A math or a simple fluid problem?

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In summary, the conversation is about solving the height of a tank as a function of time, where the inflow is a+bsin(wt) and the outflow is proportional to the square root of the height, H. A differential equation has been set up, but the problem is not yet solved. The conversation also discusses the correct assumptions for the inflow and outflow and the need to find the radius in terms of height in order to simplify the equation.
  • #1
hanson
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Hi all!
I am solving for the height of a tank as a function of time.
The tank has a constant inflow of a and is subjected to small fluctuation of bsin(wt).
So the inflow is simply a+bsin(wt).
The outflow should be proportional to the square root of the height, H.
So outflow = c*sqrt(H)
Therefore the below differential equation is obtained with k=the area of the tank:
[tex]\frac{a+bsinwt-c\sqrt{H}}{k}=\frac{dH}{dt}[/tex]


but the problem is that I don't know how to solve this ODE...
Can anyone solve the problem?
 
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  • #2
Have you been given this equation or have you set it up by yourself?
 
  • #3
I set it up myself. And I have show my deduction:
The tank has a constant inflow of a and is subjected to small fluctuation of bsin(wt).
So the inflow is simply a+bsin(wt).
The outflow should be proportional to the square root of the height, H.
So outflow = c*sqrt(H)
Therefore the above differential appears.
Am i correct?
 
  • #4
hanson said:
I set it up myself. And I have show my deduction:
The tank has a constant inflow of a and is subjected to small fluctuation of bsin(wt).
So the inflow is simply a+bsin(wt).
The outflow should be proportional to the square root of the height, H.
So outflow = c*sqrt(H)
Therefore the above differential appears.
Am i correct?

I am not sure about your assumption of the outflow. I would revise that.
 
  • #5
this problem really has nothing to do with fluids..its just a math problem..

inflow is a+bsin(wt) correct.
outflow you said is proportional to square root of the height, h..
is then right too.. c*sqrt(h)...

now if you divide volume by cross sectional area you get height.. I am thinking you need to find the radius in terms of height also by rearranged the volume equation... that way your equation will be composed only of H terms.
 

1. What is a math or a simple fluid problem?

A math or a simple fluid problem is a type of scientific problem that involves mathematical equations and concepts to solve problems related to fluid mechanics. It is a branch of physics that deals with the study of fluids (liquids and gases) and their properties, behavior, and interactions with other materials.

2. What are some examples of math or simple fluid problems?

Some examples of math or simple fluid problems include calculating the velocity of a fluid in a pipe, determining the pressure of a gas in a container, and solving for the flow rate of a liquid through a channel.

3. How do scientists approach solving math or simple fluid problems?

Scientists approach solving math or simple fluid problems by first defining the problem and identifying the known variables and equations that can be used to solve it. They then apply mathematical principles and equations to analyze and solve the problem, often using computer simulations and experiments to verify their solutions.

4. What are the real-world applications of math or simple fluid problems?

Math or simple fluid problems have numerous real-world applications, including designing efficient water and gas pipelines, optimizing air and water flow in engines and turbines, and understanding weather patterns and ocean currents. They are also crucial in the development of technologies such as airplanes, submarines, and space shuttles.

5. What skills are needed to solve math or simple fluid problems?

To solve math or simple fluid problems, scientists need strong mathematical skills, including algebra, calculus, and differential equations. They also need a solid understanding of fluid mechanics principles and the ability to apply them to real-world situations. Critical thinking, problem-solving, and attention to detail are also important skills for successfully solving these types of problems.

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