Finding the period of oscillation of a u-tube w/ water (almost solved)?

In summary, the conversation discusses using the energy method to find the natural period of oscillation of fluid in a u-tube manometer. The natural period is found to be t=2PI(l/2g)^(1/2) where L is the length of the fluid column. The speaker expresses confusion about the presence of L in the equation and mentions a lecture that may provide more information.
  • #1
jaron_denson
7
0

Homework Statement


Using the energy method( setting potential energy= kinetic energy) show that the natural period of oscillation of the fluid in a u-tube manometer is t=2PI(l/2g)^(1/2) where L is the length of the fluid column.
2. The attempt at a solution
2attempt.jpg


So as you can see I do not know where the L is coming from, although i just fuged it in when I wrote what wn^2=2g/L. Where is the L coming from? wn^2 should equal coefficents of x divided by coefficents of xprime (aka velocity).
 
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  • #2
You might find this lecture interesting at just about the 21:00 minute mark.

 
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  • #3


I would like to address the confusion about the length (L) in the equation for the natural period of oscillation of a u-tube manometer. The length (L) in this equation refers to the length of the fluid column in the u-tube. This length is a crucial factor in determining the natural period of oscillation because it affects the potential energy of the fluid and its relationship with the kinetic energy.

To better understand this, let's break down the equation. The natural period of oscillation is given by t=2PI(l/2g)^(1/2), where l is the length of the fluid column and g is the acceleration due to gravity. This equation is derived using the energy method, where we equate the potential energy of the fluid with its kinetic energy. This results in an equation where the natural frequency (wn) is equal to (2g/L)^(1/2).

Now, let's look at the units of this equation. We know that the units of natural frequency are radians per second (rad/s). The units of acceleration due to gravity are meters per second squared (m/s^2). And the units of length are meters (m). By plugging in these units into the equation, we can see that the units of L must be meters (m) for the equation to be dimensionally consistent.

In conclusion, the length (L) in the equation for the natural period of oscillation of a u-tube manometer represents the length of the fluid column and is crucial in determining the natural frequency of oscillation. I hope this helps clarify any confusion and allows for a better understanding of the concept.
 

Related to Finding the period of oscillation of a u-tube w/ water (almost solved)?

1. What is the purpose of finding the period of oscillation of a u-tube with water?

The period of oscillation of a u-tube with water is a measure of how long it takes for the tube to complete one full cycle of back-and-forth motion. This measurement is important in understanding the behavior of fluids and can also be used to calculate other properties such as density and viscosity.

2. What factors affect the period of oscillation in a u-tube with water?

The period of oscillation in a u-tube with water can be affected by several factors, including the length and diameter of the tube, the amount of water present in the tube, and the presence of any external forces such as friction or air resistance.

3. How is the period of oscillation calculated for a u-tube with water?

The period of oscillation can be calculated by measuring the time it takes for the water to complete one full cycle of back-and-forth motion, also known as the time period. This value can then be used in the formula T = 2π√(l/g) where T is the period, l is the length of the tube, and g is the acceleration due to gravity.

4. Can the period of oscillation be affected by changes in the environment or conditions?

Yes, the period of oscillation can be affected by changes in the environment or conditions. For example, changes in temperature or pressure can alter the density and viscosity of the water, thereby affecting the period of oscillation. Additionally, changes in the external forces acting on the u-tube can also impact the period of oscillation.

5. How can the period of oscillation of a u-tube with water be used in real-world applications?

The period of oscillation of a u-tube with water has many practical applications. It is commonly used in hydrodynamics to study the behavior of fluids and can also be used to measure properties such as density and viscosity. Additionally, the period of oscillation can be used to design and optimize devices that rely on fluid movement, such as pumps and turbines.

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