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?
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:
P1+ρwatergL = Pair+ρoilgL
P1 = Pair + gL(ρoil-ρwater) (1)
Where P1 is the pressure due to the air flow
Using Bernoulli's equation at the top of the tube as the reference point yields:
P1+0.5ρairvair2 = Pair (2)
Substituting equation (1) into (2) gives
And then the velocity of air can be found... Is my work good? Thanks!