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Flow rate in pipe puzzle

Cotton_Candy
Posts: 299
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7/16/2015 11:01:25 AM
Posted: 1 year ago
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Can anyone explain this mysterious change ? O_O
DizzyKnight
Posts: 19
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7/16/2015 12:44:39 PM
Posted: 1 year ago
At 7/16/2015 11:01:25 AM, Cotton_Candy wrote:
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Can anyone explain this mysterious change ? O_O

I am very uneducated in this field, but I will take a guess here. The equation states that
V = Av, where V is the volumetric flow rate, A the cross-sectional area, and v the velocity.

In the pipe example, you are assuming that the rate of discharge V is independent of the pipe's radius and by extension its cross-sectional area. In other words, you pour the same amount of water in the pipe each second regardless of how big the pipe is. Since V is constant, v must get bigger as you decrease A by restricting the pipe.

However in the tank example, the size of the orifice directly determines V, the bigger the orifice is, the larger V is going to be (more water will flow out of a bigger hole per second compared to a small hole). So it would makes sense for v to stay constant as you make the orifice larger, since the increase in A is countered by the increase in V.
Floid
Posts: 751
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7/16/2015 12:45:17 PM
Posted: 1 year ago
At 7/16/2015 11:01:25 AM, Cotton_Candy wrote:
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Can anyone explain this mysterious change ? O_O

Conservation of volume flow rate does not apply to your orifice in a water tank problem (you want to use Bernoulli's equations for that).
v3nesl
Posts: 4,505
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7/16/2015 1:29:35 PM
Posted: 1 year ago
At 7/16/2015 11:01:25 AM, Cotton_Candy wrote:
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Can anyone explain this mysterious change ? O_O

I don't think that's right. If you poke a small hole in the bottom of a water tank, water will shoot out further than if you poke a large hole, so the velocity out of the hole is not the same. If you have a water system served by a water tower, the spigot in your house is effectively the orifice you speak of, and clearly the velocity out of your spigot can be controlled.

So I'm sure you have some specific example in mind, but you probably need to spell it out in more detail.
This space for rent.
Saint_of_Me
Posts: 2,402
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7/16/2015 2:24:58 PM
Posted: 1 year ago
At 7/16/2015 11:01:25 AM, Cotton_Candy wrote:
So we all know that due to the conservation of volume flow rate, reducing the diameter of a hose pipe would increase the velocity of the water flow.(A*V is conserved)
But when the are of an orifice near the bottom of a water tank is reduced the velocity remains the same! Can anyone explain this mysterious change ? O_O

Go here to find any sort of equation you desire regarding fluid flow through pipes and other conduits of varying dimensions...................

http://web2.clarkson.edu...
Science Flies Us to the Moon. Religion Flies us Into Skyscrapers.
kp98
Posts: 729
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7/16/2015 5:49:04 PM
Posted: 1 year ago
Hmph. This thread is in the wrong place. It should be in religion because the answer is that it's God that makes it flow that way so it's impious to ask why.