A 1-m-tall barrel is closed on top except for a thin pipe extending 6.0 m up from the top. When the barrel is filled with water up to the base of the pipe (1 m deep) the water pressure on the bottom of the barrel is 10 kPa. What is the pressure on the bottom when water is added to fill the pipe to its top?

To find the pressure on the bottom when the water is added to fill the pipe to its top, we can make use of Pascal's law, which states that the pressure exerted on a fluid is transmitted uniformly in all directions.

Here's how you can calculate the pressure on the bottom of the barrel:

1. Determine the height of the water column in the barrel. The total height of the water column is the height of the barrel (1 m) plus the height of the pipe (6.0 m), which gives us a total height of 7.0 m.

2. Calculate the pressure due to the water column using the formula: pressure = density × gravity × height.
- The density of water is approximately 1000 kg/m³.
- The acceleration due to gravity is approximately 9.8 m/s².

Therefore, the pressure due to the water column is:
pressure = 1000 kg/m³ × 9.8 m/s² × 7.0 m.

3. Convert the pressure to kilopascals. Since 1 kilopascal (kPa) is equivalent to 1000 pascals (Pa), divide the pressure in pascals by 1000:
pressure = (1000 kg/m³ × 9.8 m/s² × 7.0 m) / 1000.

Simplifying the equation, we get:
pressure = 68600 Pa / 1000 = 68.6 kPa.

Therefore, the pressure on the bottom of the barrel when water is added to fill the pipe to its top is 68.6 kPa.