How Quickly Will Water Drain from a Tank with a 13mm Hole?

[robhowe]

Hi there, I've been looking at some of the drainage equations i have found aroundthese forums and I am struggling a lot to understand. I am 13 and good at maths, where i struggle is reading the advanced equations and figuring out what some of the posters mean.

Basicly i have a tank 50 cm across x 50 cm deep. The length is 300 cm. There is a 13mm drainage hole, I am trying to figure out how quickly the tank will drain.

I only need an approx answer so is there a simple equation to work this out, So i can adjust the drainage hole size??

thankyou

 

[gsal]

this was already discussed https://www.physicsforums.com/showthread.php?t=507578".

 

[robhowe]

as i explained i don't understand the advanced formula, I am looking for a simple equation. Or just a more detailed description.

 

[gsal]

It does not get any simpler than that, though...this is the simple formula that results out of the general differential formula after integrating for a tank with constant cross-section...here is again, with better subscripts:

$time = \frac{2*A_{tank}\left(\sqrt{h_{1}}-\sqrt{h_{2}}\right)}{C_{d}*A_{orifice}*\sqrt{2g}}$

A_tank is the surface (cross sectional) area of the tank and A_orifice is the cross sectional area of the orifice the water is going to come out through.

h₁ is the height (from the ground) of the water level at the beginning (when you open the orifice) and h₂ is the height at which the orifice is.

As suggested in the other post, C_d can be set to some value like 0.6 or 0.7; g is just gravity.

 

[alphy]

Hi there,

First of all, it's great that you are interested in understanding and learning about drainage equations at such a young age. It shows a strong curiosity and desire to learn, which are important qualities for a scientist.

To answer your question, there are several factors that can affect the rate at which water drains from a tank, such as the shape and size of the tank, the size of the drainage hole, and the viscosity of the liquid inside the tank. In order to accurately calculate the drainage rate, a more complex equation would be needed.

However, for an approximate answer, we can use a simple equation called Torricelli's law, which states that the velocity of a fluid exiting a hole at the bottom of a tank is equal to the square root of 2gh, where g is the acceleration due to gravity (9.8 m/s^2) and h is the height of the water above the hole.

In your case, the height of water above the hole is 50 cm, or 0.5 meters. Plugging this into the equation, we get a velocity of approximately 3.13 m/s. This means that the water will drain from the tank at a rate of 3.13 meters per second.

To adjust the drainage rate, you can change the size of the drainage hole. The larger the hole, the greater the flow of water and the faster the tank will drain. However, it's important to note that changing the size of the hole may also affect other factors such as the stability of the tank and the pressure inside.

I hope this helps you understand the basics of water drainage from a tank. Keep up your interest in math and science, and never stop asking questions!