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Dave Nichol
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 Posted: Sun Aug 17, 2003 3:44 am Post subject: simple fluids problem |
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Imagine a fire engine attempting to fill an elevated stationary tank
(open to atmosphere) that is 3/4 full of water. Which takes more work:
to pump water in through the bottom of the tank or to pump up through
a hose into the top of the same tank?
My figuring is that it is the same either way - the weight of the
column of water that the pump is working against is the same in each
case (disregarding friction friction loss in the hose).
Assuming I>m correct, are there any ideas about how to convince a
group of firefighters of the principles involved. They swear it takes
longer if you have to pump into the bottom because you have the weight
of all that water in the tank. Any tabletop experiments that could
demonstrate this?
thanks for your help,
frustrated firefighter |
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David Wilkinson
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| Posted: Sun Aug 17, 2003 10:20 am Post subject: Re: simple fluids problem |
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The gauge pressure required at pump outlet is the total head of water above
it. If the pump is level with the bottom of the tank then the pressure head
is 0.75H to pump in at the bottom with tank height H.
If you could pump the water in 3/4 of the way up the tank then the pressure,
and work done, would be the same. However, if you have to pump the water up
to the top of the open tank and over the edge then the head is the full
height H and you do 4/3 times as much work.
This neglects friction and head losses in the pipe, tank and fittings.
"Dave Nichol" <dave@rosiehippo.com> wrote in message
news:1de3ef03.0308161444.7fd6992e@posting.google.com...
[quote]Imagine a fire engine attempting to fill an elevated stationary tank
(open to atmosphere) that is 3/4 full of water. Which takes more work:
to pump water in through the bottom of the tank or to pump up through
a hose into the top of the same tank?
My figuring is that it is the same either way - the weight of the
column of water that the pump is working against is the same in each
case (disregarding friction friction loss in the hose).
Assuming I>m correct, are there any ideas about how to convince a
group of firefighters of the principles involved. They swear it takes
longer if you have to pump into the bottom because you have the weight
of all that water in the tank. Any tabletop experiments that could
demonstrate this?
thanks for your help,
frustrated firefighter[/quote] |
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JG
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| Posted: Sun Aug 17, 2003 11:15 pm Post subject: Re: simple fluids problem |
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[quote]If you could pump the water in 3/4 of the way up the tank then the
pressure,
and work done, would be the same.
[/quote]
I believe this incorrect... in both cases pumping the water from the bottom
up will result in less work. Although, probably it won>t be a very large
amount.
If your pump is connected to the bottom of the tank filling the first inch
of water will require less work than the second inch... and so on (because
the pressure is increasing at the end of the tank as you fill it up). If you
setup the hose to fill the tank at 3H/4, the work required to fill each inch
of the tank will be the same and only reaches the value of the first method
when it has reached the same amount of water (because both heads will be the
same).
My $0.02,
JG |
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David Wilkinson
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| Posted: Mon Aug 18, 2003 12:18 am Post subject: Re: simple fluids problem |
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"JG" <admin@remove-this-bit.inqu.net> wrote in message
news:KbmdnbEJZuSkVaKiXTWJgA@comcast.com...
[quote]If you could pump the water in 3/4 of the way up the tank then the
pressure,
and work done, would be the same.
I believe this incorrect... in both cases pumping the water from the
bottom
up will result in less work. Although, probably it won>t be a very large
amount.
If your pump is connected to the bottom of the tank filling the first inch
of water will require less work than the second inch... and so on (because
the pressure is increasing at the end of the tank as you fill it up). If
you
setup the hose to fill the tank at 3H/4, the work required to fill each
inch
of the tank will be the same and only reaches the value of the first
method
when it has reached the same amount of water (because both heads will be
the
same).
My $0.02,
Nope. Afraid not JG.[/quote]
If you pump in at the bottom you pump against a head of 3H/4 to begin with
rising to H at the end when the tank is full. If you pump in 3/4 of the way
up you have a head of 3H/4 in the supply pipe and atmospheric, or zero
gauge, at the tank end so you still have to pump against a head of 3H/4
initialy. This rises to a head of H as the tank fills up. The pressure and
energy requirements of the two cases are exactly the same, ignoring friction
and losses in fittings etc.
The way to do more work is to pump all the water up to height H and pour it
into the tank from the top, over the edge. The initial power required is 4/3
of the other two methods but tends to the same value as the water reaches
the top. The extra work in this case is turned into heat when the water
falls from height H back to the level in the tank, so the water is slightly
warmer when the tank is full. |
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JG
Guest
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| Posted: Mon Aug 18, 2003 1:09 am Post subject: Re: simple fluids problem |
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[quote]Nope. Afraid not JG.
[/quote]
You are correct David... sorry.
I misread the post... I thought that the tank was empty at first and it was
going to be filled to 3H/4. But instead it is 3H/4 initially and H at the
end.
Honest mistake... :-)
-JG |
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