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The Pissing Bucket


pmccarthy
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This was a favourite question of the noted hydrologist, George J. Pissing, and is still often asked of graduate students during oral exams. Consider a bucket of water with two holes through which water is discharged. Water can be discharged from a hole “B” at the bottom of a bucket which is some distance “d” below the water surface, or it can be discharged from a downspout which starts at the top “T” and has its opening at the same distance “d” below the water surface. If we neglect any friction effects the water coming out of hole “B” has

a) more speed than the water coming out of the down spout

b) less speed than the water coming out of the downspout

c) the same speed as the water coming out of the downspout.

 

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The answer has to be "C", isn't the reference called Torricelli's Law?

 

Somewhat unrelated - but - I can remember my Dad constructing a large overhead water tank on our farm, where the input pipe was connected to the centre of the bottom of the tank, instead of going up the side, and over the top.

This was to improve the fill rate for the water, as there's less head pressure for the fill pipe with this style of construction.

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21 hours ago, onetrack said:

… I can remember my Dad constructing a large overhead water tank on our farm, where the input pipe was connected to the centre of the bottom of the tank, instead of going up the side, and over the top.

This was to improve the fill rate for the water, as there's less head pressure for the fill pipe with this style of construction.

Even more thread drift: forty years ago I installed my water supply, pumping from a bore on the flat thru a pipe into the bottom of the tank on the top of the hill. That pipe also supplied all the taps on the place. 

I had very experienced water “experts” advise me to fill the tank via a pipe into the top, because pushing water into the bottom required lots more energy, because it was working against the 22 tonne weight of the tank’s contents….

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Less till it's full then it's the same. If you used a syphon that would be a different matter. Pretty difficult to organise. Trouble with the bottom connection it would drain if the pump was inactivated and it could run back. it would also drain back(potentially) if the siphon wasn't broken   People often disclose the inadequacy of their science teachers. (like Tony abot),  At present many scientists are being vilified on line. Nev.

Edited by facthunter
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Onetrack got it right first time. 

The answer is: c. The speed of the water depends on the pressure head, or depth below the free surface. The pressure heads for both outlets are the same, so water speeds are the same. Or we can look at the problem this way: Move the spout around and attach it to the hole. If the water comes out of the downspout fastest it would overwhelm the current from the hole and force its way back into the bucket at B, so you would have a perpetual motion machine with water running from T to B.

If the water comes out of the bottom hole fastest you also have perpetual motion with water flowing the other way. To avoid perpetual motion (and conserve energy), the water flowing out of both the hole and the downspout must have equal speeds.

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On 19/10/2021 at 2:48 PM, onetrack said:

Torricelli's Law

A clepsydra is a clock that measures time by the flow of water. It consists of a pot with a small hole at the bottom through which the water can escape. The amount of escaping water gives the measure of time. As given by the Torricelli's law, the rate of efflux through the hole depends on the height of the water; and as the water level diminishes, the discharge is not uniform. A simple solution is to keep the height of the water constant. This can be attained by letting a constant stream of water flow into the vessel, the overflow of which is allowed to escape from the top, from another hole. Thus having a constant height, the discharging water from the bottom can be collected in another cylindrical vessel with uniform graduation to measure time. This is an inflow clepsydra.

220px-Clepsydra.jpg

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clepsydra (n.)

"ancient Greek water-clock," 1640s, from Latinized form of Greek klepsydra, from stem of kleptein "to steal, to hide" + hydor "water".

A device for measuring time by the amount of water discharged from a terra cotta vessel into another through a small hole (it works on the same principle as the hourglass). It was used in classical Athens to measure smaller segments of time (probably 30 minutes or less) than the sundial and especially to regulate the allowed time for speeches in tribunals as six minutes seems to have been a typical time to drain the vessel.

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1 hour ago, old man emu said:

It was used in classical Athens to measure smaller segments of time (probably 30 minutes or less) than the sundial and especially to regulate the allowed time for speeches in tribunals as six minutes seems to have been a typical time to drain the vessel.

Ahhh! Of course! I was wondering why the ancients would need an accurate measure of time.

Should have realised how age-old the problem of hot air really is!

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Bet you wished you'd installed a pissaphone when you built your plane.

Pissaphone | Key Aero

 

Air Board specification from May 1918, for the, AERO URINARY APPARATUS, MARK I.

The device has the following general description:

General Description.—The apparatus consists of a rubber funnel attached at its smaller (and lower) end to a length of rubber tube, terminating in an elliptic container. Attached to the top of the funnel is an internal conical sleeve of soft rubber, the annular space between funnel and sleeve forming a trap preventing any back-flow from the connecting tube. A non-return valve of the rubber flap type is provided in the upper end of the container and a screwed vulcanite or ebonite drain plug in the lower end, the cap of the drain plug being retained by a short chain. Two rubber lugs attached to the funnel are adapted to button to an adjustable waistbelt, which supports the apparatus in use, and a suspensory bandage is attached to the lugs and to the belt by tapes. An adjustable elastic strap keeps the container against the leg of the wearer.

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5 hours ago, old man emu said:

Bet you wished you'd installed a pissaphone when you built your plane.

Pissaphone | Key Aero

 

Air Board specification from May 1918, for the, AERO URINARY APPARATUS, MARK I.

The device has the following general description:

General Description.—The apparatus consists of a rubber funnel attached at its smaller (and lower) end to a length of rubber tube, terminating in an elliptic container. Attached to the top of the funnel is an internal conical sleeve of soft rubber, the annular space between funnel and sleeve forming a trap preventing any back-flow from the connecting tube. A non-return valve of the rubber flap type is provided in the upper end of the container and a screwed vulcanite or ebonite drain plug in the lower end, the cap of the drain plug being retained by a short chain. Two rubber lugs attached to the funnel are adapted to button to an adjustable waistbelt, which supports the apparatus in use, and a suspensory bandage is attached to the lugs and to the belt by tapes. An adjustable elastic strap keeps the container against the leg of the wearer.

 

 

Boris has a bigger one.

Pissometer.jpg

Edited by willedoo
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