncan, Jeffrey A. Reimer

1st Edition

0521639565, 9780521639569

More Books

Students also viewed these Chemical Engineering questions

Question

4. Label problematic uses of language and their remedies

Answered: 1 week ago