

Pressure rise in pipe expansion
Name: ericschotz
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
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.
Replies:
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 crosssectional 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.
cdmurphy
The thing to focus on here is the kinetic energy of a given
volume of fluid as it passes from the largediameter 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.)
mooney
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).
dipper
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Update: June 2012

