# Hydrodynamics: Pressure of water coming out of a glass

• qnney
In summary, the conversation is about using Bernoulli's equation to determine the pressure needed to get water to flow at 2 m/s from a hole in a container sitting on top of a glass of water. The equation involves conservation of energy, with potential energy (static pressure) and kinetic energy (velocity) being converted from one form to the other. The equation can be modified to combine the y1 and y2 values into (y1-y2) and the pressures into patm. The conversation also discusses the importance of finding the velocity (v^1) in order to solve the equation.
qnney
"What pressure do you need to get water to flow at 2 m/sec coming out of a hole?"

Here is the visual of a container sitting on top of a glass of water with a hole poked through the bottom: http://i96.photobucket.com/albums/l168/synovial/fluids.jpg

Given: A1, A2, V2, (y1-y2)

Find: patm

Useful equations:
Bernoulli's Equation:
p1 +$$\rho$$ $$\cdot$$ g $$\cdot$$ y1 + 0.5 $$\rho$$$$\cdot$$ V12 = p1 +$$\rho$$ $$\cdot$$ g $$\cdot$$ y2 + 0.5 $$\rho$$$$\cdot$$ V22

A1V1 = A2V2

I'm not sure how to modify the Bernoulli's equation to combine the y1 and y2 into (y1 - y2) and to also combine the pressures into patm. Can someone please help me?

Last edited:
Bernoullis is just a statement of conservation of energy.

The potential energy is the static pressure = rho*g*h where rho is density and the
kinetic energy =1/2pho*v^2.

Look familiar? So we convert from one form to the other.

Almost like a kinematics problem.

I'm not sure I understand. Is the pho supposed to be rho or p*rho?

rho throughout. But as it turns out it is a common factor leaving 2gh=v^2. As I said, does this look familiar?

Yes it does... especially the 2gh=v^2.

One last question: do I need the v^1, or can I find it from what is given?

Well if you mean v^1 is velocity, yes that is what we are trying to solve for as in equal to 2m/second. So yes you need to take the square root if that is what you are asking.

Yes... thank you!

## 1. What is hydrodynamics?

Hydrodynamics is the study of the movement of liquids and gases in relation to forces and energy.

## 2. Why does the pressure of water coming out of a glass change?

The pressure of water coming out of a glass changes because of the height of the water column, the size of the opening, and the velocity of the water. As the water level decreases, the pressure at the bottom of the glass decreases, which affects the velocity of the water coming out of the glass.

## 3. How does the shape of a glass affect the pressure of water coming out?

The shape of a glass can affect the pressure of water coming out by changing the surface area of the opening, which can affect the velocity of the water. For example, a wider opening will result in a lower velocity and lower pressure compared to a narrow opening.

## 4. Does the temperature of the water affect the pressure coming out of a glass?

Yes, the temperature of the water can affect the pressure coming out of a glass. As water temperature increases, its density decreases, which can affect the velocity and pressure of the water coming out of a glass.

## 5. How can I calculate the pressure of water coming out of a glass?

The pressure of water coming out of a glass can be calculated using the Bernoulli's equation, which takes into account the height of the water column, the velocity of the water, and the atmospheric pressure. It can also be calculated using the equation for hydrostatic pressure, which depends on the density of water, acceleration due to gravity, and the height of the water column.

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