Question

Some miners wish to remove water from a mine shaft. A pipe is lowered to the water 90 m below, and a negative pressure is applied to raise the water.

(a) Calculate the pressure needed to raise the water.
a) 882,900 Pa
b) 8,829 Pa
c) 88,290 Pa
d) 882,900,000 Pa

(b) What is unreasonable about this pressure?
a) The pressure is too low.
b) The pressure is too high.
c) The pressure is reasonable.
d) The information provided is insufficient.

Answer 1

The pressure needed to raise water from a 90 m deep mine shaft is calculated to be 882,900 Pa using the hydrostatic pressure equation. However, such a high negative pressure is unreasonable because it implies a perfect vacuum and would cause water to boil at room temperature, making the premise unrealistic.

Step-by-step explanation:

To calculate the pressure needed to raise water in a mine shaft that is 90 m below the surface, we use the hydrostatic pressure equation, p = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of water. Assuming standard gravity and that the density of water is approximately 1000 kg/m3, we get:

p = (1000 kg/m3)(9.81 m/s2)(90 m)

p = 882,900 Pa

This pressure seems extremely high because it implies a perfect vacuum, which is practically impossible to achieve. In reality, water would start to boil at room temperature before such a negative pressure could be sustained, indicating that the premise of applying such a high negative pressure to raise water is unreasonable.