Question

An empty barometer tube 1 m long is lowered vertically (mouth downwards) into a tank of water. What will be the depth above the water level in the tube, when the water has risen 20 cm inside the tube? Take 1 atm = 10.4 column of water.

Answer 1

The depth above the water level inside the barometer tube after the water has risen 20 cm is 0.8 m. This calculation uses the fact that 1 atm pressure is equivalent to a 10.4-meter water column and takes into account the length of the barometer tube and the raised water height.

Step-by-step explanation:

To determine the depth above the water level in the tube after the water has risen 20 cm inside the tube, we need to use the concept of hydrostatic pressure. According to the information provided, normal atmospheric pressure will support a 10-meter column of water. This means that the pressure exerted by a 1-meter high column of water is 0.1 atm. When the barometer tube is lowered into the water, the atmospheric pressure acts on the water surface, allowing it to rise in the tube against the gravity until the hydrostatic pressure of the risen water column balances the atmospheric pressure.

Given 1 atm is equal to the pressure exerted by a 10.4-meter column of water, and the barometer tube is 1 m long, we can calculate the height of the water column in the tube that would exert this atmospheric pressure. As the water rises 20 cm inside the tube, the remaining space in the tube will not be occupied by water. This means that the pressure exerted by the 20 cm column of water inside the tube is equal to the pressure of the remaining empty space in the tube (the depth above the water level we want to find). Therefore, the hydrostatic pressure represented by the 20 cm of water plus the pressure represented by the empty space in the tube must equal 1 atm.

The space in the tube above the water level can be calculated as follows:

1. Convert the atmospheric pressure to the equivalent water column height: 1 atm = 10.4 m water column.
2. Convert 20 cm to meters to match the unit, which is 0.2 m.
3. The remaining height of the water column to exert 1 atm pressure is 10.4 m - 0.2 m = 10.2 m.
4. Since the barometer tube is 1 m long, the depth of the air remaining in the barometer above the water level is the tube's length minus the height of the water column inside it, which is 1 m - 0.2 m = 0.8 m.
   

In short, the depth above the water level inside the barometer tube is 0.8 m after the water has risen 20 cm within the tube.