# Relationship Between Velocity and Height of Water

#### physics1012

Help! Relationship Between Velocity and Height of Water

Hello, I have been given a lab paper to do on the relationship between the velocity of water leaking from a hole in a bottle and the height of water above the hole. We are supposed to focus on analyzing and finding the relationship between velocity and height with our data. I have data listed below but do not know how to go about finding the relationship. I know the formula is √(2gh) but don't know how to find it through my data. Thanks so much for any help!

Height Water - Range (cm) - Velocity (m/s)

11.8cm - 31 - 1.13
10.6cm - 29 - 1.05
8.6cm - 25 - 0.91
6.8cm - 22 - 0.8
5cm - 18 - 0.66
3.6cm - 14 - 0.51
2.7cm - 10 - 0.36

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#### HallsofIvy

Given any finite number of "data points" there exist an infinite number of formulas that will give that data. There is no way to say that it definitely is or is not a specific formula. The first thing I would do is graph the points. Yes, it does look roughly like a square root but one that crosses the "Height" axis at a positive value, not 0. If you want to try something like $$\displaystyle V= A(h- B)^{1/2}$$, take two of the given points and put them into that equation to determine A and B. Then see if that gives at least approximately the right values for the other points

#### Aerothermal

velocity equals the square root of (Density * g * height)

This is derived from Bernoulli equation.

g is gravity (9.80665 m/s^2).

#### topsquark

Forum Staff
velocity equals the square root of (Density * g * height)

This is derived from Bernoulli equation.
Since you are resurrecting a month old thread, would you mind telling us how to derive that? Just for the sake of completeness.

-Dan

#### benit13

Hello, I have been given a lab paper to do on the relationship between the velocity of water leaking from a hole in a bottle and the height of water above the hole.
Look up something called "Toricelli's law"