The period of water oscillating in a U-tube

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The professor explains that when calculating the period of water oscillating in a U-tube, the effective "length" of the water column should be greater than the average of the lengths around the inside and outside. This adjustment accounts for the differing speeds of water, as the outer water moves faster than the inner water. Since kinetic energy is proportional to the square of the speed, simply averaging the lengths will not accurately reflect the total kinetic energy of the system. Understanding this concept is crucial for accurate predictions of oscillation periods. The discussion emphasizes the importance of considering the volume and kinetic energy relationships in fluid dynamics.
TheLil'Turkey
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In the following lecture (starting at 21:00), the professor says that when predicting the period of water oscillating in a U-shaped tube, that the "length" of the water column that you should use should be greater than the average of the length around the outside and around the inside. Can someone explain this? Thanks.
 
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The length is used to calculate the volume of the water, and the volume is used to calculate the kinetic energy of the water if it's moving with a speed v.

The water on the outside will be moving faster than the water on the inside, and because the kinetic energy depends on the square of the speed, the sum won't add up to the kinetic energy of the water in the middle.
 
willem2 said:
The length is used to calculate the volume of the water, and the volume is used to calculate the kinetic energy of the water if it's moving with a speed v.

The water on the outside will be moving faster than the water on the inside, and because the kinetic energy depends on the square of the speed, the sum won't add up to the kinetic energy of the water in the middle.
Great explanation. Thanks.
 

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