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Re: fluid flowing between 2 tanks



At 04:49 PM 11/26/02, Carl Mungan, you wrote:
Consider a tank with a drain pipe in its bottom opening into an
identical tank directly below the first:

| |
|____ ____|
||
||
| || |
|__________|

The drain pipe is below the water level in the lower tank.

Let point 1 be on the free air-water surface of the upper tank and
let point 2 be on the free air-water surface of the lower tank.

How does the speed v1 compare to v2?

Answer 1. Use the equation of continuity. Both tanks have the same
cross-sectional area A. Hence v1 = v2. In Torricelli problems, this
speed is taken to be nearly zero if A is big enough.

Answer 2. Use Bernoulli's equation where P1 = P2 = P_atm. Therefore
v2^2 - v1^2 = 2gh, where h is the difference in heights of water in
the two tanks.

Obviously both answers cannot be right. I suspect the second is wrong
and that there is *necessarily* some kind of turbulent or viscous
loss of speed. Basically we converted gravitational PE into KE and
then got rid of it somehow.

I am worried about typical end-of-chapter problems involving siphons,
Torricelli tanks, etc where clearly one is supposed to ignore such
losses. I can only rationalize this if the losses *only* occur after
the water rushes out into the lower tank.

In any case, this kind of thing makes me nervous about quickly
slapping Bernoulli's equation down during a problem solution. Carl
--
Carl E. Mungan, Asst. Prof. of Physics 410-293-6680 (O) -3729 (F)
U.S. Naval Academy, Stop 9C, Annapolis, MD 21402-5026
mungan@usna.edu http://physics.usna.edu/physics/faculty/mungan/

Carl is describing the head loss which is typically considered in two parts:
1) the sum of Moody type frictional losses which are associated with
wall friction in smooth straight tubes. A Moody chart is a semi-empirical
plot of this frictional loss as a function of Reynolds number Re and a
pipe roughness number Epsilon/d
The plot uses a non dimensional number, the Darcy friction factor f
which is
f = hsubf /[(L/d)(V^2/2g)]
for L the total pipe length, V average velocity d pipe int. diameter

2) The second part comprises minor losses due to valves, bends,
elbows, changes of pipe diameter, inlets, exits. A semi empirical
factor K is defined as
K = hsubm / (V^2/(2g))

Ref: REA Fluid Mechanics Fogel/Cimbala
Brian Whatcott
Altus OK Eureka!

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.