# Solving Water Tank Problems with Maple/Mathematica

• Maple
• Hollysmoke

#### Hollysmoke

1. Consider a rectangular water tank with a length of 8m, a width of 4m , and a height of 5m. Water exits the tank by pouring over the sides.
a) If the tank is initially full of water, find the work required to empty the tank.
b) If the tank is initially half-full of water, find the work required to empty the tank.
c) If the tank is initially full of water, find the work required to pump out half of the water
d) If the tank is initially full of water, find the work F(y) required to pump out the water until the depth of water in the tank is y. Plot F(y)
e) If your goal is to pump out all of the water, at which water level y0 will half of the work be done?

2. How can I get this onto maple?

3. Done it by hand, just have no idea how to solve it on the computer =(

How do you have no idea how to do it on the computer? If you've done it by hand, then you know the equations you need to solve. Show your work!

## 1. How can I use Maple/Mathematica to solve water tank problems?

Maple and Mathematica are powerful mathematical software programs commonly used by scientists and engineers to solve complex mathematical problems. These programs have built-in functions and algorithms that can be used to model and solve problems related to water tanks, such as finding the volume of water in a tank or calculating the time it takes for a tank to fill or drain.

## 2. Are there any specific steps I need to follow to solve a water tank problem using Maple/Mathematica?

Yes, there are certain steps you can follow to solve a water tank problem using Maple/Mathematica. These include defining the variables and parameters of the problem, setting up the appropriate equations and boundary conditions, and using built-in functions or creating custom functions to solve the problem. It is also important to check the accuracy of the solution and make necessary adjustments if needed.

## 3. Can Maple/Mathematica handle different types of water tank problems?

Yes, Maple and Mathematica are flexible software programs that can handle various types of water tank problems, including problems with irregular shapes, multiple tanks, and varying inflow or outflow rates. These programs also have the ability to plot and visualize the solutions, making it easier to understand the problem and its solution.

## 4. Is it necessary to have a strong background in mathematics to use Maple/Mathematica for solving water tank problems?

While having a background in mathematics can certainly be helpful, it is not necessary to be an expert in order to use Maple/Mathematica for solving water tank problems. These programs have user-friendly interfaces and provide step-by-step guidance for solving problems. However, some basic knowledge of algebra and calculus may be required to understand and interpret the results.

## 5. Can I use Maple/Mathematica to solve real-life water tank problems?

Yes, Maple and Mathematica can be used to solve real-life water tank problems. These programs have been extensively used in engineering and scientific fields to solve complex problems and provide accurate solutions. By accurately modeling and simulating the behavior of water tanks, these programs can be extremely useful in solving real-world problems related to water storage and management.