ShmoopTube

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And here's your shmoop du jour brought to you by hail storms which are perfect [A hail storm on a road]

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for when you want your brand new car to resemble a golf ball a vertical pipe of

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uniform diameter carries water a freak hailstorm punctures two clean holes in [hail storm creates two halls in a pipe]

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the pipes and streams of water began to shoot out which of the following

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statements is true water spouting from the top hole has a higher velocity than

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water spouting from the bottom hole or the pressure at both holes is equal and

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here the potential answers... Okay so hail doesn't usually [Man with a white beard and hair in the clouds]

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move horizontally but like we said this is at freak hail storm, so freaky that it

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doesn't have to obey the laws of physics but that doesn't mean we get the same [Car driving down a road in a hailstorm and person whistles stop!]

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luxury no we have to obey the law and right now we're dealing with officer

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Bernoulli. Bernoulli's principle is an extension of the law of conservation of

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energy it states that at any two points in a flowing fluid the total energy is [example of Bernoulli's principle]

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the same well the equation is the pressure energy plus the potential

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energy plus the kinetic energy at one point equals that at the second point

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and because we're dealing with fluids instead of using M for mass, the equation

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uses row for the mass per volume now in this question the pressure at each hole

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is the same it's just the pressure from the atmosphere since the pipe is in [Arrows pointing to a pipe]

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providing pressure at the holes, so the second statement is true well to

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determine if the first statement is also true let's look at the Bernoulli [Man jumps and drags the Bernoulli principle down]

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principle again yikes we're not going to lie it's a little intimidating but we

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can make it a little easier on the eye on the brain first of all since the [Man staring at Bernoulli's principle with googly eyes]

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pressure at both points is the same we can take out the P sub 1 and the P sub 2

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now we have an equation that just deals with potential and kinetic energy or if

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we think about this scenario we can set the height of the lower hole to zero and [liquid flowing out of two holes in a pipe]

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state that the higher hole is at a certain height of H after all we don't

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really care what happens further down the pipe we'll let whoever has to fix

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this lousy piece of metal worry about that so let's say that the sub 1 part of [Man screams while repairing the pipe]

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the equation is for the lower hole and the sub 2 part for the upper one well if

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the potential energy of the lower hole is 0 the equation now looks like

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this looking at this equation we can see that the kinetic energy at the lower

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point has to be higher at the higher point some of the energy is still stored

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as potential energy so the kinetic energy at the higher point has to be

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lower than it is lower down the pipe and that means that the velocity at the

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higher point can't be greater than at the lower point so the first statement in

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the question is false and that means the correct answer is B. careful if the

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weather turns ugly as if rain and wind and lightning aren't enough sometimes [Man walking in a hailstorm]

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mother nature decides to throw falling objects at our heads it's like payback

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for that one time we forgot to recycle a soda can [Soda can hits man's head as he crosses the road]

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