# Homework Help: Gauge pressure LONG AND HARD

1. Nov 7, 2004

### Tycho

In a bourbon distillery plant, the refined product, approximated as 40% by weight ethanol, 60% by weight water, is pumped through a plumbing system. At the OUTLET, where the inner diameter of the pipe is 5.08cm, the product fills an aluminum open cylinder (Diameter .442m, height 1.26m) in 98.9 seconds. At the inlet of this pipe the diameter is 7.62 cm and the pipe is 3.85m above the cylinder. the density of the product is 922kg/m^3

a) what is the outlet speed of the product?

b) what is the gauge pressure at the inlet of the pipe (diameter 7.62cm)

WHEW! okay, question a....
the outlet speed: it fills an aluminum open cylinder in 98.9 seconds. first step, find the volume of the cylinder? the volume of a cylinder is given by: pi*R^2*length, right? so: pi(.221^2)1.26m = .19m? my units are wrong, and the volume seems AWFULLY small.
lets roll with it, though...
it fills this volume in 98.9 seconds. (1.65 mins). Now, I have the volume filled, and the time it took. (should be .019L/1.65min) how do i get this into useable figures (like L/min)?

now for question b:
the gauge pressure...
it wants the guage pressure at the inlet of the pipe. (diameter 7.62cm)
I can't do this until i get the outlet speed, correct? even if i had the outlet speed, i'm not sure how to obtain the gauge pressure?

i know this is really long and laborious.... but i've been working pretty hard on this, and any help would be appreciated. thank you all.

2. Nov 7, 2004

### ashfaque

You have to use Bernoulli's Equation
And also this one : Volume Flow Rate = Area * Flow Speed ( Q = AV )
also Gauge Pressure = Abosolute Pressure - Atmospheric Pressure
at open surfaces gauge pressure = 0

3. Nov 7, 2004

### Tycho

Bernoulli's eqn
okay, i started to write it out, but with all the subscripts and superscripts, it was looking NARSTY!

Any way you could start me out on it? i'm still drawing a blank.

btw, thanks for ALL of your assistance. you've been really nice and extremely helpful

4. Nov 7, 2004

### ashfaque

3.85 m above of what?
from the top of the cylinder or from the bottom ....?
u have the figure right?

Last edited: Nov 7, 2004
5. Nov 7, 2004

### Tycho

It says it is 3.85m ABOVE the cylinder

6. Nov 7, 2004

### pitchharmonics

tycho brache, check pm

7. Nov 7, 2004

### ashfaque

sorry for not reading ur question carefully :)

Volume of Cylinder / Time = Volume flow rate(Q)
Q = AV
A = outlet cross sectional area of the pipe
V = the outlet speed of the product
--------that's part a ---------

8. Nov 7, 2004

### Tycho

thanks! I was missing Q. that solved THAT problem!
okay so gauge pressure is absolute pressure - atmospheric pressure. since atmospheric pressure should be approximately = to 1, then it is absolute pressure -1? how do you find absolute pressure?

9. Nov 7, 2004

### ashfaque

whu says atmospheric pressure == 1?
it is 101325 Pa
:)
and for this problem u donot even need to think abt atmospheric pressure
at the atmosphere level the gauge presure will read zero

10. Nov 7, 2004

### Tycho

lol okay, so what next? gauge pressure will = absolute pressure?
what is the absolute pressure?

11. Nov 7, 2004

### ashfaque

inlet
\
\
\
\
\outlet
| |
| |
| |
| |
~~~~

apply bernoulli's eqn at inlet and outlet
:)