If I put the tip of a 100 foot pipe in the ocean and applied a perfect vacuum to the top, how high would the water rise in the pipe?
To determine how high the water would rise in the pipe when a perfect vacuum is applied, we can use the principle of atmospheric pressure. Atmospheric pressure is the force exerted by the weight of the air above a certain point. At sea level, the average atmospheric pressure is about 14.7 pounds per square inch (psi) or 1 atmosphere (atm).
When you apply a perfect vacuum to the top of the pipe, you essentially remove all the air pressure above that point. This creates a pressure difference between the top of the pipe and the ocean surface.
To calculate the height of the water rise, we can use the formula:
h = (P/V) * 13.6
Where:
- h is the height of the water rise in inches
- P is the pressure difference in psi (14.7 psi - 0 psi)
- V is the density of water (62.43 pounds per cubic foot)
- 13.6 is a conversion factor to convert pressure from psi to inches of water column
Now, let's calculate:
h = (14.7 psi / 62.43 pcf) * 13.6
h = 3.21 inches
Therefore, the water would rise approximately 3.21 inches in the 100-foot pipe when a perfect vacuum is applied to the top.