- #1

faradayscat

- 57

- 8

## Homework Statement

[/B]Suppose we have a u-shaped tube filled with water, with oil added at one end which disturbs the equilibrium. Now say one end is blocked off and the other is exposed to air flow which reduces the pressure above the water and causes the water to climb back to equilibrium with the top of the oil. What would be the velocity of the wind above the open end?

## Homework Equations

## The Attempt at a Solution

If the column of oil has a length 'L', then the pressures at the bottom level of the oil are the same:

P

_{1}+ρ

_{water}gL = P

_{air}+ρ

_{oil}gL

P

_{1}= P

_{air}+ gL(ρ

_{oil}-ρ

_{water}) (1)

Where P

_{1}is the pressure due to the air flow

Using Bernoulli's equation at the top of the tube as the reference point yields:

P

_{1}+0.5ρ

_{air}v

_{air}

^{2}= P

_{air}(2)

Substituting equation (1) into (2) gives

0.5ρ

_{air}v

_{air}

^{2}=gL(ρ

_{fluid}-ρ

_{oil})

And then the velocity of air can be found... Is my work good? Thanks!