Ask A Scientist© Engineering Archive

Index Key:   ENG023
Author:      ericschotz
Subject:     Pressure rise in pipe expansion
Text:        I have learned that while fluid is flowing through a pipe and the 
pipe expands the pressure is higher in the segment of the tube with greater 
diameter.  I have seen the equations that prove this but I am having a hard 
time grasping in physically.  I have this idea that faster flow implies high 
pressure but in this case the high pressure segment is slower.  If anyone has 
a good explanation, I would appreciate it.

Response #:  1 of 3
Author:      cdmurphy
Text:        Faster flow does not necessarily mean higher pressure.  In the 
case of pipe expansion:  In order to maintain a constant flow rate (flow rate 
= Q), an increase in cross-sectional area (pipe expansion) means a lower 
velocity because  Q = A1 * V1 = A2 * V2.  An increase in A2 (pipe expansion) 
means that V2 must be lower to maintain the same flow rate.  When V1 > V2, 
then the change in pressure (Delta P) is positive due to  P2 - P1 = Delta P = 
(V1^2 - V2^2)/2.  I know you have seen the equations to prove it, but I think 
your idea of faster flow is always high pressure is holding you back.  With a 
little manipulation of Bernoulli's equation, one can show that pressure change 
in a straight pipe is related to the density of the liquid, the flow rate of 
the liquid and the diameters of the pipes by (I hope this makes sense here)   
P2 - P1 = (8 * rho * Q^2/pi^2) * (1/D1^4 - 1/D2^4).  Here it is easy to see 
that with a constant flow rate, the change in pipe diameters is the driving 
force to the pressure change.  As for physically explaining this, I do not 
think I did that, but I hope this helps.

Response #:  2 of 3
Author:      mooney
Text:        The thing to focus on here is the kinetic energy of a given 
volume of fluid as it passes from the large-diameter pipe to the small 
diameter pipe.  In the large pipe, the volume is moving more slowly and has 
less kinetic energy than it will have when it gets into the small pipe.  So, 
the volume must be ACCELERATED as it moves from one pipe to the other, and 
this requires a force.  In fact, it requires a larger force from the fluid 
still in the large pipe that will more than balance the force acting backwards 
from the fluid in the small pipe, so then net force on the volume of fluid 
will be sufficient to accelerate it to  its higher velocity.  The only place 
that force can come from is the pressure (pressure, as you probably know, is 
just force per unit area).  What we need here is actually, a larger force per 
unit VOLUME, since this is equivalent to an acceleration (for an 
incompressible fluid, volume and mass are proportional.) 

Response #:  3 of 3
Author:      dipper
Text:        Both of the above answers are very good.  I would just like to 
add this example for you to picture.  To get honey from a squeeze bottle, the 
bigger the hole, the less you have to squeeze (and the more you can eat).