Re: Question about Poiseuille's formula.

From: Robert Clark (rgregoryclark_at_yahoo.com)
Date: 11/14/04 

Date: 14 Nov 2004 02:23:54 -0800

"George Dishman" <george.dishman@clara.co.uk> wrote
>
> His idea is to pump fuel to a rocket during liftoff.
>
> http://www.cdli.ca/CITE/sts_ascent.htm
>
> "By the end of the eighth second, ... the orbiter's
> three main engines and two solid rocket boosters
> have consumed more than 680,000 kilograms (1.5
> million pounds) of fuel ..."
>
> http://www-formal.stanford.edu/jmc/progress/hydrogen.html
>
> "Liquid hydrogen has a density of 0.07 grams per [cc]"
>
> Through a 300cm diameter pipe, that's a mean speed of
> 17km/s or Mach 50. He needs a bigger pipe, probably
> more than 5m diameter to get Mach 0.2.
>
> "By 45 seconds into the flight, the shuttle breaks
> the sound barrier. A minute into the flight, the
> pressure on the orbiter decreases and so the shuttle
> engines are returned to full power. At this point,
> the shuttle is traveling at an incredible 1,609
> kilometers per hour (1,000 mph) or about Mach 1.5.
> By the end of the next minute, it will triple this
> speed!
>
> Two minutes into the ascent, the shuttle is about
> 45 kilometres (28 miles) above the earth's surface
> and is traveling nearly 5000 kilometers per hour
> (3,000 mph)."
>
> With a big enough pipe, the fluid might be travelling
> relative to the pipe at less than Mach 1, but the
> ground end of the pipe is being rolled out at about
> Mach 4.5 with the fluid being pushed into it at Mach 5!
>
> When the pipe disconnects, the shuttle would be perhaps
> 200km down range. The pipe would contain 275 million kg
> of liquid hydrogen (and still be winding out) and the
> shuttle end would fall from a height of about 45km. I
> wouldn't like to be underneath.
>
> George

 I discussed this question of the speed of the fluid inside the pipe
in a post copied below. Note though the amount you cited of 1.5
million pounds in the first 8 seconds includes the weights of the much
heavier liquid oxygwn and solid rocket fuel consumed.

===============================================================
From: Robert Clark (rgregoryclark@yahoo.com)
Subject: Re: Further on "Rockets not carrying fuel."
Newsgroups: sci.astro, sci.physics, sci.mech.fluids, sci.engr.mech,
sci.space.policy
Date: 2004-11-06 13:45:30 PST
 

Some correspondents have raised a couple of questions about the
proposal. One is the suggestion that the fuel would be moving
supersonically. Note though it is important to distinguish between the
speed of the gas within the pipe and the speed of the pipe and rocket
through the air. The speed of the gas within the pipe need not be
supersonic. This
objection was also raised during the discussion on sci.astro last year
to which I offered this calculation:

"At a flow rate for the liquid hydrogen of 465 lbs/s, that's 211 kg/s.
With liquid hydrogen density of 71 kg/m^3, that's about 3 m^3. So for
a .3m diameter pipe that comes to about 3/(.3 x .3) or 33 m/s."

 This though was based on the fuel requirements for the shuttle
engines and liquid hydrogen and with the thrust coming from the
combination of the hydrogen and oxygen. For the thrust coming only
from the momentum of the gas through the pipe, the velocity might be
able to be determined from the thrust equation: Thrust = dm/dt * v.
Another possibility might be to use Poiseuille's formula.
 Another question raised was of the rocket moving faster than the
sound speed of the pipe material, thus causing the pipe to snap. But
for the materials I'm envisioning, such as carbon fibers or nanotubes,
their sound speed is significantly higher than orbital velocity. See
for example the table on this page:

STRUCTURAL MATERIALS
http://www.islandone.org/LEOBiblio/SPBI1MA.HTM

 Another possibility may actually be diamond which would have a
similar sound speed to the buckyball material in the table, and in
fact should now be available in large amounts in industrially produced
form:

Large Diamonds Made From Gas Are The Hardest Yet.
http://www.sciencedaily.com/releases/2004/02/040226070311.htm

  Bob Clark

===============================================================

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