# Solving Water Storage Tank Problem with Bernoulli's Equation

• VanessaN
In summary, the conversation discusses the question of how fast water will exit a completely full water storage tank with a height of 1 m if a hole is made at the center of the wall. By applying Bernoulli's equation, it is determined that the final height of the water is 0.5 m, leading to a correct answer of the square root of 10 meters for the speed at which the water will exit the tank. The use of Torricelli's Law is also mentioned as a potential solution.
VanessaN

## Homework Statement

A water storage tank is open to air on the top and has a height of 1 m. If the tank is completely full and a hole is made at the center of the wall of the tank, how fast will water exit the tank?

## Homework Equations

Pressure is the same as atmospheric pressure because the tank is open to the air. Also, linear flow speed at the surface is essentially zero, so...
Bernoulli's equation can be simplified to:

rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

## The Attempt at a Solution

[/B]
rho= density
g= 10 m/ s^2
height 1 (or height initial)= 1 m
Here is where I don't understand the solution...
height 2 is apparently = 0.5 m, but this is not in the question stem...

rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

My attempt at solving for v2 ultimately comes out to be:
v2= sq rt 2g (h1-h2)= sq rt 2* 10 m/s * (1 m - 0) = sq rt 20 meters

But the correct way to solve was:
v2= sq rt 2g (h1-h2)= sq rt 2* 10 m/s * (1 m - 0.5 m) = sq rt 10 meters

So, I guess my question is why would the final height (height 2) be 0.5 m?
Or, is there any other way to get the correct answer of sq rt 10 meters?

Last edited:
VanessaN said:

## Homework Statement

A water storage tank is open to air on the top and has a height of 1 m. If the tank is completely full and a hole is made at the center of the wall of the tank, how fast will water exit the tank?

## Homework Equations

Pressure is the same as atmospheric pressure because the tank is open to the air. Also, linear flow speed at the surface is essentially zero, so...
Bernoulli's equation can be simplified to:

rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

## The Attempt at a Solution

rho * g * h1 = 1/2 * rho * v2^2 + rho * g * h2

solving for v2, which ultimately comes out to be:
v2= sq rt 2g (h1-h2)= sq rt 2* 10 m/s * (1 m - 0) = sq rt 20

I did not get the correct answer. The correct answer is apparently sq rt 10. Can somebody please help me figure out where I went wrong? Thanks in advance!
Your post is hard to follow, since you don't define the variables used in your equations nor do you list their values. How do you expect anyone to help?

In any event, have you heard of Torricelli's Law?

http://en.wikipedia.org/wiki/Torricelli's_law

VanessaN
They asked for the case where the hole is half way down the wall of the tank, not at the bottom of the tank.

Chet

VanessaN
Chestermiller said:
They asked for the case where the hole is half way down the wall of the tank, not at the bottom of the tank.

Chet

ahhh, the case where i make a problem much more difficult by not understanding the question... the word "center" should have tipped me off to the fact that the final height would be 0.5!

Thank you for your help i appreciate it!

## 1. What is Bernoulli's Equation and how does it relate to water storage tanks?

Bernoulli's Equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation of a fluid. In the context of water storage tanks, it can be used to calculate the pressure at different points in the tank based on the height of the water and the flow rate of the water.

## 2. How can Bernoulli's Equation be used to solve water storage tank problems?

Bernoulli's Equation can be used to calculate the pressure at different points in a water storage tank, which is important for determining the stability and safety of the tank. It can also be used to calculate the flow rate of water in and out of the tank, which is important for maintaining a desired water level.

## 3. What are the assumptions made when using Bernoulli's Equation for water storage tank problems?

Some of the main assumptions made when using Bernoulli's Equation for water storage tank problems include: assuming the fluid is incompressible, assuming the flow is steady and laminar, and neglecting any friction or viscosity effects. These assumptions may not always hold true in real-world scenarios, so it's important to be aware of their limitations.

## 4. Can Bernoulli's Equation be used for any type of water storage tank?

Bernoulli's Equation can be applied to most water storage tanks, as long as the assumptions mentioned above are met. However, it may not be appropriate for very large or complex tanks, or for tanks with a highly turbulent flow. In these cases, more advanced fluid dynamics equations may be necessary.

## 5. Are there any limitations to using Bernoulli's Equation for water storage tank problems?

As mentioned before, Bernoulli's Equation relies on certain assumptions that may not always hold true in real-world scenarios. Additionally, it does not account for external factors such as temperature, atmospheric pressure, or the presence of impurities in the water. It is important to carefully consider all factors and potential limitations when using Bernoulli's Equation for water storage tank problems.

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