My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum


Reply
 
LinkBack Thread Tools Display Modes
August 30th, 2014, 01:10 AM   #1
Member
 
Joined: Aug 2014
From: India

Posts: 88
Thanks: 0

what is the mean velocity of this?

The Maximum velocity of a one dimensional in-compressible fully developed viscous flow, between two fixed parallel plates, is 6 m/s.
The Mean Velocity ( in m/s) of the flow is
(A) 2
(B) 3
(C) 4
(D) 5
Ganesh Ujwal is offline  
 
August 30th, 2014, 02:55 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,378
Thanks: 542

Quote:
Originally Posted by Ganesh Ujwal View Post
The Maximum velocity of a one dimensional in-compressible fully developed viscous flow, between two fixed parallel plates, is 6 m/s.
The Mean Velocity ( in m/s) of the flow is
(A) 2
(B) 3
(C) 4
(D) 5
Insufficient information.

Mean could = maximum or less depending on what else is going on.
mathman is offline  
September 1st, 2014, 04:23 AM   #3
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,073
Thanks: 695

Math Focus: Physics, mathematical modelling, numerical and computational solutions
There is enough information in the question; you just need to assume laminar flow through a 2D duct. Have a think about what the velocity profile looks like. Then you can use the information you've been given to solve the problem.

Hint... The velocity of fluid at the edges of the pipe is zero. What about the velocity of the fluid as you go towards the centre of the pipe?
Benit13 is offline  
September 5th, 2014, 06:24 AM   #4
Senior Member
 
Joined: Apr 2014
From: Glasgow

Posts: 2,073
Thanks: 695

Math Focus: Physics, mathematical modelling, numerical and computational solutions
Since there's not been a reply for a while...

A velocity profile between parallel plates has a parabolic shape and can be described by

$\displaystyle v(x) = a - bx^2$

where I have positioned the curve so that the maximum velocity is at $\displaystyle x = 0$ and the velocity drops to zero at the walls of the pipe/plates, situated at $\displaystyle x = \frac{L}{2}$ and $\displaystyle x = -\frac{L}{2}$. $\displaystyle L$ is the distance between the plates.

When $\displaystyle x = 0$, $\displaystyle v = 6$ m/s, so $\displaystyle a = 6$

When $\displaystyle x = \frac{L}{2}$, $\displaystyle v = 0$, so

$\displaystyle 6 - b\left(\frac{L}{2}\right)^2 = 0$
$\displaystyle 6 = b\left(\frac{L}{2}\right)^2$
$\displaystyle b = 6\left(\frac{2}{L}\right)^2$
$\displaystyle b = \frac{24}{L^2}$

So $\displaystyle v(x) = 6 - 24\frac{x^2}{L^2}$ is the velocity profile of the flow between the parallel plates.

The average speed can be found by integrating under the profile and dividing it by the total width of the pipe:

$\displaystyle \overline{v} = \frac{1}{L}\int^{\frac{L}{2}}_{-\frac{L}{2}}v(x) dx$
$\displaystyle = \frac{1}{L}\int^{\frac{L}{2}}_{-\frac{L}{2}} \left(6 - 24\frac{x^2}{L^2}\right) dx$
$\displaystyle = \frac{1}{L}\int^{\frac{L}{2}}_{-\frac{L}{2}}\left(6 - 24\frac{x^2}{L^2}\right) dx$
$\displaystyle = \frac{1}{L}\left[ 6x - 8\frac{x^3}{L^2}\right]^{\frac{L}{2}}_{-\frac{L}{2}}$
$\displaystyle = \frac{1}{L}\left(3L - L - (-3L + L)\right)$
$\displaystyle = \frac{1}{L}\left(4L\right)$
$\displaystyle = 4$ m/s

so the answer is c)
Benit13 is offline  
Reply

  My Math Forum > Science Forums > Physics

Tags
velocity



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Obtaining angular velocity given linear velocity and center of rotation 3D quarkz Calculus 0 April 18th, 2014 06:34 AM
Velocity arron1990 Calculus 7 May 31st, 2012 05:23 AM
Velocity? Kimmysmiles0 Algebra 1 April 27th, 2012 10:14 PM
Velocity ChristinaScience Calculus 3 October 9th, 2011 05:54 PM
Velocity instereo911 Calculus 5 February 24th, 2008 01:41 PM





Copyright © 2017 My Math Forum. All rights reserved.