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.