How to find the derivative for calculating water flow rate?

In summary, we have a tank of water with a constant cross-sectional area of 56 ft2 and an orifice of constant cross-sectional area of 1.5 ft2. The initial height of the water is 20 ft and its height t seconds later is given by the equation 2h^(1/2) + (1/23)t - 80^(1/2). The question asks for the rate at which the height of the water was decreasing when it reached 8 ft. The answer should be rounded to two decimal places. There seems to be confusion over whether the task is to find the derivative or solve the equation, as well as uncertainty over the meaning of 'h' in the given formula.
  • #1
miaprincess22
1
0
This due today!

Water flows from a tank of constant cross-sectional area 56 ft2 through an orifice of constant cross-sectional area 1.5 ft2 located at the bottom of the tank.
Initially the height of the water in the tank was 20 and its height t sec later is given by the following equation.

2h^(1/2) + (1/23)t -80^(1/2)

How fast was the height of the water decreasing when its height was 8 ft? (Round your answer to two decimal places.)

I thought I was just supposed to find the derivative. I keep getting wrong.
 
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  • #2
miaprincess22 said:
This due today!

Water flows from a tank of constant cross-sectional area 56 ft2 through an orifice of constant cross-sectional area 1.5 ft2 located at the bottom of the tank.
Initially the height of the water in the tank was 20 and its height t sec later is given by the following equation.

2h^(1/2) + (1/23)t -80^(1/2)

How fast was the height of the water decreasing when its height was 8 ft? (Round your answer to two decimal places.)

I thought I was just supposed to find the derivative. I keep getting wrong.
Yes, you are asked for the derivative of h. One problem you have is that what you give is NOT an "equation"! What is that expression supposed to be equal to? Is 'h' in that formula supposed to be the height?
 

1. What is the concept of related rates in water flow?

Related rates in water flow is a mathematical concept that involves determining the rate of change of one variable with respect to another variable in a system where the variables are related. In the context of water flow, this means calculating how the rate of change of one water-related variable, such as flow rate or volume, affects the rate of change of another variable, such as water depth or pressure.

2. How is the chain rule used in related rates problems involving water flow?

The chain rule is a fundamental concept in calculus that is used to calculate the derivative of a composite function. In related rates problems involving water flow, the chain rule is used to find the rate of change of a variable that is indirectly related to another variable through a series of intermediate variables. This is necessary because the rate of change of one variable in the system affects the rate of change of other variables, creating a chain of relationships.

3. Can you provide an example of a related rates problem involving water flow?

Sure, an example of a related rates problem involving water flow could be a tank being filled with water at a constant rate of 5 liters per minute. The tank has a leak at the bottom, and the water is draining out at a rate of 2 liters per minute. How fast is the water level rising in the tank when it is half full?

4. How can calculus be applied to real-life situations involving related rates and water flow?

Calculus is a powerful mathematical tool for solving real-life problems, and it has many applications in related rates and water flow situations. By using calculus concepts such as derivatives and the chain rule, we can calculate important information about the behavior of water systems, such as the rate of change of water levels, flow rates, and pressure. This information can be used in various fields, including engineering, hydrology, and environmental science.

5. Are there any limitations to using related rates in water flow situations?

While related rates can be a useful tool for analyzing water flow systems, there are some limitations to its application. One limitation is that it assumes a constant rate of change, which may not always be the case in real-life situations. Additionally, related rates problems can become increasingly complex when multiple variables are involved, making them more challenging to solve accurately. Therefore, it is essential to consider the assumptions and potential limitations of using related rates in water flow situations.

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