August 30th, 2014, 12:10 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 incompressible 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 
August 30th, 2014, 01:55 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,256 Thanks: 507  Quote:
Mean could = maximum or less depending on what else is going on.  
September 1st, 2014, 03:23 AM  #3 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,019 Thanks: 665 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? 
September 5th, 2014, 05:24 AM  #4 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,019 Thanks: 665 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) 

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 05:34 AM 
Velocity  arron1990  Calculus  7  May 31st, 2012 04:23 AM 
Velocity?  Kimmysmiles0  Algebra  1  April 27th, 2012 09:14 PM 
Velocity  ChristinaScience  Calculus  3  October 9th, 2011 04:54 PM 
Velocity  instereo911  Calculus  5  February 24th, 2008 01:41 PM 