Final answer:
The height difference between the water levels on the two sides of the U-tube can be determined using Bernoulli's equation. The pressure at points at the same height in a liquid must be the same, as long as the points are in the same liquid. The pressure at each point is due to atmospheric pressure plus the weight of the liquid above it.
Step-by-step explanation:
The height difference between the water levels on the two sides of the U-tube can be determined using Bernoulli's equation.
Bernoulli's equation states that the pressure at points at the same height in a liquid must be the same, as long as the points are in the same liquid.
The pressure at each point is due to atmospheric pressure plus the weight of the liquid above it.
In this case, the air blowing across the top of the U-tube will create a difference in atmospheric pressure on the two sides of the tube, resulting in a difference in the height of the water levels.
To calculate the height difference, we can use the equation:
(p₁ - p₂) x g x h = (1/2) x p x v²
where p₁ is the density of the water in one arm of the U-tube, p₂ is the density of the water in the other arm, g is the acceleration due to gravity, h is the height difference, and v is the speed of the air blowing across the top of the U-tube.
Since the density of the air is given as 1.2 kg/m³, we can plug in the values and solve for the height difference.
For example, if we assume p₁ = p₂ = 1000 kg/m³ (density of water), g = 9.8 m/s², and v = 15 m/s, we can calculate the height difference:
(1000 kg/m³ - 1000 kg/m³) x (9.8 m/s²) x h = (1/2) x (1.2 kg/m³) x (15 m/s)²
0 x 9.8 m/s² x h = (1/2) x 1.2 kg/m³ x 225 m²/s²
0 = 135 kg · m/s² x h
h = 0 m
Therefore, the height difference between the water levels on the two sides of the U-tube in this case is 0 meters.